{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2163,"title":"Evaluate Polynomial","description":"Given a polynomial equation coefficients in a vector p, you have to return its value at x.\r\n\r\nExample:\r\n\r\nFor inputs p and x\r\n\r\n p = [1 0 1]\r\n x = [1 4]\r\n\r\nOutput y is [1*1^2 + 1, 1*4^2 + 1] or \r\n\r\n y = [2 17]","description_html":"\u003cp\u003eGiven a polynomial 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46880]\r\nassert(isequal(polynomial(p,x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":147,"test_suite_updated_at":"2014-02-07T15:58:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T05:50:19.000Z","updated_at":"2026-03-09T18:42:08.000Z","published_at":"2014-02-07T05:50:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a polynomial equation coefficients in a vector p, you have to return its value at x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor inputs p and x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = [1 0 1]\\n x = [1 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput y is [1*1^2 + 1, 1*4^2 + 1] or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 17]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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-8159317]\r\nassert(isequal(SolvePoly(p,x),y_correct)) 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w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[1 2;3 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[ 0 -1; -2 -3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43621,"title":"Get derivarive of polynomial given as vector array.","description":"Get derivarive of polynomial given as vector array.\r\n\r\nExample \r\n\r\np=[ 1 2 0 5 0 3 ];\r\n\r\nresult=[ 5 8 0 10 0 ];","description_html":"\u003cp\u003eGet derivarive of polynomial given as vector array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ep=[ 1 2 0 5 0 3 ];\u003c/p\u003e\u003cp\u003eresult=[ 5 8 0 10 0 ];\u003c/p\u003e","function_template":"function y = PolyPol(x)\r\n y = x;\r\nend","test_suite":"%%\r\np = [ 1 2 0 5 0 3 ];\r\ny_correct = [ 5 8 0 10 0 ];\r\nassert(isequal(PolyPol(p),y_correct))\r\n%%\r\np = [ 3 2 5 1 0 2];\r\ny_correct = [ 15 8 15 2 0 ];\r\nassert(isequal(PolyPol(p),y_correct))\r\n%%\r\np = [ 15 8 15 2 0 ];\r\ny_correct = [ 60 24 30 2 ];\r\nassert(isequal(PolyPol(p),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":84,"test_suite_updated_at":"2016-10-25T09:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T09:10:39.000Z","updated_at":"2026-04-07T19:10:13.000Z","published_at":"2016-10-25T09:14:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGet derivarive of polynomial given as vector array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[ 1 2 0 5 0 3 ];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[ 5 8 0 10 0 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array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ea=[1 -1 2]; \r\nb=[2 4 1];\u003c/p\u003e\u003cp\u003eresult=0\u003c/p\u003e","function_template":"function y = PolSol(a,b)\r\n y = a+b;\r\nend","test_suite":"%%\r\na=[1 -1 2]; \r\nb=[2 4 1];\r\ny_correct = 0;\r\nassert(isequal(PolSol(a,b),y_correct))\r\n%%\r\na=[ 5 2 0 5 3 0]; \r\nb=[ 3 2 5 1 0 2];\r\ny_correct = 24;\r\nassert(isequal(PolSol(a,b),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T18:45:55.000Z","updated_at":"2026-02-10T11:32:57.000Z","published_at":"2016-10-25T18:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind scalar product of two polynomials given as vector array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=[1 -1 2]; b=[2 4 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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value.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cpre\u003e p(s) = s + 8\u003c/pre\u003e\u003cp\u003eFor s=0, value is 8.\u003c/p\u003e","function_template":"function y = your_fcn_name(x, n)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 8];\r\nn=0;\r\ny_correct = 8;\r\nassert(isequal(your_fcn_name(x, n),y_correct))\r\n%%\r\nx = [1 0];\r\nn=0;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x, n),y_correct))\r\n\r\n%%\r\nx = [1 0 5];\r\nn=1;\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x, n),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":142,"test_suite_updated_at":"2014-09-27T05:54:12.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2014-09-26T14:52:59.000Z","updated_at":"2026-03-09T18:54:14.000Z","published_at":"2014-09-26T14:52:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out value of polynomial at different value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p(s) = s + 8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor s=0, value is 8.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43625,"title":"Calculate roots of polynomial given as vector array.","description":"Calculate roots of polynomial given as vector array.\r\n\r\nExample\r\n\r\nx=[1 2 0 5 0 3]\r\n\r\nresult=[-2.7267 ; \r\n 0.4784 + 1.0983i;\r\n 0.4784 - 1.0983i;\r\n -0.1150 + 0.8680i;\r\n -0.1150 - 0.8680i]","description_html":"\u003cp\u003eCalculate roots of polynomial given as vector array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ex=[1 2 0 5 0 3]\u003c/p\u003e\u003cp\u003eresult=[-2.7267 ; \r\n 0.4784 + 1.0983i;\r\n 0.4784 - 1.0983i;\r\n -0.1150 + 0.8680i;\r\n -0.1150 - 0.8680i]\u003c/p\u003e","function_template":"function y = PolRoot(x)\r\n y=x\r\nend","test_suite":"%%\r\nx = [1 2 0 5 0 3];\r\ny_correct = [-2.7267 + 0.0000i ;0.4784 + 1.0983i ;0.4784 - 1.0983i ;-0.1150 + 0.8680i ;-0.1150 - 0.8680i];\r\ny=PolRoot(x)\r\nassert(abs(y(1)-y_correct(1))\u003c10^(-4))\r\nassert(abs(y(2)-y_correct(2))\u003c10^(-4))\r\nassert(abs(y(3)-y_correct(3))\u003c10^(-4))\r\nassert(abs(y(4)-y_correct(4))\u003c10^(-4))\r\n%%\r\nx = [3 2 5 1 0 2];\r\ny_correct = [-0.3205 + 1.2968i; -0.3205 - 1.2968i; -0.7915 + 0.0000i; 0.3829 + 0.5704i; 0.3829 - 0.5704i];\r\ny=PolRoot(x)\r\nassert(abs(y(1)-y_correct(1))\u003c10^(-4))\r\nassert(abs(y(2)-y_correct(2))\u003c10^(-4))\r\nassert(abs(y(3)-y_correct(3))\u003c10^(-4))\r\nassert(abs(y(4)-y_correct(4))\u003c10^(-4))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":90,"test_suite_updated_at":"2016-10-25T18:15:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T18:11:06.000Z","updated_at":"2026-02-25T20:52:46.000Z","published_at":"2016-10-25T18:15:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate roots of polynomial given as vector array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[1 2 0 5 0 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[-2.7267 ; 0.4784 + 1.0983i; 0.4784 - 1.0983i; -0.1150 + 0.8680i; -0.1150 - 0.8680i]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2165,"title":"Polynomial Multiplication","description":"Multiply two polynomial equation.Given polynomial coefficients a and b.","description_html":"\u003cp\u003eMultiply two polynomial equation.Given polynomial coefficients a and b.\u003c/p\u003e","function_template":"function y = multiply(a,b)\r\n y = x;\r\nend","test_suite":"%%\r\na = [ 1 5 8 9 7 4 5 6];\r\nb = [ 6 8 4 1 ];\r\ny_correct = [ 6 38 92 139 151 124 99 99 72 29 6];\r\nassert(isequal(multiply(a,b),y_correct))\r\n\r\n\r\na = [ 22 98 56 74 12];\r\nb = [78 45 ];\r\ny_correct = [ 1716 8634 8778 8292 4266 540];\r\nassert(isequal(multiply(a,b),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":138,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T06:42:09.000Z","updated_at":"2026-02-16T16:29:25.000Z","published_at":"2014-02-07T06:42:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply two polynomial equation.Given polynomial coefficients a and b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1183,"title":"Polynomial division","description":"Divide a polynomial u by polynomial v and return the quotients only.\r\n\r\nExample:\r\n\r\n u = x^4+3*x^3+5*x+3\r\n v = x^2+1\r\n\r\nAnswer:\r\n\r\n x^3+2*x+3","description_html":"\u003cp\u003eDivide a polynomial u by polynomial v and return the quotients only.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e u = x^4+3*x^3+5*x+3\r\n v = x^2+1\u003c/pre\u003e\u003cp\u003eAnswer:\u003c/p\u003e\u003cpre\u003e x^3+2*x+3\u003c/pre\u003e","function_template":"function y = poly_div(u,v)\r\n y = x;\r\nend","test_suite":"%%\r\nu = [1 3 5 3]; v = [1,1];\r\ny_correct = [1 2 3];\r\nassert(isequal(poly_div(u,v),y_correct));\r\n%%\r\nu=[4 -2 -14 -3 17 21 9]; v = [1 2 1];\r\ny_correct = [4 -10 2 3 9];\r\nassert(isequal(poly_div(u,v),y_correct));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":9752,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T04:43:36.000Z","updated_at":"2026-02-17T08:53:45.000Z","published_at":"2013-01-07T04:43:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide a polynomial u by polynomial v and return the quotients only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ u = x^4+3*x^3+5*x+3\\n v = x^2+1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnswer:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x^3+2*x+3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43618,"title":"Multiply two polynomials p and q given in in vector representation.","description":"Multiply two polynomials p and q given in vector representation.\r\nExample \r\np=[-2 0 1 -1 3 2]\r\n\r\nq=[1 0 -1 2 4]\r\n\r\nresult=[-2 0 3 -5 -6 5 -1 0 16 8]","description_html":"\u003cp\u003eMultiply two polynomials p and q given in vector representation.\r\nExample \r\np=[-2 0 1 -1 3 2]\u003c/p\u003e\u003cp\u003eq=[1 0 -1 2 4]\u003c/p\u003e\u003cp\u003eresult=[-2 0 3 -5 -6 5 -1 0 16 8]\u003c/p\u003e","function_template":"function y = MulPoly(p,q)\r\n y = x;\r\nend","test_suite":"%%\r\np=[-2 0 1 -1 3 2]\r\nq=[1 0 -1 2 4]\r\ny_correct =[-2 0 3 -5 -6 5 -1 0 16 8];\r\nassert(isequal(MulPoly(p,q),y_correct))\r\n%%\r\np=[-2 0 1 0 -3 1]\r\nq=[-1 0 -1 2 2]\r\ny_correct =[2 0 1 -4 -2 1 5 -7 -4 2];\r\nassert(isequal(MulPoly(p,q),y_correct))\r\n%%\r\np=[1 2 0 5 0 3]\r\nq=[3 2 5 1 0 2]\r\ny_correct =[3 8 9 26 12 36 15 15 13 0 6];\r\nassert(isequal(MulPoly(p,q),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T23:09:36.000Z","updated_at":"2026-02-17T14:22:13.000Z","published_at":"2016-10-24T23:09:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply two polynomials p and q given in vector representation. Example p=[-2 0 1 -1 3 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[1 0 -1 2 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[-2 0 3 -5 -6 5 -1 0 16 8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2164,"title":"Roots","description":"Find out the roots of a given polynomial equation.Given are the coefficients of the equation.","description_html":"\u003cp\u003eFind out the roots of a given polynomial equation.Given are the coefficients of the equation.\u003c/p\u003e","function_template":"function y = return_root(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 5 8 9 7 4 5];\r\ny_correct = roots(x); \r\nassert(isequal(return_root(x),y_correct))\r\n\r\nx = [1 0 0 48 50];\r\ny_correct = roots(x); \r\nassert(isequal(return_root(x),y_correct))\r\n\r\nx = [11 55 4 6 ];\r\ny_correct = roots(x)\r\nassert(isequal(return_root(x),y_correct))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":424,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T06:11:07.000Z","updated_at":"2026-02-17T09:14:55.000Z","published_at":"2014-02-07T06:11:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out the roots of a given polynomial equation.Given are the coefficients of the equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44659,"title":"Nth root of a number","description":"Given an input and a number N, find the Nth root of the number(s)","description_html":"\u003cp\u003eGiven an input and a number N, find the Nth root of the number(s)\u003c/p\u003e","function_template":"function y = rootN(a,N)\r\n y = x;\r\nend","test_suite":"%%\r\na = 1;\r\nN = 100\r\ny_correct = 1;\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = [1 64 216];\r\nN = 3\r\ny_correct = [1 4 6];\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = 1/100;\r\nN = 2\r\ny_correct = 1/10;\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = 826^10;\r\nN = 10\r\ny_correct = 826;\r\nassert(isequal(rootN(a,N),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2018-05-29T13:54:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-29T13:48:03.000Z","updated_at":"2026-02-20T14:32:58.000Z","published_at":"2018-05-29T13:48:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input and a number N, find the Nth root of the number(s)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1554,"title":"Calculate the derivative of a polynomial","description":"Example:\r\n in = [ 1\r\n 1\r\n 1 ]\r\n\r\n out = [ 2\r\n 1 ]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 153.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 76.8px; transform-origin: 407px 76.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3px; transform-origin: 404px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e in = [ 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e out = [ 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = diff_poly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4];\r\ny_correct = [3 4 3];\r\nassert(isequal(diff_poly(x),y_correct))\r\n\r\n%%\r\nc=randi(100);\r\nx = [c randi(100)];\r\ny_correct = c;\r\nassert(isequal(diff_poly(x),y_correct))\r\n\r\n%%\r\nx = [6 5 3 4];\r\ny_correct = [18 10 3];\r\nassert(isequal(diff_poly(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":14267,"edited_by":223089,"edited_at":"2022-12-11T07:09:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":240,"test_suite_updated_at":"2022-12-11T07:09:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-05T23:15:12.000Z","updated_at":"2026-03-05T12:22:34.000Z","published_at":"2013-06-05T23:15:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ in = [ 1\\n 1\\n 1 ]\\n\\n out = [ 2\\n 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44847,"title":"Say type of roots in quadratic equation","description":"Given the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\r\n \r\n \r\n ","description_html":"\u003cp\u003eGiven the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = '';\r\nend","test_suite":"%%\r\nx = [1 1 1];\r\ny_correct = 'Complex';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [1 3 1];\r\ny_correct = 'RealDifferent';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [1 -4 4];\r\ny_correct = 'RealEqual';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2019-02-13T20:27:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-02-13T20:26:09.000Z","updated_at":"2026-03-11T08:52:01.000Z","published_at":"2019-02-13T20:26:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42775,"title":"Raise a polynomial to a power","description":"In Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\r\n\r\nIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)","description_html":"\u003cp\u003eIn Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\u003c/p\u003e\u003cp\u003eIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)\u003c/p\u003e","function_template":"function q = polypow(p,N)\r\n q = p^N; \r\nend","test_suite":"%%\r\np=[2];\r\nN=8;\r\ny_correct=256;\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=[1 1];\r\nN=1;\r\ny_correct=[1 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=[1 1];\r\nN=5;\r\ny_correct=[1 5 10 10 5 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=1:5;\r\nN=3;\r\ny_correct=[1 6 21 56 126 234 369 504 594 574 465 300 125];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=5:-1:1;\r\nN=3;\r\ny_correct=[125 300 465 574 594 504 369 234 126 56 21 6 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=5:-1:1;\r\nN=1;\r\ny_correct=[5 4 3 2 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8580,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":97,"test_suite_updated_at":"2016-03-16T17:46:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-16T17:30:45.000Z","updated_at":"2026-04-03T02:46:51.000Z","published_at":"2016-03-16T17:44:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44259,"title":"Product of two multivariate polynomials","description":"MATLAB \u003chttps://www.mathworks.com/help/matlab/polynomials.html has a few functions\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as |y-x^2| or |x^2+y^2+z^2-1|. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if |p(x) = A + B x^3|, then the coefficients are\r\n\r\n c = [B 0 0 A].\r\n\r\nNote this is same order as used by the builtin functions. A couple more examples: if |p(x,y) = x - y^2|, then\r\n\r\n c = [0 -1; 0 0; 1 0].\r\n\r\nIf |p(x,y,z) = z-2|, then |c| has dimensions |[1 1 2]| with |c(:,:,1) = 1| and |c(:,:,2) = -2|.\r\n\r\nThe challenge is to create a function |polyMult| that takes two arrays of coefficients for polynomials |p1| and |p2| and returns the coefficients for |p1*p2|. See the tests for examples.","description_html":"\u003cp\u003eMATLAB \u003ca href = \"https://www.mathworks.com/help/matlab/polynomials.html\"\u003ehas a few functions\u003c/a\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as \u003ctt\u003ey-x^2\u003c/tt\u003e or \u003ctt\u003ex^2+y^2+z^2-1\u003c/tt\u003e. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if \u003ctt\u003ep(x) = A + B x^3\u003c/tt\u003e, then the coefficients are\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ec = [B 0 0 A].\r\n\u003c/pre\u003e\u003cp\u003eNote this is same order as used by the builtin functions. A couple more examples: if \u003ctt\u003ep(x,y) = x - y^2\u003c/tt\u003e, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ec = [0 -1; 0 0; 1 0].\r\n\u003c/pre\u003e\u003cp\u003eIf \u003ctt\u003ep(x,y,z) = z-2\u003c/tt\u003e, then \u003ctt\u003ec\u003c/tt\u003e has dimensions \u003ctt\u003e[1 1 2]\u003c/tt\u003e with \u003ctt\u003ec(:,:,1) = 1\u003c/tt\u003e and \u003ctt\u003ec(:,:,2) = -2\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe challenge is to create a function \u003ctt\u003epolyMult\u003c/tt\u003e that takes two arrays of coefficients for polynomials \u003ctt\u003ep1\u003c/tt\u003e and \u003ctt\u003ep2\u003c/tt\u003e and returns the coefficients for \u003ctt\u003ep1*p2\u003c/tt\u003e. See the tests for examples.\u003c/p\u003e","function_template":"function c = polyMult(c1,c2)\r\n y = c1*c2;\r\nend","test_suite":"%% Test polyMult\r\nfiletext = fileread('polyMult.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% p1 = A*x, p2 = B*y\r\nc1 = randi(1000); c2 = randi(1000);\r\nassert(isequal(c1*c2,polyMult(c1,c2)))\r\n\r\n%% p1 = y-x^2, p2 = x-2\r\nc1 = [0 -1; 0 0; 1 0];\r\nc2 = [1; -2];\r\nc = [0 -1; 0 2; 1 0; -2 0];\r\nassert(isequal(c,polyMult(c1,c2)))\r\n\r\n%% p1 = y-x^2, p2 = z-2\r\nc1 = [0 -1; 0 0; 1 0];\r\nc2 = reshape([1; -2],[1 1 2]);\r\nc = reshape([0 0 1 -1 0 0 0 0 -2 2 0 0],[3 2 2]);\r\nassert(isequal(c,polyMult(c1,c2)))\r\n\r\n%% p1 = z-x^3, p2 = y-x^2, p3 = x^2+y^2+z^2-1, p4 = z-2\r\nc1 = reshape([0 0 0 1 -1 0 0 0],[4 1 2]);\r\nc2 = [0 -1; 0 0; 1 0];\r\nc3 = zeros([3 3 3]);\r\nc3([9 21 25]) = [1 1 1];\r\nc3(27) = -1;\r\nc4 = reshape([1; -2],[1 1 2]);\r\nc = zeros(8,4,5);\r\nc([56 91 104 118 126 139 149 153]) = -2*ones(1,8);\r\nc([30 53 78 88 92 101 115 123]) = -1*ones(1,8);\r\nc([24 59 72 86 94 107 117 121]) = 1*ones(1,8);\r\nc([62 85 110 120 124 133 147 155]) = 2*ones(1,8);\r\nassert(isequal(c,polyMult(c1,polyMult(c2,polyMult(c3,c4)))))\r\n\r\n%% Commutative\r\nc1 = randi(1000,[2 3 4]);\r\nc2 = randi(1000,[4 5 1]);\r\nassert(isequal(polyMult(c1,c2),polyMult(c2,c1)))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-11T22:41:35.000Z","updated_at":"2025-12-22T12:43:34.000Z","published_at":"2017-07-11T22:43:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/polynomials.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehas a few functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey-x^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex^2+y^2+z^2-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = A + B x^3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then the coefficients are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = [B 0 0 A].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote this is same order as used by the builtin functions. A couple more examples: if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y) = x - y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = [0 -1; 0 0; 1 0].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y,z) = z-2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has dimensions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1 1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(:,:,1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(:,:,2) = -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe challenge is to create a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolyMult\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes two arrays of coefficients for polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and returns the coefficients for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. See the tests for examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46726,"title":"[Thermodynamics] Polynomial fitting of heat capacity data","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 295.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147.95px; transform-origin: 407px 147.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.867px 8px; transform-origin: 378.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn easy way to describe the temperature-dependence of the ideal gas heat capacity is by use of polynomials. Given are a vector of temperatures \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.825px 8px; transform-origin: 175.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in Kelvin) and a vector if corresponding heat capacities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eCP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.283px 8px; transform-origin: 102.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some substance (in J/mol K).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.292px 8px; transform-origin: 171.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function should perform a polynomial fit of degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.817px 8px; transform-origin: 147.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and return a function handle to that polynomial.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9667px 8px; transform-origin: 64.9667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample (hydrogen):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 91.95px; transform-origin: 404px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 288.75px 8px; transform-origin: 288.75px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 219.45px 8px; transform-origin: 219.45px 8px; \"\u003eT = [300 400 500 600 700 800 900 1000]; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 69.3px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 69.3px 8px; \"\u003e% temperature in K\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 319.55px 8px; transform-origin: 319.55px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 219.45px 8px; transform-origin: 219.45px 8px; \"\u003eCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2]; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 100.1px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 100.1px 8px; \"\u003e% heat capacity in J/mol K\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 319.55px 8px; transform-origin: 319.55px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 138.6px 8px; transform-origin: 138.6px 8px; \"\u003eFUN = cpFitting(T,CP,2); \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 180.95px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 180.95px 8px; \"\u003e% polynomial fitting and create function handle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8px; transform-origin: 42.35px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; FUN(350)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 29.0074\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8px; transform-origin: 42.35px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; FUN(940)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 29.9943\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function cpfun = cpFitting(T,CP,N)\r\n % T ... vector of temperatures in K\r\n % CP .. vector of heat capacities in J/mol K\r\n % N ... degree of the desired polynomial\r\n cpfun = @(t) t;\r\nend","test_suite":"%%\r\nT = 300:100:1000; % hydrogen @ 300K \u003c T \u003c 1000K\r\nCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2];\r\ncpfun = cpFitting(T,CP,2);\r\nassert(abs(cpfun(350)-29.0074) \u003c 1e-3 \u0026\u0026 abs(cpfun(550)-29.2505) \u003c 1e-3 \u0026\u0026 abs(cpfun(940)-29.9943) \u003c 1e-3);\r\n%%\r\nT = 500:100:1500; % water/steam @ 500K \u003c T \u003c 1500K\r\nCP = [35.22 36.22 37.5 38.74 40 41.27 42.52 43.75 44.94 46.06 47.11];\r\ncpfun = cpFitting(T,CP,3);\r\nassert(abs(cpfun(560)-35.842) \u003c 1e-3 \u0026\u0026 abs(cpfun(1000)-41.26) \u003c 1e-3 \u0026\u0026 abs(cpfun(1400)-46.0668) \u003c 1e-3);\r\n%%\r\nT = 100:100:1000; % methane @ 100K \u003c T \u003c 1000K\r\nCP = [33.28 33.51 35.76 40.63 46.63 52.74 58.6 64.08 69.14 73.75];\r\ncpfun = cpFitting(T,CP,3);\r\nassert(abs(cpfun(290)-35.993) \u003c 1e-3 \u0026\u0026 abs(cpfun(630)-54.1682) \u003c 1e-3 \u0026\u0026 abs(cpfun(950)-71.6749) \u003c 1e-3);\r\n%%\r\nstr = fileread('cpFitting.m'); % sorry, no regexp hacks :-)\r\nassert(isempty(regexp(str,'regexp')));","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":11486,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-11T12:11:15.000Z","updated_at":"2026-04-14T14:05:02.000Z","published_at":"2020-10-11T12:26:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eAn easy way to describe the temperature-dependence of the ideal gas heat capacity is by use of polynomials. Given are a vector of temperatures \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e (in Kelvin) and a vector if corresponding heat capacities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e for some substance (in J/mol K).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYour function should perform a polynomial fit of degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and return a function handle to that polynomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExample (hydrogen):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [300 400 500 600 700 800 900 1000]; % temperature in K\\nCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2]; % heat capacity in J/mol K\\nFUN = cpFitting(T,CP,2); % polynomial fitting and create function handle\\n\u003e\u003e FUN(350)\\nans =\\n 29.0074\\n\u003e\u003e FUN(940)\\nans =\\n 29.9943]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44274,"title":"Calculate the sum of two polynomials","description":"Calculate the sum of two polynomials if they are written in notation with their coefficients.\r\nexample:\r\n() + () = \r\na=[3 4 5];\r\nb=[1 4 7 6];\r\n\r\noutput =[1 7 11 11];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 172.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86.3667px; transform-origin: 407px 86.3667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276.5px 8px; transform-origin: 276.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the sum of two polynomials if they are written in notation with their coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eexample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 19px;\" width=\"79\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) + (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANkAAAAmCAYAAABJej66AAAHzUlEQVR4Xu2cS6h9UxzH//85eY1ICANKUZ4RYUCJJHnF4JbyKhmIMNDNAKEkA4+om0deGZgolAEpz6KIAUqJkVfM+X5O+5ffXXc/1t57rXXPuWft+nbOvXvtvdf6rd/3t36Ptc/+ffWoEqgSyCqB/VnvXm9eJVAlsK+SrCpBlUBmCVSSZRZwvX2VQCVZ1YEqgcwSyEGya9TnTeGEpu/v6vM64ffMY1ml2x+qzj4lnCscLvzT/H33Kg2i9jVOAqlJBsEeFx4QfhTuFC4SPhHOiuvSnm8FwT4SPhDeFE4V7hMOqHLam3OfmmQfS0zXCz84cf3SWOvD6mq2kMq9wjHCzU5Gp+v7p83fZ+jzs72pbus5qpQkw0If16IgEO8o4aRKsoWSvSPcFhgi/v+tgIt9rfDaeqrjyo4ab+3YBl+E85eSZG0Sgng/CXcJT6+YCM2tO1L9PrBA3zFGZwrLuJIRBrwaKQPiywtbjG3k5SvTDGLdKFwifCNsCe+1GM+sdTIL7pEak7RqxzPq8E0CSlOCZLjVHMu44rP6olQxx3dqdGJMwxVtg16/0sjjV32Sf+hdQHKtZMQdtwtkzjheXzGiectdgmS42d8Ltw5N2C4opvWNOXy+5/lY9auFR4W9miUldn6r0WuSeej4YPyci2TMBYy/R8BV5LhYIJ0/52CQTwp/Nfebc6+ua1GqL4WfBWKkEiQjBjtYSFXquEX32hDIYM5VeFZ0+jbkjRBT4lovg6tIn08WyHSnim9NL8gCs4JRfvEJvk5dzEkyeyir2oNCCguHy4LrklPxiY0g8VcCBiLns5ARY3pCuDR20jpn8/8TjzR9x6hh3OYcKCxz2FfntNVuWVxFi28pjTw0Z/DuWktMoQ9XCtELRgmS0c9/hWcFn7aeMvbcJEM5bxCIi2wVzkkylPNDIdoqRgotJcliHmmGNMUcxzxvqE1qkpk8ee5ow1WSZCnijZwkwxV931kpE2wukuFOvy3cP8YqDmlXc740yczKpwgJIofY2yw1yf7W03ATOUaPsY9kKAGB7AWNpSWJ4Yli2UPa4KMe0TFsiMHOhlOEKB+2R3y5SMZYvhZeEiyGiSUZqxEyOF84u5mM491YLY4kPW8JICsPbOp/YczAc98QBgPqHjmVJJm5in06QFeRw1XCeQKyCNvbbqFQz3qG2XkqJcmIb9kCx2GuIjuZbK4ZB97IY11z1kcyFPoQ4Q8BkljAB5lMSXiw7VG8Qt9fFLDOkBEf3tq9oO8pfONcJEPRjxb81q9YkjEJbCGjGGmTYWSy1dGSKMQs5whsqzpIgNT+oA+A2sucvZ4lSRbrKtKOQi3xDKURDjPayJCYnRUDks3NRqckGbqBEeWAZMwlCSXidubKznG+dSNBrLtoNSNuxPYolOlPgRgLSwaZUIqXBawUB4KizXPCHKvc3G7xkYNkZkEvD/oZSzLfP3ObPJk21YCJgnDIiCSQnxh/Pd9TBOslSTbWVURXfmsGTQyHfpAWt7iUOf68kVUom9i/U5LM7mU6bQuI9cUMqbmTOzYTxJLM140sq5Iq3RwruBwks7Rs246UKSTzxgg5kaGcm0IfIx9rW4pksa5iOAYjJq4WK8IdQnS2LkIgKUlG0o6jbyeLdyl3rMKxJPPWh4eliK+6ZGWDipBlZ5PYDBCTwbavthrQFJJ5Y0Sxcq7b1zVAW9HnyIhr566asa5i2E9vjKZkJH22b44MYraweZJ17fwJ+bGtXSzJGIh3hXJumylFMibqMoEYqS3+mUKy0BWaW7JYdpKNdRVtPN4YTdkQvWwk8/zg+zbyjiGZBYC5UtoxFillTDaFzDFjt1d7YlfTmHGPbVPCXZzqKjIWuzbFatomm5Tuot1raO597DaJZKF7MrpWMFZLOtovO8lCCzvGiCUS0eI2JUhmLt8Ud88rZI4XelOSzGcX+9xLT8Zt4VSMEvjXVSxFnWKL1BSlSkmyoeePdRetHkj2EHDsljEqQTJbsceOkb5RKyMWtixrjB4OzZc/n5Jksa6tT+ZsqxnHDI4O20ZTu5G3PmRWyKjMqevECnBZSWaGiBoQ6WdLUXtjRJIgRa0wRla5SWZvcg+5UGFfmb8tgXT9aYK9o2ZExY3k/3M39aYkGWOICQEs/NixALWRDAFyUNuywVptwGeFuBaCUYQulc5fJpLRF3awUKynuOwL7qExQo5Y7lLp/NwkMz0YKhpjfCANhgcCUQ/bEIhXfZIIxXy4kWOKdH5qklkWFV60uYyWwqckseN9wJBk/rcmrLrtd4f7pdNqHCl3jzf87vxYFpJ5oSMnv8uFzntjZNtuwiLm0FjnnM9NMrPsQ5lB/7IncsKN9qu5GSPGipx4jSnFap+aZPTPJ/58zGXFaHarhBsaFnMYksx2hbO1BZcw/FEcrrEBdJ2foxxD1y4LyTA27FSgyk/gH74K4uXYdn5onHPP5ySZdxXZVtQXJvi4NiQYYzQ58r3t/FQ55CAZfUH/bN8i26sopHMQTrESt8oiJiabOtAc19lmW+5df2KuW8K4LxsCO05y1epyzG+qe9pLm1u64a7/tsyqkSzVJNT7VAkUk0AlWTFR1wetqwQqydZ15uu4i0mgkqyYqOuD1lUClWTrOvN13MUkUElWTNT1QesqgUqydZ35Ou5iEqgkKybq+qB1lcB/7fUTRXCC8XIAAAAASUVORK5CYII=\" style=\"width: 108.5px; height: 19px;\" width=\"108.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 123.5px; height: 19px;\" width=\"123.5\" height=\"19\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea=[3 4 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eb=[1 4 7 6];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput =[1 7 11 11];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = rwpadd(a,b)\r\n p= a+b;\r\nend","test_suite":"%%\r\na=[3 4 5];\r\nb=[1 4 7 6];\r\ny_correct = [1 7 11 11];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=[1 1 1 3 -2];\r\nb=[1 3];\r\ny_correct = [1 1 1 4 1];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=[1];\r\nb=[1 2 3];\r\ny_correct = [1 2 4];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=randi(10,1,5);\r\nb=[];\r\nassert(isequal(rwpadd(a,b),a))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":38144,"edited_by":223089,"edited_at":"2022-12-12T05:56:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":"2022-12-12T05:56:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-02T18:19:55.000Z","updated_at":"2026-04-07T18:12:52.000Z","published_at":"2017-08-02T18:19:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the sum of two polynomials if they are written in notation with their coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3x^2+4x+5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) + (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+4x^2+7x+6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+7x^2+11x+11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a=[3 4 5];\\nb=[1 4 7 6];\\n\\noutput =[1 7 11 11];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0 0 1 1 2 2 3 3]\r\n y = [ 0 1 0 1 0 1 0 1]\r\n z = [-4 -1 -3 -2 0 -1 5 2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0 0 1 1 2 2 3 3]\r\n y = [ 0 1 0 1 0 1 0 1]\r\n z = [-4 -1 -3 -2 0 -1 5 2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n cxx=0;\r\n cxy=0;\r\n cyy=0;\r\n c00=0;\r\n c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2025-12-07T17:59:24.000Z","published_at":"2012-03-19T09:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0 0 1 1 2 2 3 3]\\n y = [ 0 1 0 1 0 1 0 1]\\n z = [-4 -1 -3 -2 0 -1 5 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":543,"title":"deconvolution","description":"* Suppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\r\n* In this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\r\n* Suppose there is another vector w like [1 -1].\r\n* In this example, the second polynomial is (x-1).\r\n* If x is any integer then the polynomial represented by (v/w) is integer?\r\n ","description_html":"\u003cul\u003e\u003cli\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/li\u003e\u003cli\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/li\u003e\u003cli\u003eSuppose there is another vector w like [1 -1].\u003c/li\u003e\u003cli\u003eIn this example, the second polynomial is (x-1).\u003c/li\u003e\u003cli\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/li\u003e\u003c/ul\u003e","function_template":"function yesno = integ(v,w)\r\n yesno=1==1/1; % yes\r\n yesno=1==1/2; % no\r\nend","test_suite":"%%\r\nv=[1 0 0 -1];\r\nw=[1 -1];\r\nassert(integ(v,w))\r\n%%\r\nv=[2 9 6 -1 16 -5];\r\nw=[2 3 -1 5];\r\nassert(integ(v,w))\r\n%%\r\nv=[1 4 10 20 35 50 58 58 49 30];\r\nw=1:6;\r\nassert(integ(v,w))\r\n%%\r\nv=1:10;\r\nw=1:6;\r\nassert(~integ(v,w))\r\n%%\r\nv=3:12;\r\nw=-3:2;\r\nassert(~integ(v,w))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-03-31T22:38:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-31T22:38:54.000Z","updated_at":"2025-12-08T23:40:32.000Z","published_at":"2012-03-31T22:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is another vector w like [1 -1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the second polynomial is (x-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43619,"title":"Divide polynomial p1 by p2.","description":"Divide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\r\n\r\nExample\r\n\r\np1=[3 2 5 1 0 2 ] \r\n\r\np2=[1 2 0 5 0 3]\r\n\r\nThen q=[3] r=[0 -4 5 -14 0 -7]","description_html":"\u003cp\u003eDivide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ep1=[3 2 5 1 0 2 ]\u003c/p\u003e\u003cp\u003ep2=[1 2 0 5 0 3]\u003c/p\u003e\u003cp\u003eThen q=[3] r=[0 -4 5 -14 0 -7]\u003c/p\u003e","function_template":"function [q,r] = DivPol(p1,p2)\r\n y = x;\r\nend","test_suite":"%%\r\np1=[3 2 5 1 0 2 ]\r\np2=[1 2 0 5 0 3]\r\n\r\nq_correct=[3] \r\nr_correct=[0 -4 5 -14 0 -7]\r\n[q,r]=DivPol(p1,p2)\r\n\r\nassert(isequal(q,q_correct))\r\nassert(isequal(r,r_correct))\r\n%%\r\np1=[-2 0 3 -5 -6 5 -1 0 16 8]\r\np2=[1 0 -1 2 4]\r\n\r\nq_correct=[-2 0 1 -1 3 2] \r\nr_correct=[0 0 0 0 0 0 0 0 0 0]\r\n[q,r]=DivPol(p1,p2)\r\n\r\nassert(isequal(q,q_correct))\r\nassert(isequal(r,r_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T23:36:33.000Z","updated_at":"2026-04-14T13:21:38.000Z","published_at":"2016-10-24T23:36:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[3 2 5 1 0 2 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[1 2 0 5 0 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen q=[3] r=[0 -4 5 -14 0 -7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52303,"title":"Bessel Polynomials","description":"Return the n-th Bessel polynomial\r\nAssume that n is a non-negative finite integer.\r\n\r\nbessel_poly(0)\r\nans = 1\r\n\r\nbessel_poly(1)\r\nans = [1 1]\r\n\r\nbessel_poly(2)\r\nans = [3 3 1]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 254.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.233px; transform-origin: 407px 127.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.5px 8px; transform-origin: 8.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Bessel_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBessel\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.5px 8px; transform-origin: 35.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e polynomial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39px 8px; transform-origin: 39px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a non-negative finite integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(0)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = [1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = [3 3 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bessel_poly(x)\r\n%Wear a mask\r\n%Stay home, stay safe\r\nend","test_suite":"%%\r\nx = 1;\r\ny = [1 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = [3 3 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 5;\r\ny = [945 945 420 105 15 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [105 105 45 10 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 7;\r\ny = [135135 135135 62370 17325 3150 378 28 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = [15 15 6 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 0;\r\ny = 1;\r\nassert(isequal(bessel_poly(x),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-07-14T18:48:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T18:29:16.000Z","updated_at":"2026-04-14T12:40:39.000Z","published_at":"2021-07-14T18:46:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bessel_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBessel\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[bessel_poly(0)\\nans = 1\\n\\nbessel_poly(1)\\nans = [1 1]\\n\\nbessel_poly(2)\\nans = [3 3 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1633,"title":"Find the right x in a 1. order Polynomal (y = m*x+c)","description":"Given two points in a Cartesian coordinate system, find the x-value, where polynomial of 1. order (y = m*x+c) is equal to a given value c.\r\n\r\ne.g.: \r\nwe have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8;\r\nThe input is:\r\nx = [1 3], y = [2,6], c = 8.\r\n\r\nThe answer is 4.\r\n\r\nConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line. \r\n\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 102px; vertical-align: baseline; perspective-origin: 332px 102px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven two points in a Cartesian coordinate system, find the x-value on the line y = m*x+b where the y-value is equal to a given value c.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ee.g.: we have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8; The input is: x = [1 3], y = [2,6], c = 8.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe answer is 4.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = getTheRightPosition(x,y,c)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2]; y = [5 6]; c = 5;\r\ny_correct = 1;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n%%\r\nx = [1 -2]; y = [1 -2]; c = 50;\r\ny_correct = 50;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 -2]; y = [1 2]; c = 50;\r\ny_correct = -146;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 1]; y = [1 -2]; c = 50;\r\ny_correct = 1;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n%%\r\nx = [1 1]; y = [1 1]; c = 50;\r\ny_correct = NaN;\r\nassert(isequal(isnan(getTheRightPosition(x,y,c)),isnan(y_correct)))\r\n%%\r\nx = [1 2]; y = [1 1]; c = 50;\r\ny_correct = NaN;\r\nassert(isequal(isnan(getTheRightPosition(x,y,c)),isnan(y_correct)))\r\n%%\r\nx = [1 2]; y = [2 2]; c = 2;\r\ny_correct = Inf;\r\nassert(isequal(isinf(getTheRightPosition(x,y,c)),isinf(y_correct)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":12126,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-09T10:02:33.000Z","updated_at":"2025-12-29T14:46:22.000Z","published_at":"2013-06-09T10:35:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two points in a Cartesian coordinate system, find the x-value on the line y = m*x+b where the y-value is equal to a given value c.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.: we have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8; The input is: x = [1 3], y = [2,6], c = 8.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe answer is 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61007,"title":"Pseudo-Zernike Polynomials","description":"Problem #1476 deals with Radial Zernike Polynomials.\r\nHere, generate the Pseudo-Zernike Polynomials for a given order n and degree k -\r\n%Examples pR(n,k)\r\npR(0,0) = 1 =\u003e [1]\r\n\r\npR(1,1) = 3*r-2 =\u003e [3 -2]\r\n\r\npR(3,2) = 7*r^3 + 6*r^2 =\u003e [7 6 0 0]\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions. \r\n\r\n\t\t\r\n\t","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 304.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 152.3px; transform-origin: 408px 152.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.0083px 8px; transform-origin: 28.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProblem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1476\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#1476\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.767px 8px; transform-origin: 121.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with Radial Zernike Polynomials.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere, generate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pseudo-Zernike_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePseudo-Zernike Polynomials\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.8417px 8px; transform-origin: 54.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a given order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.21667px 8px; transform-origin: 6.21667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.7333px 8px; transform-origin: 23.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003edegree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 61.3px; transform-origin: 405px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examples pR(n,k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(0,0) = 1 =\u0026gt; [1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(1,1) = 3*r-2 =\u0026gt; [3 -2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 8.5px; tab-size: 4; transform-origin: 138.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(3,2) = 7*r^3 + 6*r^2 =\u0026gt; [7 6 0 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.108px 8px; transform-origin: 264.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.0667px 8px; transform-origin: 31.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 8px; transform-origin: 15.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pseudozernike(n,k)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('pseudozernike.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, 'str2num'); \r\n\r\n%%\r\ny = 1;\r\nassert(isequal(pseudozernike(0,0),y))\r\n\r\n%%\r\ny = [3 -2];\r\nassert(isequal(pseudozernike(1,0),y))\r\n\r\n%%\r\ny = [10 -12 3];\r\nassert(isequal(pseudozernike(2,0),y))\r\n\r\n%%\r\ny = [1 0 0 0];\r\nassert(isequal(pseudozernike(3,3),y))\r\n\r\n%%\r\ny = [84 -168 105 -20 0];\r\nassert(isequal(pseudozernike(4,1),y))\r\n\r\n%%\r\ny = [9 -8 0 0 0];\r\nassert(isequal(pseudozernike(4,3),y))\r\n\r\n%%\r\ny = [165 -360 252 -56 0 0];\r\nassert(isequal(pseudozernike(5,2),y))\r\n\r\n%%\r\ny = [11 -10 0 0 0 0];\r\nassert(isequal(pseudozernike(5,4),y))\r\n\r\n%%\r\ny = [1716 -5544 6930 -4200 1260 -168 7];\r\nassert(isequal(pseudozernike(6,0),y))\r\n\r\n%%\r\nn = randi([20 30]);\r\ny = [1 zeros(1,n)];\r\nassert(isequal(pseudozernike(n,n),y))\r\n\r\n%%\r\nn = randi([30 40]);\r\ny = [2*n+1 -2*n zeros(1,n-1)];\r\nassert(isequal(pseudozernike(n,n-1),y))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-10-24T15:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2025-09-21T09:16:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-21T08:30:15.000Z","updated_at":"2026-01-26T15:39:10.000Z","published_at":"2025-09-21T09:16:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1476\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#1476\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with Radial Zernike Polynomials.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, generate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pseudo-Zernike_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePseudo-Zernike Polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a given order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003edegree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examples pR(n,k)\\npR(0,0) = 1 =\u003e [1]\\n\\npR(1,1) = 3*r-2 =\u003e [3 -2]\\n\\npR(3,2) = 7*r^3 + 6*r^2 =\u003e [7 6 0 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57427,"title":"Intersection points of a polynomial","description":"Find the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\r\nInput: a polynomial represented by a vector of coefficients p .\r\nThe function returns a vector x containing the points of intersection of the polynomial with the X-axis,\r\nwhere x is sorted in ascending order and rounded to 4 digits after the decimal point.\r\nIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable y .\r\nHint: use the polynomial functions of MATLAB.\r\n\r\nExample: for the polynomial p(x) = x^2 - 3x + 1.25\r\ngiven by its vector of coefficients p = [1 -3 1.25]\r\nx = [ 0.5 \r\n 2.5 ]\r\ny = 1.25\r\n\r\n* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 411px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 205.5px; transform-origin: 407px 205.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eInput: a polynomial represented by a vector of coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function returns a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e containing the points of intersection of the polynomial with the X-axis,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is sorted in ascending order and rounded to 4 digits after the decimal point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ey \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: use the polynomial functions of MATLAB.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample: for the polynomial p(x) = x^2 - 3x + 1.25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003egiven by its vector of coefficients p = [1 -3 1.25]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e= [ 0.5 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 2.5 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 1.25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x y] = poly_intersection(p)\r\n x = p(1);\r\n y = 0;\r\nend","test_suite":"%%\r\np1 = [ 2 -9 1 10];\r\nx_correct =[-0.9158\r\n 1.3393\r\n 4.0765];\r\ny_correct = 10;\r\n[x y] = poly_intersection(p1)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))\r\n\r\n%%\r\np2 = [1 -3 1.25];\r\nx_correct =[0.5 ; 2.5];\r\ny_correct = 1.25;\r\n[x y] = poly_intersection(p2)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))\r\n\r\n%%\r\np3 = [ 2 -14.5 0.8 14];\r\nx_correct =[ -0.9024\r\n 1.0999\r\n 7.0525];\r\ny_correct = 14;\r\n[x y] = poly_intersection(p3)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2022-12-17T10:29:59.000Z","deleted_by":null,"deleted_at":null,"solvers_count":113,"test_suite_updated_at":"2022-12-17T10:26:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-16T22:11:02.000Z","updated_at":"2025-07-05T08:30:16.000Z","published_at":"2022-12-16T22:11:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: a polynomial represented by a vector of coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function returns a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e containing the points of intersection of the polynomial with the X-axis,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is sorted in ascending order and rounded to 4 digits after the decimal point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use the polynomial functions of MATLAB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: for the polynomial p(x) = x^2 - 3x + 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven by its vector of coefficients p = [1 -3 1.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e= [ 0.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e 2.5 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61001,"title":"Stirling Numbers - I","description":"Problems #1388 \u0026 #45187 deal with Stirling numbers of the 2nd Kind.\r\nHere, generate the Stirling numbers S(n,k) of the 1st kind of a given order n, for all degree k in descending order -\r\nS(0,0) = 1;\r\n\r\nS(1,1:0) = [1 0];\r\n\r\nS(3,3:0) = [1 3 2 0];\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 97.0833px; transform-origin: 408px 97.0833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5083px 7.79167px; transform-origin: 31.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProblems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1388\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#1388\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u0026amp; \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/45187\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#45187\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.033px 7.79167px; transform-origin: 133.033px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deal with Stirling numbers of the 2nd Kind.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 7.79167px; transform-origin: 60.2917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere, generate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind\"\u003e\u003cspan style=\"perspective-origin: 52.5167px 7.79167px; transform-origin: 52.5167px 7.79167px; \"\u003e\u003cspan style=\"\"\u003eStirling numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 19.4417px 7.79167px; transform-origin: 19.4417px 7.79167px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eS(n,k)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 45.5px 7.79167px; transform-origin: 45.5px 7.79167px; \"\u003e\u003cspan style=\"\"\u003e of the 1st kind\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5083px 7.79167px; transform-origin: 52.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a given order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 7.79167px; transform-origin: 4.275px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.675px 7.79167px; transform-origin: 46.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for all degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.6917px 7.79167px; transform-origin: 67.6917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in descending order -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.25px; tab-size: 4; transform-origin: 42.35px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(0,0) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.25px; tab-size: 4; transform-origin: 0px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.25px; tab-size: 4; transform-origin: 65.45px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(1,1:0) = [1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.25px; tab-size: 4; transform-origin: 0px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80.85px 8.25px; tab-size: 4; transform-origin: 80.85px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(3,3:0) = [1 3 2 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.108px 7.79167px; transform-origin: 264.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = stirlingI(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('stirlingI.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\ny = 1;\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 1;\r\ny = [1 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 3;\r\ny = [1 3 2 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 4;\r\ny = [1 6 11 6 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 7;\r\ny = flip([0 \t720 \t1764 \t1624 \t735 \t175 \t21 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 8;\r\ny = flip([0 \t5040 \t13068 \t13132 \t6769 \t1960 \t322 \t28 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 10;\r\ny = flip([0 \t362880 \t1026576 \t1172700 \t723680 \t269325 \t63273 \t9450 \t870 \t45 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 14;\r\ny = [1 91 3731 91091 1474473 16669653 135036473 790943153 3336118786 9957703756 20313753096 ...\r\n 26596717056 19802759040 6227020800 0];\r\nassert(isequal(stirlingI(n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T08:00:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-13T07:58:07.000Z","updated_at":"2026-02-10T22:53:50.000Z","published_at":"2025-09-13T07:58:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1388\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#1388\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/45187\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#45187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deal with Stirling numbers of the 2nd Kind.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, generate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eStirling numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS(n,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the 1st kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a given order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for all degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in descending order -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[S(0,0) = 1;\\n\\nS(1,1:0) = [1 0];\\n\\nS(3,3:0) = [1 3 2 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61165,"title":"Breaking straight lines","description":"Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\r\nBreak the given line by building a piecewise linear function constituted by two branches:\r\none branch stands for the parent polynomial p;\r\nand another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).\r\nGiven (P, p), find\r\nR, the breaking point;\r\nr, the 1×2 array that represents the perpendicular line. If r violates the definition of a function, return r = ''.\r\ninput: (P, p)\r\noutput: (R, r)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 508.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 254.275px; transform-origin: 408px 254.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a point in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane and let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone branch stands for the parent polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand another branch stands for the perpendicular line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that passes by the point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the breaking point;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array that represents the perpendicular line. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e violates the definition of a function, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(R, r)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 213.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 106.9px; text-align: left; transform-origin: 384px 106.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"251\" height=\"208\" style=\"vertical-align: baseline;width: 251px;height: 208px\" 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alt=\"Break line\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [R, r] = breaking(P,p)\r\n R = x;\r\n r = x;\r\nend","test_suite":"%%\r\nP = [1 1];\r\np = [2 1];\r\nR_correct = [0.2 1.4];\r\nr_correct = [-0.5 1.5];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1];\r\nR_correct = [0.8 0.6];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1.5];\r\nR_correct = [1 1];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [1 -1];\r\nR_correct = [1.5 0.5];\r\nr_correct = [-1 2];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nfiletext = fileread('breaking.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nP = [1 1];\r\np = [0 2];\r\nR_correct = [1 2];\r\nr_correct = '';\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.2 2]; \r\nR_correct = [15/13 23/13];\r\nr_correct = [5 -4];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-29T17:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-29T17:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-15T15:30:33.000Z","updated_at":"2026-04-09T10:19:31.000Z","published_at":"2026-01-26T14:18:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a point in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane and let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eone branch stands for the parent polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand another branch stands for the perpendicular line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that passes by the point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the breaking point;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array that represents the perpendicular line. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e violates the definition of a function, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Laguerre polynomials","description":"Given an integer _n_ \u0026ge; 0 and a scalar _a_, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials Generalized Laguerre polynomial\u003e of association degree _a_.\r\n\r\nFor simplicity, assume that _a_ is a non-negative integer.\r\n\r\n*Examples*:\r\n\r\n genLaguerrePoly(0,1)\r\n ans =\r\n 1 \r\n\r\n genLaguerrePoly(1,1)\r\n ans =\r\n -1 2 \r\n\r\n genLaguerrePoly(2,1)\r\n ans =\r\n 0.5 -3 3\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0 and a scalar \u003ci\u003ea\u003c/i\u003e, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials\"\u003eGeneralized Laguerre polynomial\u003c/a\u003e of association degree \u003ci\u003ea\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eFor simplicity, assume that \u003ci\u003ea\u003c/i\u003e is a non-negative integer.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e genLaguerrePoly(0,1)\r\n ans =\r\n 1 \u003c/pre\u003e\u003cpre\u003e genLaguerrePoly(1,1)\r\n ans =\r\n -1 2 \u003c/pre\u003e\u003cpre\u003e genLaguerrePoly(2,1)\r\n ans =\r\n 0.5 -3 3\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = genLaguerrePoly(n,a)\r\n P = n*a;\r\nend","test_suite":"%%\r\nuser_solution = fileread('genLaguerrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\na = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 0;\r\nP_correct = [-1 1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 0;\r\nP_correct = [1 -4 2]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 0;\r\nP_correct = [-1 9 -18 6]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 0;\r\nP_correct = [1 -16 72 -96 24]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 0;\r\nP_correct = [-1 25 -200 600 -600 120]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 0;\r\nP_correct = [1 -36 450 -2400 5400 -4320 720]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 1;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 1;\r\nP_correct = [-1 2]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 1;\r\nP_correct = [1 -6 6]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 1;\r\nP_correct = [-1 12 -36 24]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 1;\r\nP_correct = [1 -20 120 -240 120]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 1;\r\nP_correct = [-1 30 -300 1200 -1800 720]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 1;\r\nP_correct = [1 -42 630 -4200 12600 -15120 5040]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 2;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 2;\r\nP_correct = [-1 3]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 2;\r\nP_correct = [1 -8 12]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 2;\r\nP_correct = [-1 15 -60 60]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 2;\r\nP_correct = [1 -24 180 -480 360]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 2;\r\nP_correct = [-1 35 -420 2100 -4200 2520]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 2;\r\nP_correct = [1 -48 840 -6720 25200 -40320 20160]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 3;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 3;\r\nP_correct = [-1 4]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 3;\r\nP_correct = [1 -10 20]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 3;\r\nP_correct = [-1 18 -90 120]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 3;\r\nP_correct = [1 -28 252 -840 840]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 3;\r\nP_correct = [-1 40 -560 3360 -8400 6720]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 3;\r\nP_correct = [1 -54 1080 -10080 45360 -90720 60480]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 4;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 4;\r\nP_correct = [-1 5]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 4;\r\nP_correct = [1 -12 30]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 4;\r\nP_correct = [-1 21 -126 210]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 4;\r\nP_correct = [1 -32 336 -1344 1680]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 4;\r\nP_correct = [-1 45 -720 5040 -15120 15120]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 4;\r\nP_correct = [1 -60 1350 -14400 75600 -181440 151200]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":"2013-04-28T07:10:43.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-27T14:47:51.000Z","updated_at":"2026-04-08T15:26:08.000Z","published_at":"2013-04-27T14:58:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0 and a scalar\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGeneralized Laguerre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of association degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor simplicity, assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ genLaguerrePoly(0,1)\\n ans =\\n 1 \\n\\n genLaguerrePoly(1,1)\\n ans =\\n -1 2 \\n\\n genLaguerrePoly(2,1)\\n ans =\\n 0.5 -3 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57725,"title":"Sequence problem","description":"find the nth term of the sequence:\r\n790\r\n1303\r\n2033\r\n____\r\n4366\r\n6095\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.3125px; transform-origin: 407px 97.3125px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efind the nth term of the sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3125px; transform-origin: 391px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e790\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1303\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e2033\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4366\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6095\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sequence(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfunctions={'polyfit','polyval'};\r\nassessFunctionAbsence(functions, 'FileName', 'sequence.m');\r\n\r\n%%\r\nx = 1;\r\ny_correct = 790;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1303;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 6095;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 8293;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 18511;\r\nassert(isequal(sequence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2900827,"edited_by":2900827,"edited_at":"2023-02-20T05:07:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-02-20T05:07:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-19T16:34:33.000Z","updated_at":"2025-09-14T11:31:23.000Z","published_at":"2023-02-19T16:35:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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*string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Chebyshev_polynomials\"\u003eChebyshev polynomial of the 1st Kind\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e chebyshev1stKindPoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e chebyshev1stKindPoly(1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e chebyshev1stKindPoly(2)\r\n ans =\r\n 2 0 -1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = chebyshev1stKindPoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('chebyshev1stKindPoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [2 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [4 0 -3 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [8 0 -8 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [16 0 -20 0 5 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [32 0 -48 0 18 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [64 0 -112 0 56 0 -7 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [128 0 -256 0 160 0 -32 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [256 0 -576 0 432 0 -120 0 9 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [512 0 -1280 0 1120 0 -400 0 50 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [1024 0 -2816 0 2816 0 -1232 0 220 0 -11 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [2048 0 -6144 0 6912 0 -3584 0 840 0 -72 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [4096 0 -13312 0 16640 0 -9984 0 2912 0 -364 0 13 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [8192 0 -28672 0 39424 0 -26880 0 9408 0 -1568 0 98 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [16384 0 -61440 0 92160 0 -70400 0 28800 0 -6048 0 560 0 -15 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":"2013-04-30T12:30:22.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T11:25:32.000Z","updated_at":"2026-04-01T10:38:08.000Z","published_at":"2013-04-30T11:27:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Chebyshev_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChebyshev polynomial of the 1st Kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ chebyshev1stKindPoly(0)\\n ans =\\n 1\\n\\n chebyshev1stKindPoly(1)\\n ans =\\n 1 0\\n\\n chebyshev1stKindPoly(2)\\n ans =\\n 2 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1583,"title":"generate a matrix of Legendre polynomials","description":"input = x - the degree of the polynomial\r\noutput = matrix of Legendre polynomials","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 8px; transform-origin: 123px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003einput = x - the degree of the polynomial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126px 8px; transform-origin: 126px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eoutput = matrix of Legendre polynomials\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = leg_poly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = [0 1; 1 0];\r\nassert(isequal(leg_poly(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = [0 0 1; 0 1 0; 1.5 0 -0.5];\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [0 0 0 1; 0 0 1 0; 0 1.5 0 -0.5; 2.5 0 -1.5 0];\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [0 0 0 0 0 1; 0 0 0 0 1 0; 0 0 0 1.5 0 -0.5; 0 0 2.5 0 -1.5 0; 0 4.375 0 -3.75 0 0.375; 7.875 0 -8.75 0 1.875 0]\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":14267,"edited_by":223089,"edited_at":"2023-02-27T05:04:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2023-02-27T05:04:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-06T13:55:33.000Z","updated_at":"2026-01-18T14:21:40.000Z","published_at":"2013-06-06T13:55:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput = x - the degree of the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput = matrix of Legendre polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43753,"title":"Laguerre Polynomials","description":"Create a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\r\n\r\n 1\t0\t0\t0\t0\t0\t0\r\n 1\t1\t0\t0\t0\t0\t0\r\n 2\t4\t1\t0\t0\t0\t0\r\n 6\t18\t9\t1\t0\t0\t0\r\n 24\t96\t72\t16\t1\t0\t0\r\n 120\t600\t600\t200\t25\t1\t0\r\n 720\t4320\t5400\t2400\t450\t36\t1\r\n\r\nSee \u003chttps://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials\u003e for more information.","description_html":"\u003cp\u003eCreate a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1\t0\t0\t0\t0\t0\t0\r\n1\t1\t0\t0\t0\t0\t0\r\n2\t4\t1\t0\t0\t0\t0\r\n6\t18\t9\t1\t0\t0\t0\r\n24\t96\t72\t16\t1\t0\t0\r\n120\t600\t600\t200\t25\t1\t0\r\n720\t4320\t5400\t2400\t450\t36\t1\r\n\u003c/pre\u003e\u003cp\u003eSee \u003ca href = \"https://en.wikipedia.org/wiki/Laguerre_polynomials\"\u003eLaguerre Polynomials\u003c/a\u003e for more information.\u003c/p\u003e","function_template":"function y = laguerre(n)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 6;\r\ny_correct = [1,0,0,0,0,0,0;1,1,0,0,0,0,0;2,4,1,0,0,0,0;6,18,9,1,0,0,0;24,96,72,16,1,0,0;120,600,600,200,25,1,0;720,4320,5400,2400,450,36,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = [1,0;1,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = [1,0,0,0;1,1,0,0;2,4,1,0;6,18,9,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = [1,0,0,0,0,0,0,0,0,0,0;1,1,0,0,0,0,0,0,0,0,0;2,4,1,0,0,0,0,0,0,0,0;6,18,9,1,0,0,0,0,0,0,0;24,96,72,16,1,0,0,0,0,0,0;120,600,600,200,25,1,0,0,0,0,0;720,4320,5400,2400,450,36,1,0,0,0,0;5040,35280,52920,29400,7350,882,49,1,0,0,0;40320,322560,564480,376320,117600,18816,1568,64,1,0,0;362880,3265920,6531840,5080320,1905120,381024,42336,2592,81,1,0;3628800,36288000,81648000,72576000,31752000,7620480,1058400,86400,4050,100,1];\r\nassert(isequal(laguerre(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93456,"edited_by":223089,"edited_at":"2022-09-02T13:57:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-12-07T22:24:15.000Z","updated_at":"2026-01-02T17:37:55.000Z","published_at":"2016-12-07T22:24:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 0 0 0 0 0 0\\n1 1 0 0 0 0 0\\n2 4 1 0 0 0 0\\n6 18 9 1 0 0 0\\n24 96 72 16 1 0 0\\n120 600 600 200 25 1 0\\n720 4320 5400 2400 450 36 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLaguerre Polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44261,"title":"Multivariate polynomials - sort monomials","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array Problem 44260\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of |5*x| is 1 and the total degree of |x^3*y^5*z| is 9.\r\n\r\nWrite a function \r\n\r\n function [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\n\r\nto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\r\n\r\nExample: Consider the polynomial |p(x,y,z) = 3*x - 2 + y^2 +4*z^2|, which is represented as:\r\n\r\n exponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]\r\n\r\nThe sorted version is\r\n\r\n exponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].\r\n\r\nYou can assume that a given combination of exponents is never repeated.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array\"\u003eProblem 44260\u003c/a\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of \u003ctt\u003e5*x\u003c/tt\u003e is 1 and the total degree of \u003ctt\u003ex^3*y^5*z\u003c/tt\u003e is 9.\u003c/p\u003e\u003cp\u003eWrite a function\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\n\u003c/pre\u003e\u003cp\u003eto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\u003c/p\u003e\u003cp\u003eExample: Consider the polynomial \u003ctt\u003ep(x,y,z) = 3*x - 2 + y^2 +4*z^2\u003c/tt\u003e, which is represented as:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]\r\n\u003c/pre\u003e\u003cp\u003eThe sorted version is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].\r\n\u003c/pre\u003e\u003cp\u003eYou can assume that a given combination of exponents is never repeated.\u003c/p\u003e","function_template":"function [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\ncoeffs = 0;\r\nexponents = 0;\r\nend","test_suite":"%% Test sortMonomials\r\nfiletext = fileread('sortMonomials.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%%\r\nunsortedCoeffs = [-10 7 -10 -7 6 6 3 1 -7 2]';\r\nunsortedExponents = [5 4 2; 2 5 3; 2 1 5; 1 5 4; 1 4 3; 1 3 3; 1 2 1; 0 4 1; 0 2 1; 0 0 5];\r\n[sortedCoeffs,sortedExponents] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\nsortOrder = [1 2 4 3 5 6 8 10 7 9];\r\nassert(isequal(sortedCoeffs,unsortedCoeffs(sortOrder)))\r\nassert(isequal(sortedExponents,unsortedExponents(sortOrder,:)))\r\n\r\n%%\r\nx = randi(1000); y = randi(1000);\r\n[coeffs,exponents] = sortMonomials(x,y);\r\nassert(isequal([x y],[coeffs exponents]))\r\n\r\n%%\r\nunsortedCoeffs = randi(1000,[4 1]);\r\nough = ['hguot '; 'hguoc '; 'hguolp'; 'hguod '];\r\nunsortedExponents = ough - repmat(randi(100),size(ough));\r\nunsortedExponents = [unsortedExponents -sum(unsortedExponents,2)];\r\n[sortedCoeffs,~] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\n[~,ia] = sort(ough(:,5));\r\nassert(isequal(sortedCoeffs,flipud(unsortedCoeffs(ia))))\r\n\r\n%%\r\nz = [1 3 5+randi(10)];\r\nv1 = perms(z); \r\nv2 = perms(z+[1 0 0]);\r\nv = [v2; v1];\r\nunsortedCoeffs = randi(1000,[size(v,1) 1]);\r\nunsortedExponents = v(randperm(size(v,1)),:);\r\n[sortedCoeffs,sortedExponents] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\nassert(isequal(sortedExponents,v))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-13T18:24:47.000Z","updated_at":"2017-07-15T05:42:59.000Z","published_at":"2017-07-13T18:25:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44260\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5*x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 and the total degree of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex^3*y^5*z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function [coeffs,exponents] = sortMonomials(coeffs,exponents)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: Consider the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y,z) = 3*x - 2 + y^2 +4*z^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sorted version is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that a given combination of exponents is never repeated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1464,"title":"Laguerre polynomials","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre polynomial\u003e.\r\n\r\n*Examples*:\r\n\r\n laguerrePoly(0)\r\n ans =\r\n 1 \r\n\r\n laguerrePoly(1)\r\n ans =\r\n -1 1 \r\n\r\n laguerrePoly(2)\r\n ans =\r\n 0.5 -2 1\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Laguerre_polynomials\"\u003eLaguerre polynomial\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e laguerrePoly(0)\r\n ans =\r\n 1 \u003c/pre\u003e\u003cpre\u003e laguerrePoly(1)\r\n ans =\r\n -1 1 \u003c/pre\u003e\u003cpre\u003e laguerrePoly(2)\r\n ans =\r\n 0.5 -2 1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = laguerrePoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('laguerrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(laguerrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [-1 1]/1;\r\nassert(isequal(round(laguerrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [1 -4 2]/2;\r\nassert(isequal(round(laguerrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [-1 9 -18 6]/6;\r\nassert(isequal(round(laguerrePoly(n)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [1 -16 72 -96 24]/24;\r\nassert(isequal(round(laguerrePoly(n)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [-1 25 -200 600 -600 120]/120;\r\nassert(isequal(round(laguerrePoly(n)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [1 -36 450 -2400 5400 -4320 720]/720;\r\nassert(isequal(round(laguerrePoly(n)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [-1 49 -882 7350 -29400 52920 -35280 5040]/5040;\r\nassert(isequal(round(laguerrePoly(n)*5040),round(P_correct*5040)));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [1 -64 1568 -18816 117600 -376320 564480 -322560 40320]/40320;\r\nassert(isequal(round(laguerrePoly(n)*40320),round(P_correct*40320)));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [-1 81 -2592 42336 -381024 1905120 -5080320 6531840 -3265920 362880]/362880;\r\nassert(isequal(round(laguerrePoly(n)*362880),round(P_correct*362880)));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1 -100 4050 -86400 1058400 -7620480 31752000 -72576000 81648000 -36288000 3628800]/3628800;\r\nassert(isequal(round(laguerrePoly(n)*3628800),round(P_correct*3628800)));\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2013-04-28T07:10:18.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-27T14:28:54.000Z","updated_at":"2026-04-08T15:24:34.000Z","published_at":"2013-04-27T14:30:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLaguerre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ laguerrePoly(0)\\n ans =\\n 1 \\n\\n laguerrePoly(1)\\n ans =\\n -1 1 \\n\\n laguerrePoly(2)\\n ans =\\n 0.5 -2 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1475,"title":"Chebyshev polynomials of the 2nd Kind","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev polynomial of the 2nd Kind\u003e.\r\n\r\n*Examples*:\r\n\r\n chebyshev2ndKindPoly(0)\r\n ans =\r\n 1\r\n\r\n chebyshev2ndKindPoly(1)\r\n ans =\r\n 2 0\r\n\r\n chebyshev2ndKindPoly(2)\r\n ans =\r\n 4 0 -1\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Chebyshev_polynomials\"\u003eChebyshev polynomial of the 2nd Kind\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e chebyshev2ndKindPoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e chebyshev2ndKindPoly(1)\r\n ans =\r\n 2 0\u003c/pre\u003e\u003cpre\u003e chebyshev2ndKindPoly(2)\r\n ans =\r\n 4 0 -1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = chebyshev2ndKindPoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('chebyshev2ndKindPoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [2 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [4 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [8 0 -4 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [16 0 -12 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [32 0 -32 0 6 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [64 0 -80 0 24 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [128 0 -192 0 80 0 -8 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [256 0 -448 0 240 0 -40 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [512 0 -1024 0 672 0 -160 0 10 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1024 0 -2304 0 1792 0 -560 0 60 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [2048 0 -5120 0 4608 0 -1792 0 280 0 -12 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [4096 0 -11264 0 11520 0 -5376 0 1120 0 -84 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [8192 0 -24576 0 28160 0 -15360 0 4032 0 -448 0 14 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [16384 0 -53248 0 67584 0 -42240 0 13440 0 -2016 0 112 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [32768 0 -114688 0 159744 0 -112640 0 42240 0 -8064 0 672 0 -16 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":79,"test_suite_updated_at":"2013-04-30T12:30:53.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T11:26:00.000Z","updated_at":"2026-04-08T15:02:56.000Z","published_at":"2013-04-30T11:27:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Chebyshev_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChebyshev polynomial of the 2nd Kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ chebyshev2ndKindPoly(0)\\n ans =\\n 1\\n\\n chebyshev2ndKindPoly(1)\\n ans =\\n 2 0\\n\\n chebyshev2ndKindPoly(2)\\n ans =\\n 4 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47578,"title":"Find a real root of a quintic function without using roots function","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGeneralized version of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47563\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 47563\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind a real root of a polynomial (5th degree) without using roots function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = noRoot(coeffs)\r\n\r\nend","test_suite":"%%\r\nfiletext = fileread('noRoot.m');\r\nassert(isempty(strfind(filetext, 'roots')))\r\n\r\n%%\r\ncoeffs = [6 8 7 9 12 467];\r\ncandidateX = noRoot(coeffs);\r\nassert(isreal(candidateX))\r\nassert(abs(sum(coeffs.*(candidateX.^(length(coeffs)-1:-1:0)))-0)\u003c0.0001)\r\n\r\n%%\r\nfor idx = 1:10\r\n coeffs = randi([3 100],1,randi([6 6]));\r\n candidateX = noRoot(coeffs);\r\n assert(isreal(candidateX))\r\n assert(abs(sum(coeffs.*(candidateX.^(length(coeffs)-1:-1:0)))-0)\u003c0.0001)\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2020-11-23T09:07:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-20T11:22:56.000Z","updated_at":"2020-11-23T09:07:05.000Z","published_at":"2020-11-23T09:07:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGeneralized version of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47563\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 47563\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind a real root of a polynomial (5th degree) without using roots function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61006,"title":"Shapiro Polynomials","description":"Given an order n, return the coefficients of 1st Shapiro polynomials Pn(x) - \r\n\r\n%Example\r\nP1(x) = x + 1 =\u003e Output = [1 1];\r\n\r\nP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u003e Output = [1 -1 1 1 -1 1 1 1];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 142.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 71.3667px; transform-origin: 408px 71.3667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 8px; transform-origin: 48.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.65px 8px; transform-origin: 91.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the coefficients of 1st \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Shapiro_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eShapiro polynomials\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePn(x) - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eP1(x) = x + 1 =\u0026gt; Output = [1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 315.7px 8.5px; tab-size: 4; transform-origin: 315.7px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u0026gt; Output = [1 -1 1 1 -1 1 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = shapiro(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('shapiro.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\n\r\n%%\r\nx = 1;\r\ny = [1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = [-1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = [1 -1 1 1 -1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [-1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 1 1];\r\n\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 5;\r\ny = [1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-20T15:17:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-20T03:25:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-19T17:23:37.000Z","updated_at":"2026-01-26T15:34:27.000Z","published_at":"2025-09-19T17:23:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the coefficients of 1st \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Shapiro_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eShapiro polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePn(x) - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nP1(x) = x + 1 =\u003e Output = [1 1];\\n\\nP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u003e Output = [1 -1 1 1 -1 1 1 1];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60950,"title":"Find the longest runs of primes generated by polynomials","description":"Cody Problems 60942, 60943, and 60944 involve polynomials that generate primes. No polynomial can generate only prime numbers, but some can generate sizable runs of primes. For example, for = 0, 1, 2,…,10, produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For , both terms in the polynomial are divisible by 11, and the result (253) is composite. \r\nWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\r\nTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \r\nRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\r\nMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 144.3px; transform-origin: 408px 144.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60942\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60942\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60943\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60943\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60944\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60944\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.675px 8px; transform-origin: 25.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involve \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003epolynomials that generate primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.975px 8px; transform-origin: 92.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. No polynomial can generate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eonly\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.8667px 8px; transform-origin: 20.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e prime numbers, but some can generate sizable runs of primes. For example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.9667px 8px; transform-origin: 49.9667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0, 1, 2,…,10, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"19.5\" alt=\"f(n) = 2n^2+11\" style=\"width: 103px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.825px 8px; transform-origin: 43.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" alt=\"n = 11\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.592px 8px; transform-origin: 141.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, both terms in the polynomial are divisible by 11, and the result (253) is composite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.167px 8px; transform-origin: 374.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 61.3px; transform-origin: 392px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 358.867px 8px; transform-origin: 358.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 347.608px 8px; transform-origin: 347.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 360.975px 8px; transform-origin: 360.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n,p] = polyPrimeRun(a)\r\n% a = vector of coefficients of the polynomial--e.g., for f(n) = 2n^2+11, a = [2 0 11]\r\n% n = length of longest run of primes (ignoring sign)\r\n% p = distinct primes in the longest run, sorted low to high \r\n q = a.*(0:1000);\r\n n = length(max(isprime(q)));\r\n p = distinct(isprime(q));\r\nend","test_suite":"%%\r\na = [1 1 0 17];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 11;\r\np_correct = [17 19 29 53 97 167 269 409 593 827 1117];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%%\r\na = [2 0 11];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 11;\r\np_correct = [11 13 19 29 43 61 83 109 139 173 211];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Honaker\r\na = [4 4 59];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 14;\r\np_correct = [59 67 83 107 139 179 227 283 347 419 499 587 683 787];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Legendre\r\na = [1 1 17];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 16;\r\np_correct = [17 19 23 29 37 47 59 73 89 107 127 149 173 199 227 257];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% A. Bruno\r\na = [3 39 37];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 18;\r\np_correct = [37 79 127 181 241 307 379 457 541 631 727 829 937 1051 1171 1297 1429 1567];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% E. Pegg Jr. \r\na = [1 0 29 0 101];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 20;\r\np_correct = [101 131 233 443 821 1451 2441 3923 6053 9011 13001 18251 25013 33563 44201 57251 73061 92003 114473 140891];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% R. Frame\r\na = [3 3 23];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 22;\r\np_correct = [23 29 41 59 83 113 149 191 239 293 353 419 491 569 653 743 839 941 1049 1163 1283 1409];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [7 -371 4871];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 24;\r\np_correct = [41 97 167 251 349 461 587 727 881 1049 1231 1427 1637 1861 2099 2351 2617 2897 3191 3499 3821 4157 4507 4871];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Legendre (1798)\r\na = [2 0 29];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 29;\r\np_correct = [29 31 37 47 61 79 101 127 157 191 229 271 317 367 421 479 541 607 677 751 829 911 997 1087 1181 1279 1381 1487 1597];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% J. Brox\r\na = [6 -342 4903];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 58;\r\np_correct = [31 43 67 103 151 211 283 367 463 571 691 823 967 1123 1291 1471 1663 1867 2083 2311 2551 2803 3067 3343 3631 3931 4243 4567 4903];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [7 -371 4871];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 24;\r\np_correct = [41 97 167 251 349 461 587 727 881 1049 1231 1427 1637 1861 2099 2351 2617 2897 3191 3499 3821 4157 4507 4871];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [8 -488 7243];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 62;\r\np_correct = [37 43 101 139 149 181 197 251 379 523 683 859 1051 1259 1483 1723 1979 2251 2539 2843 3163 3499 3851 4219 4603 5003 5419 5851 6299 6763 7243];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% J. Brox\r\na = [43 -537 2971];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 35;\r\np_correct = [1297 1319 1361 1427 1511 1621 1747 1901 2069 2267 2477 2719 2971 3257 3881 4591 5387 6269 7237 8291 9431 10657 11969 13367 14851 16421 18077 19819 21647 23561 25561 27647 29819 32077 34421];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac\r\na = [42 270 -26436 250703];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 40;\r\np_correct = [44927 44939 48479 48767 55343 56663 65267 68879 77999 85667 93287 107279 110879 130523 133967 151967 165983 174959 199247 203579 224579 247007 250703 296519 352367 414803 484079 560447 644159 735467 834623 941879 1057487 1181699 1314767 1456943 1608479 1769627 1940639 2121767];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Euler\r\na = [1 -1 41];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 41;\r\np_correct = [41 43 47 53 61 71 83 97 113 131 151 173 197 223 251 281 313 347 383 421 461 503 547 593 641 691 743 797 853 911 971 1033 1097 1163 1231 1301 1373 1447 1523 1601];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Speiser\r\na = [103 -4707 50383];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 43;\r\np_correct = [131 503 661 971 1439 1619 1867 1873 2371 2557 2917 2953 3041 3257 3319 3391 3449 4673 5231 6599 7219 8731 9413 11069 11813 13613 14419 16363 17231 19319 20249 22481 23473 25849 26903 29423 30539 33203 34381 37189 41381 45779 50383];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Fung and Ruby\r\na = [47 -1701 10181];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 43;\r\np_correct = [379 419 577 599 1321 1451 1483 1667 2129 2273 2617 2843 2851 2969 3463 3571 3877 3989 4079 4129 4421 4493 4759 4813 5003 5039 5153 5171 5209 5231 5501 6679 6967 8221 8527 9857 10181 11587 13411 15329 17341 19447 21647];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% S.M. Ruiz\r\na = [3 -183 3318 -18757];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 47;\r\np_correct = [37 41 59 109 229 409 419 499 739 829 877 1201 1531 1597 1669 1823 1999 2389 2749 2917 3061 3271 3307 3469 3491 3529 4789 5441 6367 7691 8221 10259 10369 12829 13163 15619 16421 18757 20051 24071 28499 33353 38651];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Fung and Ruby\r\na = [36 -810 2753];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 45;\r\np_correct = [89 163 359 397 613 647 811 953 991 1153 1277 1297 1423 1531 1619 1621 1693 1747 1783 1801 1979 2357 2753 3167 4049 5003 6029 7127 8297 9539 10853 12239 13697 15227 16829 18503 20249 22067 23957 25919 27953 30059 32237 34487 36809];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Kazmenko and Trofimov (2006)\r\na = [-66 3845 -60897 251831];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 46;\r\np_correct = [811 3529 8537 8681 10613 16553 19249 23057 28211 30139 32089 32911 35027 35221 36637 38639 39301 40637 43891 57413 57593 65539 70309 77719 80651 82183 92639 92863 101281 101963 103421 107713 109789 111539 112363 131627 144889 189961 194713 251831 256049 330287 413071 504797 605861 716659];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac (2006)\r\na = [1 -99 3588 -56822 348272 -286397];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 47;\r\np_correct = [1409 2441 3517 5227 5669 7963 8209 8543 9733 10429 14243 24251 27763 29531 32411 39971 41051 52301 52561 59971 60443 62903 64811 91673 106531 156353 196003 210011 212123 270631 286397 327491 336121 355331 377021 402851 412123 424163 584411 900061 1321283 1869383 2568091 3443681 4525091 5844043 7435163];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Beyleveld (2006)\r\na = [1 -97 3294 -45458 213589];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 50;p_correct = [109 271 541 673 1409 1873 1949 2069 2251 2341 3719 3881 4019 4451 4951 5227 5273 5449 6029 7109 7129 7789 8573 9209 9739 10223 10399 10529 10789 10889 15173 17669 25919 27449 39769 40129 56123 57149 75869 78509 99829 104323 128489 135089 162359 171329 201973 213589 247889];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac (2006)\r\na = [1 -126 6217 -153066 1987786 -13055316 34747236]/36;\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 55;\r\np_correct = [461 1091 2423 3583 4493 4549 6271 6961 7019 7933 8443 9007 9157 10429 12007 13241 13553 15443 15733 16193 20873 23993 32423 32969 35051 45737 46769 54959 56597 57397 61613 63421 64693 67993 98321 163561 166693 272563 318467 429409 552089 653687 887543 965201 1352093 1977581 2800877 3864349 5216353 6911743 9012401 11587787 14715509 18481913 22982693];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Dress and Landreau (2002), Gupta (2006)\r\na = [1 -133 6729 -158379 1720294 -6823316]/4;\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 57;\r\np_correct = [383 1721 3733 3923 4259 5323 10181 12547 12659 19373 20611 23887 26539 27847 32687 33073 37571 53149 65993 70123 87977 106207 124351 134077 142019 158923 174907 189977 204331 218389 228581 232823 248587 266947 289511 318259 355049 355573 404267 467617 519643 549391 653879 729173 785923 950947 991127 1154987 1313701 1404721 1705829 1707499 2071373 2505127 3018307 3621251 4325119];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2025-06-30T16:26:09.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-29T03:20:05.000Z","updated_at":"2026-02-06T13:37:00.000Z","published_at":"2025-06-29T03:20:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60942\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60942\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60943\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60943\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60944\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60944\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involve \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epolynomials that generate primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. No polynomial can generate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e prime numbers, but some can generate sizable runs of primes. For example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0, 1, 2,…,10, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n) = 2n^2+11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n) = 2n^2+11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, both terms in the polynomial are divisible by 11, and the result (253) is composite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1473,"title":"Legendre polynomials","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Legendre_polynomials Legendre polynomial\u003e.\r\n\r\n*Examples*:\r\n\r\n legendrePoly(0)\r\n ans =\r\n 1\r\n\r\n legendrePoly(1)\r\n ans =\r\n 1 0\r\n\r\n legendrePoly(2)\r\n ans =\r\n 1.5 0 -0.5\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Legendre_polynomials\"\u003eLegendre polynomial\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e legendrePoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e legendrePoly(1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e legendrePoly(2)\r\n ans =\r\n 1.5 0 -0.5\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = legendrePoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('legendrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(legendrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0]/1;\r\nassert(isequal(round(legendrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [3 0 -1]/2;\r\nassert(isequal(round(legendrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [5 0 -3 0]/2;\r\nassert(isequal(round(legendrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [35 0 -30 0 3]/8;\r\nassert(isequal(round(legendrePoly(n)*8),round(P_correct*8)));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [63 0 -70 0 15 0]/8;\r\nassert(isequal(round(legendrePoly(n)*8),round(P_correct*8)));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [231 0 -315 0 105 0 -5]/16;\r\nassert(isequal(round(legendrePoly(n)*16),round(P_correct*16)));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [429 0 -693 0 315 0 -35 0]/16;\r\nassert(isequal(round(legendrePoly(n)*16),round(P_correct*16)));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [6435 0 -12012 0 6930 0 -1260 0 35]/128;\r\nassert(isequal(round(legendrePoly(n)*128),round(P_correct*128)));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [12155 0 -25740 0 18018 0 -4620 0 315 0]/128;\r\nassert(isequal(round(legendrePoly(n)*128),round(P_correct*128)));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [46189 0 -109395 0 90090 0 -30030 0 3465 0 -63]/256;\r\nassert(isequal(round(legendrePoly(n)*256),round(P_correct*256)));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [88179 0 -230945 0 218790 0 -90090 0 15015 0 -693 0]/256;\r\nassert(isequal(round(legendrePoly(n)*256),round(P_correct*256)));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [676039 0 -1939938 0 2078505 0 -1021020 0 225225 0 -18018 0 231]/1024;\r\nassert(isequal(round(legendrePoly(n)*1024),round(P_correct*1024)));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [1300075 0 -4056234 0 4849845 0 -2771340 0 765765 0 -90090 0 3003 0]/1024;\r\nassert(isequal(round(legendrePoly(n)*1024),round(P_correct*1024)));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [5014575 0 -16900975 0 22309287 0 -14549535 0 4849845 0 -765765 0 45045 0 -429]/2048;\r\nassert(isequal(round(legendrePoly(n)*2048),round(P_correct*2048)));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [9694845 0 -35102025 0 50702925 0 -37182145 0 14549535 0 -2909907 0 255255 0 -6435 0]/2048;\r\nassert(isequal(round(legendrePoly(n)*2048),round(P_correct*2048)));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T10:43:53.000Z","updated_at":"2026-04-01T10:26:23.000Z","published_at":"2013-04-30T10:45:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Legendre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLegendre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ legendrePoly(0)\\n ans =\\n 1\\n\\n legendrePoly(1)\\n ans =\\n 1 0\\n\\n legendrePoly(2)\\n ans =\\n 1.5 0 -0.5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1068,"title":"Guess the Coefficients!","description":"Given a polynomial p known to have positive integer coefficients, deduce the values of the coefficients.\r\nFor example:\r\n p = @(x) x^2 + 2*x + 15;\r\n c = guess_the_coefficients(p);\r\noutputs\r\n c = [1 2 15]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 81.65px; transform-origin: 407px 81.65px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60px 8px; transform-origin: 60px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a polynomial\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e known to have positive integer coefficients, deduce the values of the coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 112px 8.5px; tab-size: 4; transform-origin: 112px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e p = @(x) x^2 + 2*x + 15;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 136px 8.5px; tab-size: 4; transform-origin: 136px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = guess_the_coefficients(p);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.5px 8px; transform-origin: 23.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eoutputs\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = [1 2 15]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = guess_the_coefficients(p)\r\n c = p(0);\r\nend","test_suite":"%%\r\nassert(isequal(guess_the_coefficients(@(x)3*x^2+5*x+7),[3 5 7]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)x^2+2*x+15),[1 2 15]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)2*x^3+4*x^2+6*x+8),[2 4 6 8]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval(53,x)),53))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([54 87],x)),[54 87]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([49 40 68],x)),[49 40 68]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([75 53 35 15],x)),[75 53 35 15]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([59 27 5 76 25],x)),[59 27 5 76 25]))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":134,"edited_by":223089,"edited_at":"2023-01-07T11:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2023-01-07T11:04:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-27T06:47:08.000Z","updated_at":"2025-11-16T14:54:18.000Z","published_at":"2012-12-05T06:28:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e known to have positive integer coefficients, deduce the values of the coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = @(x) x^2 + 2*x + 15;\\n c = guess_the_coefficients(p);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutputs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [1 2 15]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60998,"title":"Bernstein Basis Polynomials","description":"Return the coefficients of a Bernstein Basis Polynomial B(v,n) for degree n and order v - \r\n \r\n%Examples\r\nB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\r\nOutput = [-10 30 -30 10 0 0];\r\n\r\nB(3, 3) = x^3\r\nOutput = [1 0 0 0];\r\n\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 274.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 137.3px; transform-origin: 408px 137.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.05px 8px; transform-origin: 85.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the coefficients of a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Bernstein_polynomial#Bernstein_basis_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBernstein Basis Polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eB(v,n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.7833px 8px; transform-origin: 35.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8417px 8px; transform-origin: 33.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.21667px 8px; transform-origin: 6.21667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 61.3px; transform-origin: 405px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 227.15px 8.5px; tab-size: 4; transform-origin: 227.15px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.5px; tab-size: 4; transform-origin: 115.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [-10 30 -30 10 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eB(3, 3) = x^3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 8.5px; tab-size: 4; transform-origin: 73.15px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.167px 8px; transform-origin: 262.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = bernstein(x)\r\n x = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bernstein.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'elseif') || contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 5;\r\nv = 2;\r\ny = [-10 30 -30 10 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = randi(100);\r\nv = n;\r\ny = [1 zeros(1,v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 7;\r\nv = 0;\r\ny = [-1 7 -21 35 -35 21 -7 1];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 1;\r\nv = 0;\r\ny = [-1 1];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 7;\r\nv = 3;\r\ny = [35 -140 210 -140 35 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 10;\r\nv = 4;\r\ny = [210 -1260 3150 -4200 3150 -1260 210 0 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 12;\r\nv = 10;\r\ny = [66 -132 66 zeros(1,v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 25;\r\nv = 16;\r\ny = [-2042975 18386775 -73547100 171609900 -257414850 257414850 -171609900 73547100 -18386775 2042975 zeros(1, v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 13;\r\nv = 9;\r\ny = [715 -2860 4290 -2860 715 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:26:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-13T06:26:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-10T15:17:42.000Z","updated_at":"2026-01-26T14:24:46.000Z","published_at":"2025-09-10T16:33:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the coefficients of a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bernstein_polynomial#Bernstein_basis_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBernstein Basis Polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB(v,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examples\\nB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\\nOutput = [-10 30 -30 10 0 0];\\n\\nB(3, 3) = x^3\\nOutput = [1 0 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1304,"title":"Hermite Polynomials","description":"Return the _n_-th \u003chttp://en.wikipedia.org/wiki/Hermite_polynomials Hermite polynomial\u003e of the physicists' type.\r\n\r\nAssume that _n_ is a non-negative finite integer. \r\n\r\n*Examples*:\r\n\r\n hermite_poly(0)\r\n ans = \r\n 1\r\n \r\n hermite_poly(1)\r\n ans = \r\n 2 0\r\n\r\n hermite_poly(2)\r\n ans = \r\n 4 0 -2\r\n\r\n hermite_poly(3)\r\n ans = \r\n 8 0 -12 0\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eReturn the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Hermite_polynomials\"\u003eHermite polynomial\u003c/a\u003e of the physicists' type.\u003c/p\u003e\u003cp\u003eAssume that \u003ci\u003en\u003c/i\u003e is a non-negative finite integer.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e hermite_poly(0)\r\n ans = \r\n 1\u003c/pre\u003e\u003cpre\u003e hermite_poly(1)\r\n ans = \r\n 2 0\u003c/pre\u003e\u003cpre\u003e hermite_poly(2)\r\n ans = \r\n 4 0 -2\u003c/pre\u003e\u003cpre\u003e hermite_poly(3)\r\n ans = \r\n 8 0 -12 0\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function p = hermite_poly(n)\r\n p = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('hermite_poly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [2 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [4 0 -2];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [8 0 -12 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [16 0 -48 -0 12];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [32 0 -160 -0 120 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [64 0 -480 -0 720 0 -120];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [128 0 -1344 -0 3360 0 -1680 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [256 0 -3584 -0 13440 0 -13440 -0 1680];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [512 0 -9216 -0 48384 0 -80640 -0 30240 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1024 0 -23040 -0 161280 0 -403200 -0 302400 0 -30240];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [2048 0 -56320 -0 506880 0 -1774080 -0 2217600 0 -665280 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [4096 0 -135168 -0 1520640 0 -7096320 -0 13305600 0 -7983360 -0 665280];\r\nassert(isequal(hermite_poly(n),P_correct));","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":91,"test_suite_updated_at":"2013-04-28T07:05:09.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-02-27T09:28:44.000Z","updated_at":"2026-04-08T15:27:48.000Z","published_at":"2013-02-27T09:28:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Hermite_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHermite polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the physicists' type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ hermite_poly(0)\\n ans = \\n 1\\n\\n hermite_poly(1)\\n ans = \\n 2 0\\n\\n hermite_poly(2)\\n ans = \\n 4 0 -2\\n\\n hermite_poly(3)\\n ans = \\n 8 0 -12 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61179,"title":"Rotating 2d curve around a vertical axis","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the Oxz plane, around the vertical axis that passes through the vertex by an angle θ (see figures below).\r\nGiven the x-value of a point P, xP, belonging to the 2d curve, find R being the rotated point P.\r\nHint. Find critical points for their identification and behavior.\r\ninput: (p, xP, theta)\r\noutput: R\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 443.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 221.9px; transform-origin: 469px 221.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxz\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eθ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figures below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of a point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003exP,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e belonging to the 2d curve, find \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e being the rotated point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Find critical points for their identification and behavior.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, xP, theta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 251.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 125.9px; text-align: left; transform-origin: 445px 125.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"106\" style=\"vertical-align: baseline;width: 326px;height: 106px\" 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\" alt=\"Rotating 3d\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = rotate3d(p, xP, theta)\r\n R = x;\r\nend","test_suite":"%%\r\np = [3 -20 12 96 -39];\r\nxP = 4;\r\ntheta = pi/2;\r\nR_correct = [-1 5 25];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 1;\r\ntheta = pi/3;\r\nR_correct = [0 sqrt(3) 52];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 0;\r\ntheta = pi;\r\nR_correct = [-2 0 -39];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [2 0 0 0 0 0 -16];\r\nxP = sqrt(2);\r\ntheta = 3*pi/4;\r\nR_correct = [-1 1 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\nfiletext = fileread('rotate3d.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-11/4 7 11/4 -7 0];\r\nxP = 0;\r\ntheta = 2*pi/3;\r\nR_correct = [3 -sqrt(3) 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [-1 28/11 1 -28/11 0];\r\nxP = -1;\r\ntheta = pi/2;\r\nR_correct = [2 -3 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-02-14T16:56:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-01T12:37:27.000Z","updated_at":"2026-04-01T09:52:04.000Z","published_at":"2026-02-14T16:56:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxz\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eθ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figures below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of a point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exP,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e belonging to the 2d curve, find \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e being the rotated point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Find critical points for their identification and behavior.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, xP, theta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61148,"title":"Shifting vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u0026lt;b\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined such that the endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stand for the least and the greatest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values of the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = y_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the highest local maximum of the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see non-scale figures below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they exist. Otherwise, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb = '' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see Hint 1);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe shifting constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 1. An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomial has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n a = x;\r\n b = x;\r\n k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe shifting constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 1. An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomial has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b, k]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuMAAAIFCAIAAAD3AmRsAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6gEGDic7AlCSYwAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAwNi1KYW4tMjAyNiAxNDozOTo1OXUi7RYAACAASURBVHic7N1/XFRV/j/wMzEQrkNq5q/EAhR/pKiZKaUGbGb+KNvU1CwVSv1mZa4ubVrtMtRu5mddd9N2K3MDrdy00PJHaalgsoW6ZRplgsK4gj8gTGQIEHC+fxy6c+bMD+7cuXPvnXtfz4d/DOPMcLkz58z7nvc572NyOBwEAAAAQJOuUvsAAAAAALxCpBJczc3Ne/fuTU1NTUhIiIuLi4uLu/nmm+fOnXv48GFuNOv111+nD0hPT/f9mh4f2djYuH79+pEjR8bFxfXs2XPEiBFffPGFx6dXVFQkJSXFxcUNGjTo22+/DfxvDBW7d++m523GjBl2u12B19f9qbbb7TNmzKB/9e7du/19enp6On3u66+/HozDI8F/00FndP+BCdFOCZFKENXU1CxcuHDOnDmff/55bW0tvbO6unrPnj1Tpkz5wx/+0NjYKNfvys7OzszMPHPmDCHE4XA0NjZ26tSJ/ld5efnrr7+uy1bng8Ph+OKLLz788EO1DwS0qLm5+cMPPywoKFD7QEBv0PMEAyKVIHr33Xc//vhjj//lcDj+/e9/b9q0SZZfVFtbu3//fjpIs3jx4uLi4v/85z9xcXF1dXVr1qwZO3bs559/LssvChXl5eVPPPHEzJkzz507p/axgOYUFRVNmTJl8eLFRgvfIdjQ8wSJWe0D0K0LFy5s3bqV3p4wYcIzzzzTvXv3K1euHDt27Lnnnvv2228dDsfmzZsnTpwYFRXl1ys/9thjjz32GHtPQ0PDjz/+SG/37ds3LCwsLCyMEPKf//zn5Zdf5p7euXPnffv2SfyrQsTf/va3nTt3cneOHj26pKREleMBtbi/6Xa73Wq1HjlyRK1DAi0LsJfw2PNA4DCmEixNTU0042OxWObMmRMdHW0ymcLCwgYMGPD8889HRkYSQk6fPi1L6C38LgAAAJ1BpBIsZrO5bdu25JdruEOHDjU3N9P/uvXWW7///vuSkpKDBw/Gx8e7P7eoqGjOnDl9+/aNi4sbOXLk+vXr2Rkt3Iza9PT0xMTE06dP0/+dN29eXFzc6tWrZ8yYMW/ePHpnQUHBwIED6RQqjzOqhNfcvXs399vXrVtXV1fHHh47ezchIWHJkiXFxcW+Z1Y6HA6r1Uof8Pe//539r+Li4mHDhsXFxQ0bNqy4uJje2dzcvGPHjjFjxvTs2bNnz54pKSlr1qy5dOmS8Czhr0hKStq7d+/YsWPpwWRmZg4aNGjz5s30Yf/3f/8nTI7zNleurq5u8+bN48ePj4+Pp1OelyxZUl5ezh3/wYMHp02bRk9Lz549R44cuXz5cvaQWnX8+PFbb701Li5uxIgR//vf/9j/2r17d8+ePVudxyfyzAszVbds2bJ48eL4+Pj4+Pi5c+fSo7106dLy5ctvv/12+piEhITp06cfPHhQmOLNntuSkpLly5fTw6a/sbKy0uOxXblyRXjL4uPjH3jggUOHDok/OUVFRdOnT6eH+sADDwjHE+BJ49703bt3Dxw4UJieQhuLMDO9qKho7ty5N998M33KsGHD3D8J7oSz/emnn3JnoLCwkP0kx8fHT58+vaioiHuF8vLyJUuW0En3CQkJHmfc19XVrVu3LiUlhf7Jffv2nTBhwo4dO4RehfjZij2iKwCEz/nNN9/81FNPsQe8b9++Pn36xMXFTZ48uaamRri/oaFhzpw59Le/++679E7aah544AHasm6//faXXnqpoqLC49nz+Fl1F+zz4N5LCNPGk5KSzpw5w73Fwgf122+/9dbzBHIqHnnkkZkzZ9I+Z9u2bezj8/Pz6Xsxfvz4Cxcu0DvpZ1hYwCHyM6x9iFSCpUOHDomJifT2kSNHpk2bNnjw4FmzZm3cuNFbX0999tlnEydO3Lt37+XLlwkhZ86csVqtmZmZTU1NChz21q1bud+emZn55z//WfjtjY2NGRkZVquVzt6tra3dtGnTlClTvvvuOx8vazKZRo8eHR4eTgjZv38/28d9+eWXNHV12223xcbGkl9mIi9YsODEiRMOh8PhcJw6derll1+ePn26e5M7f/78okWLaGcaHR192223+fX31tTUPP744+np6T/88APt7Kqrqzdt2vSb3/zmm2++ER62c+fOWbNmHTp0iJ4Wh8Nx5syZN954Y8GCBeLnOvTs2fP2228nhJw9e3b//v3C/U1NTdu2baP93dixYy0Wi8enSzjzy5Yt+/DDD5ubmyMjIydOnHjNNdfU1NQ8+eSTb7zxhjCYV1tbe/DgwVmzZu3Zs4d7+sWLF+fOnfvGG29UVVUJv3HGjBkeO77nn39eeMuam5u/+uqrmTNnilwQtH379smTJx88eLC5uZk+96GHHlq7dq3D4QjwpIn3ySefTJw4cc+ePdXV1fSeH3/8cdOmTZMmTfr+++/FvEJmZuZTTz3FnoG0tLQZM2awdx48eHDmzJnsd//evXvHjx+/adMmOixaW1u7Z8+eqVOn0j+fPqaxsfHFF1/MzMw8deoUvfPy5cvHjh176qmn3nrrLfcjabUVe1RTUzNnzpw5c+YIn/Pq6urt27dPmDDhzTffpL83ISGhZ8+ehJDi4mL2r7DZbDSh1r179zvuuIMe87Jlyx588MGvvvqKtqxz586tXbv23nvv9Zh6c/+suj9GmfPgTUNDw7PPPst9yD02HPfDlnwq7r///rFjxxJCHA7H7t27hSOnP9Ir2DFjxlx77bWEkG+++eahhx7as2ePMMROP8OPPvoo7TRCFyKVYDGZTIsWLRo5cqRwT21tbX5+/tKlS4cPHz527NgvvvjCY9m9mpqa8ePHf/XVV8XFxU8//bTJZCKEfPrpp6WlpR5/0YoVKwoKCnr06EF/XLNmTUlJyYIFCzZs2LBmzRp6Z2Ji4tGjR48cOZKQkOD7sLdv305/+/HjxxcvXuz+2zdt2rRx40ZCSMeOHf/1r38VFxfv2bMnLi6ODT48GjRo0IABAwghhYWFQvusq6vbu3cvISQ8PHzSpElms9nhcKxZs4bORB43btyBAwe+++67BQsWmEymH3744eWXX+YWTF2+fDkiIuL9998vKSn55JNPxowZc+TIkUmTJtH//f3vf19SUrJhwwaP32RNTU3Lly+ns3Z+85vfsH91VVXViy++SP+oysrKV1555fLly7Gxsbt27Tp58uR7771HZxcdOnTo2LFjvv9wgdlsHj16ND2lubm5DQ0N9P6zZ89+/fXX9JQOHz7c29MlnPmqqqqnn366uLj422+/vffeewkhW7Zsyc/PJ4QsWrTo+PHjR48evf/+++lp/PDDD7kevKampry8/KWXXjp+/Pj+/fuHDRtGCDl58mRmZqb7hemlS5foI7/66qsRI0bQ13zvvfeEP9OHY8eO3X///d98881333339NNPR0RENDc3v/rqq4WFhQGeNM7o0aOPHj0qXELQxrJixYqampq1a9devny5c+fOW7ZsOXny5NGjR6dOnUoIqaysfOONN8R8t1VVVT333HPHjx/fs2cPjbmrqqr++9//zp49++jRo/v377/55pvpCwoz2EpLS//4xz/W1NRERUX985//LC4u3rFjR2xsbHNz8+rVqw8ePEgf9sUXX+Tk5BBC7r///qNHjx4/fnzRokWEEIfD8fHHHwuhlaDVVuyObQvDhg3bt29fcXHxunXroqOjm5ub//rXv9LpF9dee+2YMWMIIXa7ffv27cLTDxw4QMPZO++8Mzo6mhCybdu2f/3rXw6HY9CgQXv27CkuLl62bFlERERlZaXVav3pp5/czx73WXWnwHnwoaKioqCggH7IDxw4wH3IExISvPU8AZ6KO+64o3v37oSQL7/8UjjyH3/8kQ4NduzYcdy4cYSQurq6v//971VVVVFRUe+9997Jkyd37dpFP4dFRUXCZylEIVIJoqioqDfeeCMjI6Nz587cfxUVFc2cOVO4UmH17t176dKlHTp0CAsLmzJlSkxMDCGkqqqqrKxMgWMWfjsNHa6//nr2t9vt9h07dtBjXrBgQUpKSlhYWGxs7PPPP9/qRW1UVNR9991HCGlsbNy9ezd9kRMnThw+fJgQ0rNnTxpFnTt3jvaAnTt3Tk9P79SpU5s2bR577LFRo0YRQvbt23f06FHuladNm3bLLbdI+GNLS0s//fRTQkj37t0XLVpE/+qZM2cOHDiQMBHVkSNHaFpq3Lhx8fHxJpPppptu6t+/PyGkvr7evX/0ITExkeb7jhw5YrPZ6J3ffPMNveIZPnw4vWB1J+3MDxw4cMaMGXR6NX0R+n3TrVu3++67Lzw83GKx0G6OEHLhwoX6+nruFaZPnz5t2rTw8PDu3bsvW7aMfh4KCgrchxmER3bo0OGRRx6h3wqlpaViEmSDBw9++umnr7nmmjZt2syZM+euu+4ihNTU1NCxdMknTby6ujo6sNfc3FxXV3flyhWLxfL4449369aNuH5D+JCYmPjggw+Gh4fHxsbSoIQQEh8fP3/+fIvF0r1795SUFHqnMKC1a9cu+lfMmDHj7rvvDgsL69ev3x//+Mfw8HC73b5hw4ampiaHw7F9+/bGxsbIyMjp06dbLJbw8PDk5GQaK1+4cME9FvTdij06cuQIjZ+uv/76ZcuW9ejRIywsbNSoUUuXLg0PD798+fI//vEP+p06bty4jh070tNCh4eFz1V4eDgNK+12+wcffOBwOCIjI59++unY2NiwsLCpU6dOnz6dEHL06FEaLrO4z6o7Zc6Db8KHvFOnTjNmzKB3+v6QB34qoqOj77zzTkLIjz/++OWXX9I7hU5p0KBB9DtC6EtHjRo1ZMgQk8kUHx8vfA5DfS0SIpXgatOmzezZs//zn//s2rVryZIlgwYNEj5/Dofj1VdfdQ91e/Xq1aFDB+HpXbp0oQ9mE7HBw/72a665hg7VCL/90qVLdEJMhw4dhg4dKjyrT58+N910U6svnpycTLv+goIC+sWwZ88eOiQgDGCePHmS9t1xcXFCSZg2bdrQ8Ri73f7DDz9wLzt48GBpf+yJEyfoYfTp00eIJtu1a7dly5aSkpLjx4/TIbHRo0efPHmSjlR98803a9aseeihhw4cOCDhN3bq1Gn06NGEkKqqKvoKTU1Nu3btcjgcJpPp7rvvNps9L8eTduZ79uzZrl074UeLxbJhw4aSkpL8/PyIiIiPP/44PT198eLF3p5uMpmSkpJozEEI6dGjBz3VdrudTY1RgwcPFh553XXX0fiJftH6OCHUbbfdJqyACw8Pp/0yIeTkyZO1tbWST5p4wqyyqqqqGTNm0ETtl19++eGHH/qYT8YZMGBAmzZt6G365UEIuemmm6677jrht9AbFy9ebGhoaGho+O9//0vvueWWW4SzFxsbS59SXFx86dIlk8n0l7/8paSk5Pvvv+/Zs2dubu4LL7wwd+5cH2NpvluxR4cOHaJ5zGHDhgkHT5hAsKSk5MSJE4SQnj170kGs0tJSGrAeP368sLCQnoFBgwYRQs6ePUsf3KlTp169etGXMplM9PPjcDjoeBiL+6y6U+Y8+MZ+yKOjo+mH1veHPPBTYTKZJkyYQBdh7N27t66uTkh9mkym++677+qrryaE0EGdkpKSv/3tbyUlJevXr58xY8ZHH30k7S/VGqxSVkJYWBidHjVv3rzGxsZt27ZlZmbW1NTQaxFu7DoyMjLwnlcy37+9qqqKXj1YLBah/6XPYn/05vrrrx86dOi2bduKi4sLCgruuOMOOtosDGASQurr62l+h84Cdn8R2uzZX+27g/Ph1KlT9Eb79u1pa/fI4XAcOnRo2bJlR48eDXyfrJSUlPXr19vt9r179z7wwANlZWU0Wr3++ut9hFzSznzXrl25ey5duvTaa6+9++67YqbXcL/LbDbT7pIQ4l60MJCZItxzhR+F7wBpJ028a6+9dsGCBYsWLaITGmiill7s9u7d22q1CgkjkX+F0Iiuuuoq4btN8PPPP9MT+PPPP9N7hMnvrB9//LGqquraa6+tq6vbtGnTa6+9xs3B9EZCHyI0q969e7MHHBER0b59e8IMH5rN5rvvvvuTTz5pbGzcvHnziBEjcnNz6cfpvvvuo1/e9fX1dITj9OnTHk/d6dOnGxoa2Ebn/ll1p8B58E3Ch1yWU9G3b99+/fodPnz466+//v777zt16kRj3Pj4ePY1i4qKli1blp+fr8xlrZIwphIsS5cupbOvrVYr+/VGxyHnzp1Lf2x1eoeemM3mSZMmhYeH0+lg33zzDb0m69+//w033CDyRbgzFh4eLnx9BsmePXtmzZpFM0EJCQlLly7dsWMHnbQhwU033TRkyBBCyOHDh0+cOHHw4EE6riMk+GXEdax2u33BggVvvPGG3W63WCyTJk3KyspavXq1vL80GBQ4aePGjdu6deuvf/3riIgI9v6ioqLU1FR2Mq9iGhoa6uvrm5qa/vznP2dmZlZUVERERIwbN+7VV19dv369v3WYZCTk477++uvCwkI61cyvCUNCrCZoNQjQ4HmQhZhTIaTO7Xb7/v379+/ff/bsWUJIYmKicC1RWFj40EMP7du3r7m5OTY29vHHH9+1a9dvfvMbRf6IoMOYSrAMHz6czn/cvXv37Nmz6cwmyuFwhGj5k3bt2lkslpqamosXL54/f17ImNTX1wul53wbMmTIgAEDDh8+fPTo0bCwsMbGRpPJNHnyZGHYPCwszGQyORyOxMTENWvWBL6mw4cbb7yR3jhz5gz98nZ/TENDw3vvvUcvtdPT0x977DGahr/qKolRfps2bX79619//vnnNTU127ZtowsowsPDU1JS3C++BYGfeULIN998Q2fhxcbG0smShBAfy3NqamrKysqEWdhNTU3CRBZ5vx7Onz/P/iiM9/zqV7+i68WknTR/9e7de+3atY2NjaWlpXl5eZ988gldZnz58uWPP/6YzpSSkclkEq7416xZQzNc7oqLi+lsqqioqOzsbDrzQPYdW4TERFFREU0r0B8vX7588eJF4jp42alTp7FjxxYVFZ05c2br1q108tDtt98uTBgKCwujf1qPHj3ef/9994l6EgizyoJ6HmQn16lISUl58803y8vLv/zySzoAY7FY7r33XuGdysnJoZOaJ0+e/NJLL9GGI7mb0hqd/BkadMstt9AJ22fOnJk/f35BQQENnC9cuPD6669nZWXRh3lMcMjuypUrsrzOtddeS7/da2pq6Owt6rvvvhO5kjMqKor2+KdOnaJbY9xwww3sxItevXrRiW8lJSXCcu7KykpaMWXgwIFfffWV+AP2vWSjV69e9IqE/V1c6ZeGhgahVgGdTksIuXDhgpA5kiAlJYV+NjZu3EhDB2FCsTeBn3lCyE8//UQ/hF26dKFD+oQQ9xknrI8//li44Dt79iwdWLJYLH379hX5S8UQ5mYSQpqamnJzc+ntAQMGCKPiEk5aq4Q/bdu2bUJploaGht69e8+bN2/Lli0LFy7kHimjtm3b0oEiQshXX30ljLyuX7+efvwWLlzY1NR06dIlGiC2b9+engFCyMmTJ+Udjr311ltppH7w4EFh2jIh5MCBAydPniSE9OvXj33TR40aZbFYHA5HdnZ2fX29yWS69957hcCrR48edLJLZWWlkFeqq6tLTU31WBpEDGXOg1yEnkeuU9GtWzf6aTl06BDNSw4YMKBPnz7CrxOuWHr27EnDlOrqavre6QAilWCJjo6eOXMm/WIrKiqaMWMGrdIzdOjQv/zlL/QavXfv3t4upGTRpUsXeu1rs9kqKyvtdruYJaM+WCyWKVOm0D9q9erVdKSxsLDw2WefFV9WRFg7QCUlJbF52ejoaLr0o6KiIiMjo7y8vLGxcePGjXSie2Jiopipu8IFYmFhYUNDQ3V1tcfEbWxsLF1yWVFRsXTp0vLy8ubm5ry8vB07dhBCOnXqNH78+KuvvppO9SWEfPTRR5cuXaqsrFy+fDkdfZVG6HRqamroJ0GYUOyNLGeeLoIghHz33XdfffVVU1PTzp073377bR9P2blz5z//+c+6urrKysqXX36ZVlIR+S6IR/PrNJBav379rl27yC/nX3iMhJPmkcVioaEwIeTo0aNNTU3V1dUjR46k1wwHDhyg2TFCyOnTp+lXAp1ZLMPf6Wb8+PF02vg777yzadOm5ubmkpIS+o5ERERMmTLFbDZfc801NL957tw5WlHj8OHDK1eulPdIBg4cSP/GM2fOLF269PTp083Nzfv371+2bFljY2NERMScOXPYgTQhH0fFx8fTubRUVFTUpEmTTCZTfX39Cy+8cOzYsebm5s8++4yGmH369BEz74ejzHkIkHvP86tf/UqWUyGkzoV72DJCZrNZSAN99tln5eXldrv9lVdecV8pGaIQqQSLyWRKS0t79NFHvY1OR0dHr1ixQug0g6Fr1650rU1FRcWdd945cODAwNPt995777Rp0wghVVVVaWlp8fHxEydObGxsFP+HCLW8iNsAJnGtQ5Ofnz9q1Kg+ffqsXLmSFgHLyMgQ8kQ+9OvXjzbpTz/9tF+/fhMnTqTjohyz2fzMM8/QDvrgwYOjRo2Kj49/9NFHq6qqIiIirFZr7969r7766unTp9O5Czt27Bg8ePDw4cM/+eQTYXKM+1qkVnGdjsViEZNZCPzMDx48mHaLNTU1aWlpvXv3fvzxx+vr6+mRnD592n2x5YABA1atWtW/f3/6VxNCxL8L4g0aNOijjz665ZZb+vTp86c//YnWyKHnX3iMtJPmkTCQ+cYbb/Tu3Xv+/Pnh4eEvvvhidHS0w+H4xz/+MXDgQFqTlM7bnTZtGq2+JTs6XTciIqK2tnbp0qXx8fF0oZnJZFq8eDFtBUI83djY+Pzzz/fu3Xvy5Mlnz56lp+Knn34KJGgWhIeH//GPf6S/8eDBg0lJSfHx8bNnzy4rK4uIiHj22We5M9CmTZvJkycLLXfs2LHCSj1q6tSp9ONaVFQ0YcKE+Pj43/72t5cvX+7YseNLL73EPVgMZc5DgDz2PHKdCpo6p7fZRe/U5MmT6RXg4cOHR40aNXDgwOzs7IiICOFqOfDVACpCpBJE4eHhS5cu/eCDD+655x4h4I2IiOjXr9/SpUu3b98ufOyCpFOnTitWrLjlllvo0ujrrrtOWGsgWXh4+B/+8IeMjAz6BdmxY8f/9//+38aNG8VPiTWbzUJ0wg5gCmgdmhUrVtDdFoXfkpOTI4z6+jZy5MjMzEx6hGFhYddcc423iUG04hb7u9q1a3fPPfds3bpVWI505513vvXWW3379qU7N/Xt23f16tXr1q2jFzR79uxxr93UKqHWp7eT4C7wM2+xWFavXp2amkpX5LZr127q1Km7d++mX0JnzpwRyswLnnjiiVdffZXOsmrbtu3UqVM3bNgg8l0Qb/78+atWrRI21xw2bNjGjRuF8y+QcNI8euCBB5566inarUdERISHhzc2Ng4YMGD79u0LFiy48cYb6Yezbdu2w4YNW7t27Ysvvshey8pr3LhxH3/88eTJk+kskLCwsFtuueXf//733Llz6WGYzebnnntu6dKl9IDbtm1755137tixY/78+YQQukWALF9CnTp1ysrKWrt27a233kpDc6EtzJo1y/2Ka+jQofSzFxUVJSwsF9Dgj301+vn58MMPpS3XUuw8BMJjzyPXqYiKiqLjzYSQxMREbi75gAED3n333WHDhtGpfjfeeGNGRsZHH31ED4ZL6oUck4pvrd1uf+KJJ+i3KXv/hQsXHn74YfdL1UmTJnGPBI2w2+3z5s2j33M+5gaCgD1jVqt11qxZgb+OXGe+oqLigQceoOVbNPVuynXSACC0qLb2p7m5+e23387Pz6fFvFnnzp07f/5827ZthaI9FPcjaAet7EkIsVgsEsZ1Dai0tJTu1+PX2k53hjrzcp00AAgt6kQqdXV1K1eufOuttzyO6Jw/f/7ixYvPPvvso48+qvyxgW/p6em0xnnHjh3Xrl07aNCghoaGjz76iK5AoTuFqn2M2kVXBPz8889r1qyhaxYSExNFnjHDnvlAThoA6IAKkUpRUdEzzzxz9OjRfv36lZSUuD/g+PHjhBD0RNo0duzY7du3X758uaqqihsPa9u27fz580O9EFNQHTt27OGHHxbWVXbs2PHRRx8VOQfCsGc+kJMGADqg9Ixau91utVoLCwsXLVqUmZnp3t04HI6ioqKOHTvKXq8TZDF69OitW7fec889nTt3Zvd5mTx58kcffaSdOQ3a1LVrV1r6KSIi4tZbb/3nP/8pfkqdYc98ICcNAHRA6Rm1drt91apVU6ZM6d2797fffvvwww/fdddd7DxZu90+Z86cysrKMWPGbNu27cyZM23btp0wYcKCBQtkX3EAAAAAGqf0mIrFYnn22WfZMgmcCxcunD59urS09J133unfv//UqVM7d+68adOmSZMm0fqYAAAAYBya2/enuro6LCxsxIgRq1atoot9mpub16xZs2LFiuXLl3vbCKagoIBuBw8AAAChaPjw4R6L9mqu8ltCQsLnn3/+9ttvC2uSw8LCHn744cGDBxcWFnrbxeDAgQPuRatAmpycnLKyMrWPQg/KyspycnLUPgqdKCgoQBuXC9q4XNDGZeRjxEFzYyoeRUVFxcbGHj58WNjGzF1iYqKwnRgEIicnZ+HChZjRHDja8PCxlBFOpizQxuWCNq4MzY2pEEK8baRHa5krfzwAAACgFs1FKitWrBg4cGBWVhZ7Z2VlZWFhIZYuAwAAGI3mIpWUlBSLxZKTk1NaWkrvoQVti4qKxowZQ3dKAwAAAIPQ3DyVIUOGPPnkk8uXLx83btwdd9xxzTXX5OfnV1RUDBs2bOHChWaz5g4YAAAAgkdzX/wmk2nu3Ll9+vR59dVXc3Nzm5ubr7/++qVLlz744IMe1ycDAACAjqkZqSQkJHgs5mYymZKSkpKSkpQ/JCCErFy5smvXrmofhR4MwjnZPAAAIABJREFUHjx45cqVah+FTtx99934WMoFbVwuaOPK0Nw8FVBdly5d1D4E/cDJlAu+WWWEj6WMcDIVgEgFAAAAtAuRCgAAAGgXIhUAAADQLkQqAAAAoF2IVAAAAEC7EKkAAACAdmmu8hsAAGWzkbw8MngweeUV0tRkaWxsatOGLFlC3nuPZGSofXAAoBREKgCgITQ62bev5QbDTPur7GxCCLFaSUwMSU4mSUkkNVX5wwQA5SBSMYTsbLJvHyGE2GwkI4MkJ6t8PADubDaybh2xWv14fHY2yc4mmZkkNRWjLKBReXkkM5PExJCYGHLjjQispUCkYgjr1jkvT2fPVvNIANz5G6O4P91qbfmHeAW0Zt8+Z/ebnIxIRQpEKoYQE+O8feqUaocB4C4z01eMQlM8hJC6uvrwcLPZbLbbyQcfeH4w4hUAXUKkYjg2m9pHAEAI8T6UIkxAEcIUQsjFi/WEkPbt27PPpQkgjtVK8vJIbm7QjhvAH2yXi8y7NIhUDIEdUwHQgrw8kpbGx800NMnIaP0TGxPTMnCSkeEh3MnLI7GxJCsLXwygPlwcBg71VAzhxhudt9FsQF02G8nMJCkpLh9FGnnk5pKsLP8Ca/rE0lI+WLHZSEqKhxEXABWxXTGIh0jFcBCpgIo8ZnxotEEXHksjBDqctDSSkiLxNQFkwUXkIAEiFUNgmwciFVALHU3hwpTkZJKbK8+CiORkUlrKZ3zy8hCsgJrQ5QYOkYohIJAH1dlsJC3NJR0TE0OsVpKbK+fnMyamJYXEQrACanGfiQUSIFIxBK55IMYHhdEwha05GxNDsrKCtZw4NZXPBCFYAS1ApCINIhUjQqQCSqKTW7kwJTc3uAtzaFKJRRcEASgJk1RkgUjFKDBVBVRBR1O4/lrejI83dNoKdzAYWQEIOYhUjALhPKiC3cmBKBimCL+OC1ZoHRcAZWBMRRaIVIwCBfVBedxKH4XDFOGXcsEK3dcQQAHobGWBSMWIkP0BBeTl8WGKv1Xd5EIjJBY3vRdAARhTkQyRilGgkYCS3GeEpKaqWdvefYItN8kXIBi41CdIg0jFKFBQHxTjHqZoYX/j5GS+6BwmrACEBEQqRoRIBYIqM9PlM5aaqn6YQmVkuIzrYCkQKAmb/kiGSMUosEoZlMHNV6XTU7SDq+OSl4ccEAQR1v7IApGKUaCRgAJo9RSB+1RWLeAiJ25XZwAZ4aMlC0QqRoGC+hBsXJhCCMnI0GKI7HEpEIDssOmPXBCpAIA8uCJvqany7JAcDMnJfA4oM1O1gwGDQKQiGSIVA8FUFQgem81D9RQt42rQWa2YsAIywyQVuSBSMShEKiAj9+kpGg9TKO4gMawC8kI3KxdEKgaCoB6ChFtBo26RN/G4CivIAYG82FL66H4DgUjFQLD1DwSD+4CKRqqniMFVWLFacR0MQYFIJRCIVAwK3THIJRTzPiwursI6IJAL5qnIBZGKgaCpgOy4vA+3piYkJCe7rFFCLTiQCy4I5YJIxUCw9Q/IK0Qn0rrjNnnGsArIDqX0A4FIxaAQqUDg1q1z+SCF0PQUd+zB22yYWgsyQPZHLohUDAT1VEBGXAEVLocScrj1SiivAoFDNysXRCoGgoL6IKPQXe/jDcqrgIxQSl9GiFQMBE0F5KKDibTuuHk2mFoLMkL3GwhEKsaCBBDIgh1vCN2JtO5SU13aCIZVQDJMUpERIhXjQqQC0mRnuww26CDvw2L/nLw8kp2t2pEAAIVIxVgQ2kOAuHUxMTGhPZHWHTe1FsMqIA3GVGSESMVYUFAfApSX59IF6ybvw+JWLGNYBSRABysjRCrGhewP+Isr9aaPibTuuL8LheBAAoypyAiRirGgwUAg1q1z+VFnM1RY2AwIAoRIRUaIVIwFBfUhEGypN24+h85wwypIAEEgUEo/QIhUjAuRCviFK/U2e7Z6h6IIbgoOhlXALxhTkREiFWNBPRWQhptYqtcZKixuWVN2NpoM+AGfFhkhUjEWhPYgDbcyWcczVFiorw/SoJS+vBCpGAu2/gEJ3AdUjNPzYlgFAmec9hIkiFQAoBXGHFChMKwCEmCSirwQqRgO22ywARu0ysgDKhSGVQDUhUgFAHzhBlR0v+THHTeGhGEVaBXGVOSFSMVw2CUbqPcMvhlwyY8790VAAL6ha5UXIhVDwzg2+MbmB405oEJhWAUkw5hK4BCpGA6aDYhkkF1+xOCGVdhavQDukP2RFyIVw0FBfRAJAyosblgFOSDwAV2rvBCpGBqaE3hjs7nsRzh0qHEHVChuWAXF9UEkbPoTOEQqhoOC+iBGXp7LmMoTT6h2JNrBjSphWAW8QfZHXohUDAfNBsRgB1SMPEOFxZ0H9hQBsHARKC9EKoaDgvrQKm5ARYWitHR5dFoaSUkhJhMxmdp36NC+QwfFj4PHDqtwZwmA4jpVRPmBM6t9AKAg2oAwqAKt4aq9KdfV0tkxGg4BUlNJZqbzq2jdOnwPAQQdxlSMITaWmEwkNpbExpLsbBTUBx9sNjUGVGw2kplJUlKI1arxDyV7QlBcH9xhkorsEKkYAwrTgmjcgAq74CUoaIwSG0us1pD42k9Ndfn6QRU44CBSkR0iFeOx2RC3gDfu5fOD/vvoOIo7mnayWkluLikttX/77cXDh4N8NGJhz0LwAZ2q7BCpGIP3wB6dLLC4am/BTf3QoRT3j2BqKo1OSG4uycig2zc3RUdr5/qUOy1YBATeaOYzG9oQqRiDa2FaNB7wiOZhBMnJQe5nuaEUmmrKzSVZWdqfp4ri+uANF+5D4BCpGI/NhoL64JHN5vJ5CHr5fIfDeTsmRv4Yhc4iD878XFSBAzFQoFYWakYqdrt99uzZ6enp7v9VXl6+YMGCvn37xsXFjRw5cv369Y2NjcofoX54L0yLSAUE3ICKEuMaDgeJiSFWKyktlfny02Qi5Jd5MEEIVlAFDrzBjFrZqRapNDc3v/322/n5+e7/9f3330+aNGnnzp1DhgyZNGlSU1OT1WrNyMhAsCIXFNQHd+osTiaEZGUF/ZcFJ1hBFTjwCJ2q7NSJVOrq6l5++eUVK1Y42OFfQgghjY2Nr732WnV19apVqzZs2LBixYrPPvts5MiRmzdvLigoUOVo9cD16jiG2Ngf0a6AqFjtLRi/yWYjY8a43BOEYIVbroxhFSBu3SnGVGShQqRSVFQ0Y8aMt956q1+/fpGRkdz/lpSUFBQUJCYmJv/Sf0VFRS1cuDAiImLr1q3ukQ1IgMYDHG5xctBrqARbTAzZtYuPgYITrAgwVQXcobOVhdKRit1ut1qthYWFixYtyszMDA8P5x5w7NixqqqqoUOHtmnTRrgzNjY2Ojr6u+++++mnn5Q9Xh1xTfkgAQQsbrVC0OfSKiM3N9jBCpe2QrACmKQSDCqMqQwYMGDHjh1PPvlkRESE+/+eO3eOENK3b1/2zoiIiPbt21dXV9vtdoWOUt8wqRZcsZmLmBgd9bC5ufwAkdzBCvvyqFcL6E6DQelIxWKxPPvss7179/b2gFOeyvu1bdu2a9eudru9uro6mEena65fPuxPqKhocOrvnBxUWVl8wZO0NBlfnh1/4mYlgwGx3al+In61aW4vZY8LfEwm01VXtRJU5eTkuE+5feaZZ7p06SLbwYWyDl26CHOC7IWFXbrUE9Jyx7Fj9WfPOtNqFRUVJpMpLCxM8WPUm4aGhqqqKrNZc62M84c/dBK6gujopj59Ks+eVfeIPLh06RIhpK6uTsqT583rsHNnpNA/2GxNo0ZVbtoky4H16UOiozuVlbWcwNdfr+/TR+tJarRxubi38ZqaKEIs9HaXLi5dKwjOnz+/fPly7s7y8vLJkyd7fLzm+lD3mSuEEIfDceXKFd9PHD58eGJiIndnr169ZDuyEGdmTmzk+fNssB8ebo6KihJ+tFgsFotF+9+v2mc2mxsaGthzq0E2G8nPd77XGRlEmwfc3NxMiPRja/rsM3LvvcKIhzk/v9PUqfWffCLLsT33XNP8+S3ncOPGyOefj9L4xTTauFzc2/j5885lIr16mbXZmlQXFRU1ZcoU7s4PPvjA2+M190m90VNJv9ra2nPnzlkslnbt2nl7YnR0tLdwDAghhAnazGZz377O5lRWZrZYLMKPv/rVr9CLycJsNtfX17PnVoMqK523Y2LInDlm4YpQU5qamgghAZ3MrCySkiLMIzDn51v++ldZcl2PPUbmz3f+eOiQZcCAwF81iNDG5eLexsvKnP8bHm62MPExsVp1l1uVzv37uow9d640V02fRionTpxg77x8+fLFixfbtWun8U5f07yX0McUMMOy2cgLLzh/lK2yiTYna9CC/SyrVa5DZb+AHnlElpeEkMR2p0lJrv+H0vpSaS5S6dWr13XXXVdQUMAmpE+ePGmz2fr379+hQwcVjy3kORwt/3JzsUoZiNsMUHkWJ9tsJC2NmEwt9ew1xT1YkWl2LRfkaTNUAwXw3SlWLctBc5FKdHT04MGDCwoKdu/eTeu81dTUrF69+sqVKxMnTjRpsO8LFa5rNdFkgARpo5/MTGfvrMEGm5zsEqzIFKdjGyAgHgvU4kJQDpqLVNq0afP4449HRUUtXrz4oYceSk9Pv+uuu/Lz8ydNmuQ+YRYk4yIVtCYDCsqASna2S/kz5Wry+4MNK+Qre82ewOxstCng9y3BBaJkmotUCCGDBw/etGlTUlLS119/vXnzZrPZbLVaPRa0BbmgVzUgri6tDBX0ad6HfdGsrIBfNDiysloyofLhTiASQAbUSqoHkYpUas79TkhIOHLkiMf/io2NXbt2rcLHYzQxMc52hUjFgNgMhQxjH1yYQgjJyNBu1xycA0tNdY4opaWF/vZJECBMUpGJFsdUQBloOEbG1aWVJ/XDvmJqqgG/qLnTiGEVo9m3z3kbHayMEKkYFwrqGxk7lzYmJuAxFZuNxMa6vKJm8z7BlJzs0qwwr9boMKYiE0QqQAiyPwbDzaWVYewjVKanBB9bWAVbKxsN25EmJ+MSUDaIVIwLIb5hcXNpAy2bmZ3t8oqyLXcOSVzYh2DFUFBMJUgQqRgXWy8RCXVDYbMSgfafNhufSTLwgArFBitIABnWjTciUpENIhXjQplaY+JSP4EOqLB13ghBmEJca6jn5aFxGQgikyBBpGJcaEjGJOdcWpuNr/Nm4LyPIDXVpXGxJxx0zGbzmf3hNwECPyBSMS6UqTUgLrQIaC5tCNV5Uxx7YjFVxZgQtMsIkQqAgXDxaECXee4riDBM9wsup4ZgxQg8pH5w/ScTRCqGxn6zYFKtEci5JSE3oBLohBe9Yc8tWxAMjMLDdoUgESIVQ0PbMRSZtyQsLXXum8PuTqwnAcwxwYaFRsOPqcTEuOwthd42AIhUDCY2lphMLf/y8lCm1lDk35KQEOJw8JVZ9YG2EatVcoiBDQuNxmsXKvdemAaESMXAXLtgXPPpnpxlVFg6G1Cx2YjJ5PwxgGEVFFYxFL5ALcgHkYrBuI6i6O9KGLyRuYyKjnHDTVwFXn+gsIqh4P0NHkQqBuNa7o0tU4tmpm/cgAqu+XzhlltLHQ9BYRXDYrtWCBwiFWiBPLq+cTvzQCusVuftAIZV2FONtcr6hgK1wYNIxWBcGxCak0Hk5cm66scIMjJkGQ/hTjWuB3QMw9LBg0jFYFzzPdy1NVqaXiH1IwU7l4eL9UTj1kVhXq1eoXhKUCFSMTAEJsYgZwV9Q5Fpmgkb8CABpFeIVIIKkYrBuG2gjDK1uselz7Hqxw9yDKtwoSGCFd1DmCI7RCoGg20JjYfbPBn8INOwCirr6x6m0wYVIhWDcWtDbB+KMrX6gzIqgZJjWAWV9XUPnWdQIVIxHrcEkJefQA+4CvqYS+s3OYZVUFlf9zCmElSIVIzNZkOj0rdgVdA3FLlnqyABpD+IVIIKkYrxuDYjlKnVMXlSPykpLvvgGJAcwypsZX0kgPQNBWplh0jFeLxv/YPeU2dkSP0IQwh0b2HDCnhYhYt2kADSGYypBBUiFWPDPBVdY1M/EmeoYOEQxQYaDoe0s8k+CSXgdAadZ1AhUjEe1+8blKnVKy71I6WCPhYOsTIyiMNBHA7JL4CtlfXKQ9k3mjOl/7A1ZcAQqRgPZqYYgwwV9NPSXF7C4NVtA/7zsbWyXnGpH37wEfNWAoZIxXhSU1suDR0OkptLUKZWpwLdPJkbUDF4mCITbK1sFJi3IitEKoB2pEMybJ7MzVAxeOpHJthaWZfYZect3SmGq2WFSAVcIhVUetAHruv0e0yF29UQBeNkgq2VjQjXggFDpAJoRzoUaN6GW98sZUwGPGPfDiSA9IHPtGJjZbkhUgFMsdWbQFM/Npsc03HBMy6NhgSQDmGSitwQqYALRCo6wIUZfneVXKSDGSpyQwJIZ9huk12LDnJBpAI+tiyE0MPNMJGS+uEKxmFARW5s7IcEkA7w3aaHGbYQEEQqgOJvusK9fX5f4WFAJfiwtbKeYFKKAhCpAOhKoDNM/vSnwJ4PoiABpBvl5Wb2x5gY1+AFLUgOiFSAENd+88CBSNWOAwITaOrHZiN79jh/xIBK0CABpEsophIkiFSAEIxY6kWgqR9uQAZ1aYMGCSDdKChoI9z20JGilL4cEKkAIa4NrKwsXLXjgMAEOheWbsInPB+CCVsr6xZWKcsNkQrwysrMrT8ItEe2urJ0TyhUexOPbpnrZxaHPcFIAIUutsNsaXTI/sgNkQoQ4pom4CaIQagINPXDwZiKGCkpxGRque3nwAgSQPrAd5hYCxQEiFSAhzGVEIUyKCpgB0a4Bd4iIAGkA2yHmZTklvpBpCIHRCpACD9PBZFK6MGWgupITQ1kwTESQDqADlMBiFSAkOxsLu5H2ws5Mqd+QDxuwbE/cxS4BBCClZDDdZUxMYQkJ7fM9HI4SGmpSselN4hUjCotrWUaoMlETp3CCGWo++c/nbeR+lFUYPNN2HeKLcIOoQgdaZAgUoGW63G2jWFyX2ix2cj77zt/RME2pbHBSlqaX09FCbiQxo6pIEwJHkQqRoVWpSNYFKkybkW3P5E+N/qFi4TQgsopykCkYlRs5USbjbj2mKdOKXw0EBCs+lEZd9L9nFeLFUChC12lMhCpgIdLclyjhxCs+tGErCznbT/n1WIFUOjCXoTKQKRiVOxIpc1GsFokZGHVjyZwQ//+ZHFQAi504aJOGYhUjIqL/10bHPrKEILUj1YEMK82gJosoBXYizB4EKlAC7dBFggNbFiJMEVNAcyrxQqgEMW+yZhRGzyIVAzMdV0y18wQrISEvDyXdwqpHzUlJ0seG0ECKBRhhx/FIFKBFmhmoYitFRYT48+Yis3m3FoP5BLA2AgSQKEOXWjwIFIxMLd1ySj+FnLYt4m7Lhf1TFqkGOQSQHl8JIBCDoqpKAaRChBCkOwJSdzevf6lftjL9pQUmY4IXIMVJIB0DZGKYhCpGJhb20Lxt9ASUOqH/SZE+X0Z0YCRblCXm+vXU5EACi3oJBWDSMXA3MrUsjDIon3SUz+Zmc7b/sU40JrUVOJwSHsq+z4gAaR9KPumGEQqQAjxsEkhaJ/E1A9X1Na/GAeCiFvmjKsFjcMbpBhEKgbmVkGFHWRBmlzjpA+LcCUgsLJZM7hlzuxbDBrX0nnSKer0H/pQ+SBSMTC3Cioo/hZCpKd+2BkQcXEYttYUJIBCCF/2DfVVggaRioHFxLTM+6P/YmLQskIFNyPWv9QP+8w//EG2YwI5cG8lLhg0q/WwBP2pfBCpgBPK1IYKdljEv9SP9GeCElJTUdYoJPFjKghTZIVIBVwgARQSpO/1g12CNI99W9iF6KApHsIS9JhBg0gFvEK70yYugcMtGPGFKxXnxzNBOWwCKDsbzVCjPLwvbH0VjKnICpEKuEDxN+3j5vEh9aMzSACFhFbCEkQqskKkAi569XLexsWcNnHxhlgooxI6kADSPrZ7HD3a7S5EKrJCpAIumprUPgLwSXodfC7wRBkVDUMCSPvYN6Wl28T7FDSIVMAFir9pnPTUD1tHLDkZqR8tw26F2seGJS2RpYe7QB5ajFQuXLgwfvz4ODfp6elqH5r+Ye2PxklP/WAubUhhgxUkgDTIQ/eIHjNotBipnDt37vz5823bto121aFDB7UPTf+4K200PU2RnvqhVf6E25ikonlcAgg0xUPZNxSoDSaz2gfgwfnz5y9evPjss88++uijah8LgIZwM/b8TuDQYCUlRbYDAr+YTCQ5meTminlsaipJS3P+mJ2N8FJDuJYYE0OIzfURiFRkpcUxlePHjxNC4uLi1D4Qg8IKSc3idiWUSNw3JcgmO7tlyzpCSF6e+IFKrAAKJVj4E0yai1QcDkdRUVHHjh2jo6PVPhaDio52rv9BSRXtwFSTUMUVSBG9RTL7FiMBpCls4Mh2mBAkmotUamtrz5w5ExUVtXnz5pEjR8bFxSUkJCxZsqS8vFztQzOK7t2dDQ/zVLSDey+QCwglkrZI5t5iBCvawTbGlg6TDV4wpiI3zUUqFy5cOH36dGlp6TvvvNO/f/+pU6d27tx506ZNkyZNOnLkiNpHZwi4RNAmdtUPlhiHGG4ETHRWFQkgbWIjFXSYCtDcjNrq6uqwsLARI0asWrWKLvZpbm5es2bNihUrli9fvmbNGovF4vGJOTk5OTk53J0rV67s0qVL0A9aX371q8uEtJzk3bubTp8+q+7xhK6GhoYLFy7I9Wq7d3cTGuwtt9hPn/5JrlcOCdXV1SaTqaamRu0DkaRnz27R0eayMvpT/euvV/bsKeZ5EyZE5uV1orezs8kLL5yW5XDOnj3b3NwcFhYmy6sZUH19J0Ii6e2oqKrTp38ijzxCHnnE+YjT8rxTenX+/PnFixdzd5aVlS1cuNDj400OYe2ihtXU1KSmphYXF7/99tuDBg1yf8Arr7zi8Y/s2rWrIgcYwsx//jOxWuntpocfJllZH3zw44MPOs9bYyOuGCSqr6//8ccfZZlxlZdH7rrLeV3x2WdNRhtWuXjxosPhCN1SBea5c9n8TVNjo8gnhofL/76XlZV17drVbNbclWqoYN+Uf//73JQp16l4MCHq3Llz3D10rMFjsBIan9SoqKjY2NjDhw9XVlZ6ewytuaLkUekEU7fBnJ9PzOYRI1z60LIyM7Ku0pjN5rCwMFm+D/7zH+ftmBgyenRotFwZ0dMYwl+uWVlspGLOzxeZw4uJceYa3n3X3LLFTGDoxzKET6aquBljN97owJmUwK/va83NUyGE2O32hoYG9/tNJhOGK4MLE2i1ip3YgLm0oYoN+dlpRz5JmowLQcRNUsE8FQVoLlJZsWLFwIEDs7Ky2DsrKysLCwuxdDkoPA2YsG0PJVVUx61Pxo4ioYotKiw66ODeblxNgAFpLlJJSUmxWCw5OTmlpaX0nrq6upUrVxYVFY0ZMyY2Nlbdw9MhLlKx2dzvA3Vxe/0YbYaKfkhadsxVY8GVg+pQTEV5motUhgwZ8uSTT5aUlIwbN27evHnp6ekpKSkbN24cNmzYwoULkQ4MCrdtCdk7sDZSdeyXE8KU0CZp2THWKmsWu/k8BI/mIhWTyTR37ty33norISEhNzd38+bNZrN56dKla9eu7dSpk9pHZwA2G0Hz0xKUptUVSXVnud0KkQBSF9seMfysDM1FKoQQk8mUlJT0/vvvFxcXl5SU5Ofnz50711sZFZABe8l26hTB1j9awnWLGFMJbUgA6QsiFWVoMVIBNbllf3ABpy5ukopY2DBZs9hgBQmgEIQxFeUhUgEPrc3TLFtQAZf6YdeOtP40un8v3cIXtINLAIlrXVwCCNTCvV2IVJSBSAVcp6Vg7Y+WcDvJi0394KJPy7h3UdwbhN0KNQKRiioQqYCrX77kkBfXgldfdd72o0+UmDECpaSmEoej5Z8/TxIgAaQFaFuKQaQCnle+ohGqzmYj7J6bYlf9SMwYgYJcK1uKJGnZEMiMjRHRSSoGkQq0XvwNF3Cq4MaZxRbRx2IhneLeSYx0qg6RimIQqQAhxKXNmcvLCRqhBrABoh/xBlI/+sV+DERvHARywhwwVSBSAZ65rIx4mGULSpNSmhapH11DAkhTaCcZuXEjVtgFGyIVIIS4fBOGl5Vx/4lxZuVJ3JUQqR9d4zKAuIRQnvuYSkuHSSsCoI5RcCBSAR4dU+G+49AnKkziroRI/egd+65mZqp2GMbU+hJlNLrgQKQChBBCsrKEZZM//e1vBC1Obeylm9i5tEj9GAAbs+L6QV20k4w8cIC/C+SGSAW8QkkVtSD1A96wH4a8PAQriuIqMXqAzV2DA5EKeIXLA7VIDDnY1A/CFJ3CboUq8lhMxcxO7EOnGRyIVMArlFRRi5SQgxuHEVsnDkIPdivUDnNZmdltCQLIDpEKeIXLA1XIEHIg9aNr3G6FSAAppvXCAWh3wYFIBbxCSRVVSNyVMC3NeRvdpa5xM6yRAFIF7R6R+lEGIhUQBb2hYtilp2K7PqR+DAa7Faqi9Rm1EByIVMArXJkrT2LIERPj3JgXqR8D4BJAoACbzdPQMnYsVAQiFfDK08aFEFwSdyUUOByktFSugwFF0SKnbBbPO+6DgWBFeR4uBxCpBA0iFfCFbXqIVBTw2WfO2xgZMYrsbOfGMaKnyLIfj+Ji2Y8JeJ5TP9ixUBGIVEAsRCoK+OIL523MNjEKSVNk2RLEL70k49GAZ63neVD2LWgQqYAvqNygpLw8XKEZlf9TZLEzlyZgkq0iEKmAL2h6SuIu2pD9MRBJNVKwW6GSPBdTQYSoCEQq4As7nImFysEmZVdC0AdJCSA2lkXzDDY2JmkJLFvfWxnkgUgFfMGMWsVI3JUQdMP/BBD7IfG8hhZk4vn0cqkfRCpBg0gFfEEuXDHYCNno/E8AYbdCtbQ0z+Tk+rq60//7n7oHYwSIVICRkkJMph433GAODxdKNKArVAY2Qja6gBNHnOInAAAgAElEQVRAmPMePK1MnEUdoyBDpAIM7J6sElTDB0ICTQBht8LgQSladSFSAYanJoiLNgVI3JUQdMb/IvnYrRCMoCVSqaurKyoqamxsVPdoQGWedk/GBYQCpOxKCPojqUg+ditUgOclyqCUlkilpqZm7ty5Q4YMefrppw8fPtzc3KzuYYH6folUsFA52JD6ASd23x9JCSAINpSiVV5LpBIZGTlw4MDGxsacnJzJkyfffPPNL7zwQmlpqYPuzgoG4WlRMhYqBxt3VnHFZmh33OG8jQSQZqB4tLpaIpVrrrlm9erV33777bp16379619fvnw5Ozv7zjvvvO222/7617+WlZUhZDEET4uSsVA52Ngr5+Rk9IPGJikBxDZSdhEZyAIF3lTnMqM2PDx81KhRa9eupSHLhAkTLl68+I9//OOOO+4YPXr0m2++WVlZqdaBgoowrBJUUlLgaWnEZHJuwAt64v8kdjZjiASQ7FDgTXWe1/7QkIWOsuTk5Dz44IN1dXXLli1LTEwcM2bMBx98YLfbFT5QUEhr5VMQqchLSmlam835dWQyYccXvfE/7sDeC0GFXQhV18oq5YqKikOHDh0+fJiOpjgcjhMnTvz+97+/7bbb3nzzTawV0iEsVFYWO1Yvdn0yFy2i8L7OCHGHw0FEp92xW2HwnDql9hEYntn9LofDUV5evnHjxi1btpw5c4YQYjKZBgwYMHv27LvuuosQsmvXrr/97W8vv/xybW3tb3/7W6UPGYKK7fCuXHG/D+QlZVdC7Lmse/7PC0xOdo6/5OWRjAx5D8jQsERZdc5IxeFw2Gy2TZs2bdmypaKigt4ZGxs7ffr0KVOmdOjQQXjklClTevToMXfu3E8//RSRip7t308eeYRgoXLQSNyVEHsug5ukJJdIxWbDBUZQYImyKloilcrKytmzZ//www/0x+uvv37GjBn33Xdf9+7dPT4tNja2Q4cODQ0NCh0mKIbt8LBQOcik7EqYl4c9l8FdairJzHQ2z7w8BLGywRJl1bVEKg6Ho7a2tmPHjvfff/+sWbO6d+9u8rmsoLGx8cEHHxw8eLAiBwkq+aWBui9URnOVBTdJRRSkfsALNgG0bx8iFXlgibIWtEQqUVFR7777brdu3cLCwsQ8rXv37o899lgwDwxUIuKbD5GKLLjUj9iJBUj9gBfseGh2NsnKUvNgdANLlLWgZe1PmzZtoqOjRYYpoGdcQ0QCKGik7EoocWILGIKkonHQCs/dnc1GCxpFtmmj8PEYE/ZSBjeeSqqw36NYsycLKbsSSlnTDAaC3Qplx3Z3znbKxC892A0QIDgQqYBPv/R8GFORl8RdCbFcEnzCboWy89zmmE6wKTpauaMxKkQqwDv9+edNjY1c1Sl2bR4ilcBJ2ZUQey5Da7BbYVA5u0EMLCsLkQr4Dd1f4KTsSihlTTMYDnYrlJfnJcrMpUb98OHKHY1RIVIBUbhrNQyrBEhKGkfKmmYwHOxWKCOvS5TRAyoLkQpIgXYaCIm7EkpZ0wyGg4sKGXldosz8R11ionIHZFSIVEAsTKqVS6C7EiL1Az6xTRUJoEB4XaKMHlBZiFRALCxUlouU4m1S1jSDQbFNFbPKAuF5ibIrzFNRACIVkAJXFJJJLN6Wm+tcjYXUD/jEfqjoboUgDZYoawQiFRCL7f7Q90kW6AoehwOpHyMymVr+iZglm5rqsXwjBMS5RBndn+IQqYAU6Pskwwoe8FtKivO2uNKzbDSLYrWSeV6izOSEMKaiDEQqIBbWFAQOK3hACv9XHnPFatFaJRC1RBl7bykCkQpIhL5PAqzgASn8Lz2LYrWBE7NEGZSBSAX8gIXKAcIKHpDI/5XH2K0wQF5PGtv34WpDEYhUwA9IfgcCqR+Qjo07JCWAIBAu1xW4SlMcIhXwA4YBAoHUD0jHzYcQ8WXJJYAQrPir1SXKhKBPVAgiFfADu6MyOj5/YdUPSMftYylu4gkGQQPheeIs+y64zF6BIEKkAq1hSjhwwwAYBPWLlF0JAQT+xx3YrVAyXxXzaQ1Gh4OUlip5SEaGSAW8SEtrqTRFnPUDcP0gGVcqFGsbwW9c3OF/AggrgMRDrlZTEKmACEyrRe1LadhrYHR8IIWkBBB2K5QGA8aagkgFvPBSPB+Zb2mk7EoIwPG/+bHPQAJIPDF7E4JiEKmACF7GVEAkibsSAnD8X3ns/5ohIASzyjQGkQp44aXKG5b/SMCt+kHHBxL5v/IYuxVKg1llmoJIBbzwss4HYyoSSLk+S0lpmc4MwPK/9Cwytv7ytfAH1IBIBcT5peFiobK/pJSmFZ5Dl19h8AoE/ieA/F8zBC4wCKo6RCrgnZcEEAaT/cJtHC9qUAp1MMEbdkzF4RDzDElrhgyNW6IMqkOkAt6xlxLMVHgvd4NnUkrTsmP0ycm4pgMXQuUx0ZAA8gtXUwBUh0gFxPEyZIyRZN8k7kqIhQcgKy5lhGbrG9qf1mg0UikvL1+wYEHfvn3j4uJGjhy5fv36xsZGtQ/KeLxcTbC9HkaSfSsvNwu3xa76wZpmkBu3ZujAgUh1jiMEsasdQS1ajFS+//77SZMm7dy5c8iQIZMmTWpqarJarRkZGQhWlMa2Uea708v0FfDglVc6CLfFDiNjTTMEARusFBS0Ue04NI+7UkD2Rws0F6k0Nja+9tpr1dXVq1at2rBhw4oVKz777LORI0du3ry5oKBA7aMzGC8hCZb/iFRWZi4ocF68IvUDKmLH5nJyLOodSIhBE9QCzUUqJSUlBQUFiYmJyb98QKKiohYuXBgREbF161aHP5PIIFDeQxIsJRCjrCzg1A+7wBQgAFwC6J13zJ4fZ3hY+KNBmotUjh07VlVVNXTo0DZtnOOTsbGx0dHR33333U8//aTisRmdl2EVLP/xJjPTeVtKl4fUD8gKK4DEwMIfDdJcpHLu3DlCSN++fdk7IyIi2rdvX11dbbfbVTouoxIxJwXZH4+4wRGxIUdamvM2ukmQFVcCDjzy2mzz8loqMZpMJDZW4aMyOM1FKqc8XaG3bdu2a9eudru9urpa+UMyNC+DJ142WgYn7rSIWsEjcU0zgChcAgh5W/9gsEU9mktVelzgYzKZrrqqlaCqrKysrKyMu7Nr166yHZlhNDc3NzU10dv089EkvCm/3M9+cvLySJPzfmixb5/zFEVHN40cSVo9SWYmummKjiZinmMYTU1NDocDn7QAxcQ4P2X/+lfTyJFqHow25eU5W+6IEc5PnJmJ7JpGjKBts+kXih5i6KPJE/E0F6mEh4e73+lwOK5cueL7iQcOHJgxYwZ358qVK7t06SLbwRlDRUUFISQsLIwQQl54gbzwAjl7lnvMnXcSQnoIPx46VBkdjbbqYufOToS0LPyZNq3+7NnWp1h1WrrUuVIoJuas22k3surqapPJVF9fr/aBhLYnnoh8+ulO9PY775hfeum0usejNTYbYXu2tm0rz55t6dk61dcLzbO+vv6ns2cJIQ0NDT/99JPZrLlvUu176KGHuHvKysoWLlzo8cGaO783eqqzU1tbe+7cOYvF0q5dO29PnDx5src/EvzVrVu3VtteTIwzwXH8eLfbbgv2QYUSm42wa+rvucfSo0dr60Jdn2N+9NEePXr4eLjRREVFEULat2+v9oGEtvR08vTTzh+bm3sgj8E6edJ5OyaG3HZbN+fPzDCA5Z57LD16EELq6+uvvvpqNFUJPv/8c+6eV155xduDNTdPhUYqJ06cYO+8fPnyxYsX27VrZ7GgDACEAK5ylNj1ySx8gUBwsJ8stsogEB9zUWw2zMhTkeYilV69el133XUFBQV1dXXCnSdPnrTZbP379+/QoYOP54KSsOLRB/YLYO1acc/BroSgiOefd962WlU7DG3yWkyFC1PQPJWluUglOjp68ODBBQUFu3fvpnXeampqVq9efeXKlYkTJ5pMJrUPEFpg+Y833AoeOuGndRkZzg1y0Q9C0PTs6fIjGi9LVNk3jHcqTnPzVNq0afP4448fPnx48eLF//73v6+//vr8/PyKiorp06cnJiaqfXTgGZY7sgLdtweFmMFfwiVcaWmr36PJyS6TzNatw3J4J697g2KJsqo0N6ZCCBk8ePCmTZuSkpK+/vrrzZs3m81mq9WamZnpcVkQqIWrzYArMwHb2Q0fjrUqEGRsFTJxFw3sxxKXGQJfU8XY/8OQp+K0GKkQQmJjY9euXfvDDz+UlJTk5+fPmjULYYoGYfcfd1zqZ8qUGtUOBQzC/yljiYkukQouMygu9eNrngooS6ORCoQETKp1x6Z+oqObMKYCQcdmKbKzxXynTp5cwxZAwmUG5SvDw55VUQWnQU6IVEA6pGvdsZ3+iBGohgfBl5oqYXiTvczAWmXK644/WKKsNkQqIB1bpQ8bnhG31A83lQcgWPwf3mTHBZAAosSOm2CeiuIQqYB0mFTLkVLwDSBwXAJIBEkDMXrma9xE1NplCCJEKhAQdHYsdhQdYQooh7toEBesYJ4Zi4tGXNovliirDZEKyObUKbWPQFVc6mf2bNWOBIwoJcV52/8EkLiZuHomdjotIhU1IFKBgLBXHgbv6ZD6ATXNmuW8jQSQ/7xOpyWIVNSHSAUC4n9+XLe40rQAiuISQP6vAEICSMCuFSCEkNzclp0uHA4U9FUFIhUQwWYjJpPzH4P7SjbysAr71YDeDFTg/y7JSABRXOoWVxpag0gFRPAejyDHQbHjSUj9gDrYAFl0Aohl2ASQr+m0oAGIVEAc7wltpLqJ6xXsLbeodxxgZJJGONlgxbAJIMP+4aECkQqI4308FKlubuj4ySdVOxIwNLpLskDcdQMSQARTZjUPkQqIwzZf13iE7emM2c1JXPWTkuJx6g+AdP5fNyABRLBTsuYhUgFxxF1oGLObk7LqhxuHMeaJA9lJGiExeAKIa4vYf1CDEKmAON73+DF4TX2umxO76gfVVyAYhBopdEmtuMAZCSAW2qIGIVIBcXx2eUaeVCsx5ED1FQiS0lLicPj1DIMngDBJRfsQqYA43Dew62WXkSfVStnrR+I4DECwGDkBhF19tA+RCogmbqGyoUjc6wfVG0BjjJwA8lVHH7QBkQqI5j0e8T6JReckpn4yM12eBqA2I+8BhOm02odIBUTzvlDZsJNqZUj94CIOtMGYOVyus8KFgzYhUgHRMKnWlQypH4KLONAKYyaAuEwsIhVtQqQCorE5HrdghL0gM0hr55bviB0cYS9Xk5MxpgIaYeQEEGWQjisUIVIB0dh27HbBdcMNztvitnENeRJzOEj9gFaxn0eDtGJ2zhjfHG02kp1txJBNexCpgGg+FyrHxjpvG2FSrfTUD+bvgVaxn8e8PEMkgFppjmlpzl0vQD2IVMAf3keHjTapVmLqR+LTAJTAJYB0P6zSynRalITTDEQq4A9a/pL+42ITg02qlSH143YCAVTHfpitVrWOQiFclQE+GkFJOM1ApAKyMc4qx7w8pH5An7gPs74vOVrZ0wJTyjQDkQrIhlvlqGPctZbYTgy7EoLmJScbKwEkQHPUMkQqIBvuokSvU1XoggCBHzkcKXXiAJTGfqR1fMnR+hAnRkA1A5EKyIb78tXruLHN5hKE+dGD5ea2TPEh4jNGAPIRd/XA7Zip44Ys8DDEieK1WoJIBeTEtvZTp1Q7jKDiCjBIGRxxODCmAsqhi2xNJvFBhxEKq7QyXxbFa7UEkQrIyWdxOD3Apj0QYtLSnLdFT3Rnh/z0mgBqpSFj4Y+WIFIBOel+Ui13oYUcDmidpDbJzb7SZVtuZRYKiqloCSIVkJPu67+xqR8MCUMIkBp06LvoQOuzUBCpaAkiFZCZjuu/cakfbuIhgEZJCjq4BJDOrjq4SiqtFFPBwh+1IVIBmen4Ugz1UCAkSZp1wo3F6Oyqg2vLPCz80RhEKiAzHU9VaaWiJYA2SQ062Ofp7KqD5eGSAwt/NAaRCshMr/XfuNRPVpZqRwLgN0l1Z/WaAGq95hsW/mgMIhWQmV7rv7We2AbQLEl1Z7nK+ux08pDWSs030B5EKiA//Q0ao4wKhDZu3ED08Aj7UddNMrf1ERO0do1BpALy0994AxepoIwKhBjX4ZGonByRz9Pl1sqtxyHCxhcOB9b4aQEiFfCfzeasz20yuV+f3Xij87Y+rsO4Miq4yoLQw3xqIw8cEP8knVXWb32SCmgPIhXwX2tjJjqr/4YyKqAHzHdyZEGBuaxM5PP0XVkfVx0hAZEKSNJafTc91X/jSi9wcRhAaEhNldYsdVZZH7UGQhEiFZCktfpueqr/Jrlrixw3rscNN8h9OABSSW2WbLAS6gkgTJYNRYhUQJLWvrF1U/9NeupHeCadzRPqI0ugA1yzFJ2XZZ+XlxfC+VxMjQ9RiFRAktYmzepmxJgbUPHjIgy190FrmGbZ1NgofoSQSxyFbmEVVFIJUYhUQBIRTVwHCSCbzSXG8q9fQz4cNMjhIA7H6f/9z9/n6aOwCmrPhihEKiCJiJr5bNcWuqkP9i/zY6wY64VAX7iPcIgmgDBJJUQhUgGpWltHwCaIbLaQ7NrS0py3ucISfsAoM4Q+7lMcigkgVFIJXYhUQCq23zp1yv3/pS6K1IqAJt+xMQ5GmUEX2GGVUNywEJNUQhciFZCK/QL20mmF9FQVbp6JH2VUsMAA9Ij7ag+5YRWu0jSEEEQqIJWIhcihu1bZZiNWq/NH/y6/uGs3lIoDvZC0JbNWsO0SAyqhBZEKyMTTsEroltXnDtW/YRHm2q0pOlqW4wHQAm5ebQgFK9xUOUxSCS2IVEAq7qrESxgSolNV2IFi/+bSuqZ+7JMny3dQACrjpneEUL1a6YWRQAMQqUAAdDpVJaAlxq7noW74cDmOCEAr2PHFEKpXi/XJIQ2RCgRARBgSilNVuJl3kgu+1ScmIvsDOhOK9WrFznFPS2vZ+wI0BpEKBIANQ7xcW3FTVbSfAAqoLi33ZCTDQY9Cbl4t1zl5bdTC40ym0AjBDAORCsjB4SC5ud7+k70C035im9uux7+5tGJ7RIAQFnLzatkBX19hCgrDaRUiFQhAairdRsT3o0Lr+zqgmXfsk6UXtQXQutCaVytlkgoar5YgUoGgk7rVvAry8gLbrkd63ggglHDzarWc1RU7VsKVQQItQaQCQRdCZfUDmktLWjaqbRlkwugxhBZ/WibXqLU8rMLlc702auyzrGGIVEAJIbFWWc79jx0OjKlAaKCrXUwmf8ONUNkGiEvJeoV1zBqGSAWUEBIJIG5ABUXwQf/YfKWfM2O5BqLNtTJ+7MGF6bQahkgFlKD9BFBAi5MBQlRgVQTYvbG0eQUiNvXDHTqyPxqDSAUUovHFAlyPFlDqByCEBDDfhGsmGmzXYlM/3HRaRCoag0gFFMKOp2qtCLfNRtLSnD8mJ6OnAsPg5pv4iR2UYYdYtMCP1A+m02obIhVQiJYTQNzB+FftDSCkBZYA0nIVOD9qI2E6rbYhUgHlaDMBZLOhYBsYWwAJIC4C0NS8Wj/CD3aMF9NptQeRCihHmwkgORcnA4SiwBJA7LO5mekq8iP1Y7NppTMCLxCpgHK0mQAKtNobQKgLLAHEDUNqZLjUj9QPN50WXYD2aDFSuXDhwvjx4+PcpKenq31oECit9WhcIfCsLNWOBEBNgVWc1WBxfT9SP5hOq3lajFTOnTt3/vz5tm3bRrvq0KGD2ocGgdJaAggDKgCEyLACiP2KV322ih+pH4LptCFAi5HK+fPnL168+Nvf/vZzV88995zahwaB0lQCKDsbM1QACCGBJoCIa/NRfVgloB3RQXu0GKkcP36cEBIXF6f2gUBQsL0GW8VEYdySH5TPB6MLLAGUmqqhpu3fKElurnNvUVyvaJLmIhWHw1FUVNSxY8fo6Gi1jwX8IexzZjL5Tupwc0HUWimAGSoALgJLABHXJIuKi4C4SAVNWwc0F6nU1taeOXMmKipq8+bNI0eOjIuLS0hIWLJkSXl5udqHBj75k9RRfV6t+4CKlPFhLcwbBJBLwAkgblhFrdkq7O9F3kcfNBepXLhw4fTp06Wlpe+8807//v2nTp3auXPnTZs2TZo06ciRI2ofHXg3dqzzNjuX3hPVVwrIM6Cybp1zGAlABwK+hlC9tgrXtJHM0Qez2gfAq66uDgsLGzFixKpVq+hin+bm5jVr1qxYsWL58uVr1qyxWCwen1hQUOCeMLr77ruDfsS68/PPP9vtdrPZv8+GedCgyF9uN+3eXW+3+3jwlCkkM9Mi5Ij+9a+moUPr/T9SicrKzJmZwsGSkSObhg71fbwemMvKIpluuH7Jkqbnn+ceU19fX1tba/f3pcETehr9/ViCR97auHnatEjhez472756tb+vPHQoGTkyMj+/5ZXT0siUKYp+/jMznV8Q0dFSmrZf0MalOXfunPvQQ1lZmbdZH5pr9gkJCZ9//jl7T1hY2MMPP7x79+7CwsKTJ08OGjTI4xPLy8s/+OAD7s6ePXt26dIlWMeqU3a7vW3btmFhYX49q019vfDlby4rq/vhh6bu3X08fuHCpkWL2tPb77xjXriwrnv3JimH67+dO9vYbM5I5Xe/s9fU1Pn7IubCwkjmx/rExLqaGu4xDQ0NP//8c43b/SBBbW0tIcTfjyV45LWN33dft/nzL27ZUjd8OCGESPro/u53Tfn57YUfrVbyu98p1ARsNpKX54xUpk2rD3brQxuXpm3btu7f1+Xl5d4iFZPD4Qj+UXlgt9vnzZtXUFAg3JOYmOhjyCQ9PX3z5s1r1qwZPXq0+/++8sorhJCFCxcG6WgN5fTp0926dZNy8comQbKyWl1Lwz48NVWhiW82G4mNdf6YnExycyW9UEqKc5TZy6vU19dXVlb26NFD0i8AFxcvXiSEtG/fvtVHQqukt3Fx2MZBCCktVaigWmamcz/nmBhSWhr034g2LiMf3+Oam6dCCLHb7Q0NDe73m0wmXFFpGtsbnTrV6sPZSEaxfDa7eDImRmp45F9hKQBj4WaHKLNi2WZzhikEc2n1RbVIxWKxbNiwoYSxYcMGi8WyYsWKgQMHZrl+gVRWVhYWFmLpstaxfYOI6rPK7xfPzbZLTpZ6qce+CiqxALhKTnZpE8rMmud+BS4f9ERzYyopKSkWiyUnJ6f0l5G7urq6lStXFhUVjRkzJpYduAetYUvli4g7FN4v3maTaUCFuJXABABXWVkuLUOBYRW2UXKbJkKo01ykMmTIkCeffLKkpGTcuHHz5s1LT09PSUnZuHHjsGHDFi5ciJn/msYNLYgYVuFKRQX1wmvdOpcjkr58kTtQrIME8IRbsRzUYAWNUt80F6mYTKa5c+e+9dZbCQkJubm5mzdvNpvNS5cuXbt2badOndQ+OmiNn5v6cNsABa8vc89hS8/YcKkfXLsBeMIVguO22ZKR+3ApGqXOaC5SIYSYTKakpKT333+/uLi4pKQkPz9/7ty53tYEgbawPURr9d8odn6+zRaUHJB7RxbQJRdSPwDicAnWIGV4163jlxqBzmgxUoEQ5udUFYoNb6xWMVkj/3AdGXep5x+MMgOIFhPjMpaZlyd/sIIlP0aASAVkxY0xiAs6grqmMS/PpSOTeUAF/SKATxkZ/KWIvDkgOYdLQasQqYCsuG9ucX1ScjJ/4SVXX2azkZQU548yFIPybzt5AODLInJ14QLBzX3xY8lPXh626wohiFRAbmxXIaL+G5WRIf/UWvflBoHWPeFiKFRsABCHvRQhMk1Y4aa1+Vd3gM6io9uLslczoEmIVEBubMThz5QTtpeRZWqt+/SUQEeGT5503kbqB0A0LgeUlydDeBBQ3QEMjoYURCogt6ws4nC0/POntho3chtgPjs7m5+eEui+QjYbmTPH+SPq0gL4IzeXD1YCKUvNNXC/6w6wnQu7DgA0CYXUQEOysly2D0xJ4Xs3kdiNygghMTFStyFkxcQQh8OZ25a1dysoKDhw4ICML6g/9fX1hJDIyMhWH2lAw4cPT0xMVPsoWsc18LQ0cuqUlJHO7OzAJtJyY72oNaB5GFMBDaHBAMvfyXc0bcQlxblJMAGhY0VyF+s+cOAAu684uIuMjESY4pFCYa7JFPj0MfdrBqvV71d1n39WWupnc+SKNyJS0TyMqYDmpKa6DAuLH1mx2ci6dXyYkpUVhESNDEM0vMTERI/bnQOoiR2+yM4OPOpPTiZZWS6hRnY2sdnENimbjXCbv3HtXRQUbww1GFMBzXGPLVJSWk9p0ystrtuyWjGfBCAAXPuRY3lxaio/aSwvjzz4YOvz77OzPYQpgU6Tx3TaUIBIBbQoK4vvQNLSSGys53iFxiixsfyYrgy9GACwwQo7GhHYS3KDKO+9R2JjSVqa53glO5ukpHgoOiClgXNlpjGdNhQg+wMalZvLT1KhEUlmpkvP6bFMHF3pg4slABkkJTkvEWh7k6NpJSe3tHFWdjbJziYxMa23cfeBGbHYUAi1BkIEIhXQrtxc8utf89de3DYf7uisPWSfAeSRmkoyM51f8OvWyfXtnpxMSkv5hA4R0cZjYwMoOsDunIpuIkQg+wOatncvsVrF9ic041Naiv5Hc15//fU4NzfffPOSJUvKy8vVPjpNsNvtM2bMSEpKqqioUPtY3LBDHIFUQXFDl/uJnxVL23hJSQC/EjXfQhAiFdC6jAxSWtpKvCLEKJiYomWjRo2azrjhhhvef//91NRUtYKVioqK5cuXf//996r89lDCtStZgxXCtHEf5GnjmKQSmpD9gdCQkUEyMkhmJsnPJ01NzvuvuorccQcClNAwc+bM0f+/vXuPiyl/HwB+phoazaDU6mZrJlG+RrFNDb+hWqFEqXWZXLZYtSyVyn1RWS+trEvIpUhil7SxGxEioyTlEnIJXXY1bTUpNZOGps7vj7M7xpQoNefM9Lxf+4c+c+bM0+yczjPP5+bkJP0RRdH9+/dv3RTymugAACAASURBVLo1KSlp2bJlio/n1KlTv/322+TJkxX/0srHweHdPZ7H6/I5ddjqbdg1fu0a0tLy7iENDYTD6aJrXG7UPdRUlARkKkCZQEaiSkgkkpOT0+HDh+/cudPQ0KClpYV3RODDvL3f3ea7YmGVD+neaxxWUlFO0PsDAMBNv379KBSKRCJBURRBED6fv3r1altbWwaDYWZm5ujomJCQ0NTUhPw3jCMkJCQuLs7CwoLJZKakpGDtW7ZsYbFYDAaDyWRu3Lixvr4eO3l6ejqDwThz5szOnTuxAzgcTkpKSnNzM4Igy5cvj4yMFAqF7u7us2fPFolErcPDTj5ixAgGg+Hs7Hzx4kUul4sd3GY8zc3Nqamprq6uFhYWWDy+vr4lJSWy8aSkpGzcuNHCwsLMzMzDwyMvL0/uRQsLC7lcrrm5uYWFhb+/P1HG8cgVUTqy+SiByNZU4HuP8oCaCgAE9fm7SePF3v5Ty+rPnz8XCAS2trZaWlrl5eXfffdddXX1jBkzhg8f/tdffyUmJoaHh/fu3XvWrFnY8enp6ffv39+wYUNlZSWTyRQKhUuWLLl+/TqHw/Hw8Lh3715SUtLz58+jo6NpNBr2lJ9++olCoSxduhRBkLi4uBUrVpDJZBcXlzlz5rS0tKSlpQUEBFhbW7deql8kEi1ZsiQ7O9vNzW3s2LGZmZn+/v4oitrY2EiPkYsnLi5u69attra2WNjp6ekXLlz4559/jh49qq2tjT1l06ZNFAplzZo1CILExMTMmzdvz5490k6xsrIyX19fV1fXOXPmXL9+PTk5uby8PD4+Xvrr4CkkBNm27d9/OzrK73xBfHJznaGmojwgUwGAoDqzTDgxhIV9PFNpbm4uKCjYuHFjS0uLm5sbiUS6detWZWXlzp077f8b5zh+/Pi5c+fm5eVJMxWxWLxu3TrpAQkJCVlZWStWrFi0aBGJRJo2bZqtrW1QUNChQ4ekA18YDEZsbCx2p2ez2XPnzr18+bKLi8vIkSNv3rx5+fLl//u//2Myma0jzMjIuHHjxooVK3x9fUkkkru7u5WVVfj7+aNsPLW1tTweb+zYsXv27KFQKAiCuLu7h4eHnz59uqysTJqp9OvXLz4+3sjICPsFvb299+3bZ2dnR/pv88vNmzd7enoiCDJlyhRNTc3Tp0+Xlpa2GaGiTZnyLlNBkK5aWEVxHBzebTIK2/0oFej9Ad2PROqS7c2AsvPz85NOUTY3N/fw8CgqKgoICBg9ejSCIG5ubnfv3rWXmY6hra3dp08f2TPo6+tbWlpi/25oaEhPTzcwMHB1dZXe5seOHTtq1Cgej1dXV4e1cDgcaUFCT09PT0+vqqqqoaGh/VAlEsmFCxeMjIymTp2KnZxEIrm4uJibm38oHm1t7WPHjh06dAhLU7Cn6Ovry5153rx5WJqCIIixsbGLi0tpaemLFy+wFkNDQ+muyCQSyc7OTigUVlZWth+tgshtzNlF69UqGrbJ6H9dckApQE0FdCe57c06v1qTwmE7oSldfZvYxo4dK71Ja2hojBgxYvTo0dIWjEgkev78eWlpaV5eXnZ2dllZGYvFkj5qYGAgzV1ev37N5/O1tLRu3br14MED6TEtLS3V1dXSXERD491fuV69evXv3186LKYdYrG4pqbGwMBAttuFQqHo6OjIHiYbD6a5ubmiouLx48fFxcVZWVl3795VU3vvC6GhoaHcGWpra8vLy7/88ksEQdTU1GQDJpPJ7cepaIoaVwuALMhUQHfy8ZHfNVVZNgzEvi9KC8V4fANTlreqNROTttvlZinLqa2t3bBhw7lz51AUVVdX//LLL0eOHFlTUyN7jOxdH0VRiURSUlKyfPlyuVPRaLSXL192/hf4ZHLxXL58efXq1VjM/fr1YzKZVlZWsllUm0gkkrq6evcG2lXkrujwcGX6+gGUFmQqoJt18zIM3UJuNW+cOuN71C0ARdHdu3dfunRp48aN7u7uVCoVQZCqqqrbt29/6ClaWlomJiYGBgYHDx7EjpfzOZ0mmpqaOjo6Dx8+FAqF0pO/ffv21atX/fv3b/Mpz549+/HHHwcPHhwREfHll19iycf+/fvlMhW5qJ4/f96/f/+BAwd2OlRF8/F5t/Jbj/qMAvzAOBXQzby93/27q5e27C5yMzBlfwXQPRoaGp48eaKnp+fo6IhlBiiK5uTkVFRUvHr16s2bN62foqWlNWrUqPz8/MzMTGkjn8+fMGECl8utra396IuSyWQURVtkVxn7j4aGxqRJk/h8/pkzZ6RdRdevXy8qKvrQ2f7++2+BQMDhcOh0Opam1NbWXr16VSwWSwfNIAhy5swZoVCI/busrOzatWtMJpPeevMbwsIm92KjPQBQCKipAMUqLVWCjm3Z+R1yowhB96BSqba2tjk5OcHBwR4eHgiCpKam3rx5E0XR169fY0uqtPbdd9/duXMnICDAzc3NwcHhxYsXiYmJlZWVwcHB0rk27TAxMRGJREePHq2pqWGz2dKRsBhHR8fRo0dv3bq1sLAQm6Wcnp7eejKz1NChQ42MjGJjY+vr662srAoKCk6fPl1bW9vU1CQWi6WH5ebmzpo1y9vbWyQS7du3j0QiLVu2jEKhtLmgCxFhW/UAoEBQUwHdzMfnvdSk9fbtRCO3MwgsD6Uo33//fUBAQFFR0Zo1azZt2tS3b99z5865u7u/ePHiQwUSGo22Z8+ehQsX3rhxIzAwcNeuXfr6+gkJCc7Ozp/yinZ2dtOmTfvzzz/XrVsnEAjkHqVSqbt37543b97FixdDQkIeP368bds26Uyf1gYNGrRv374hQ4YcPnw4ICAgLS0tKCjo2LFjNBqtoKBAetiSJUvYbHZoaOjWrVutra1//fVXa2vrT4kWgB6L9NEx8EohKioKQZDAwEC8A1EFL168MDAwkJ2A8Lnmz3/X7+PjQ/S+bdloP28srVgsFggEgwYN+uiR8AFWClVVVTNmzGCxWL/88ksnnp6enu7n57dy5cpFixZ1YVSd+PB0/TXeU336NQ4+qp1PMtRUQPeT3bCU4ENVSkvfixD6fXqw2NhYZ2fnZ8+eSVtu3rxZUVExePBgHKMCoAeCTAV0P7n5PkTuAJLbahXG0vZgo0ePfvny5cKFC48cOZKamhoeHr527Vo6ne7m5oZ3aAD0LJCpAIWQHapC2KUtS0vfi83cHGoqPdnw4cP37t2rr68fERHh7+//xx9/zJgx4+TJk3JLtwEAuhv0UwKFCA1VgsVq5cbSrl2LWySAGFgsVmJiYledzcnJqbi4uKvOBkDPATUVoBBK0QEEk5MBAIB4IFMBikLwvc2uXoXJyQAAQECQqQBFIfhitbIFFVNTKKh0ucbGxoSEhMmTJ5ubmzMYjJEjRwYEBDx9+lR6QHp6OoPB2L9//4fOsHz5cnt7+6qqKgRBUBQ9duzYiBEjGAzGt99++9G9kT9q//79n7JHjwKIRKLZs2dLf1MAAGQqQFGI3AEEq711M6FQ+MMPP4SFhdXX17u7u3O5XFNT0/Pnz7u5uZ0/f74TJywoKNi6dSudTt++fXtgYKCamlpiYuJvv/3W5ZEDJXb1KkIi/bvPKFBmMKIWKJDsboVHjhCobiFXUFGKbRSVytWrV69duxYcHLx48WLpvsGPHz+eP39+VFSUjY2Nnp7eR08iu95aZWWlUChctGiRi4sLgiAPHjzYvHnz4sWLuyl+oJSkvcwkEuLggGRk4BoN6DyoqQAFknYAoSixpv/IBkOc/EmFZGdnU6lUe3t7aZqCIIilpeX06dPLy8v5fH7nTksmk7soQKByYBVHFQKZClAgHx/ibsGKBWZqSqwUSlWYmJiIxeJSuU2qEWT58uX379+X3fhGLBbHxsayWCwGg8HhcFJSUpqbm6UH29vbl5aWzp4928/PD0EQPz8/KyuruLg4d3d3oVAYGRkpHWvS1NSUkJDA4XAYDIaFhYW/v79sPoSiaHZ29uTJk83MzJhM5k8//dT+SBeRSLRlyxZsWIyzs/PFixe5XO7s2bNFIhE2rCQkJCQuLs7CwoLJZKakpCAI8vTpU19f35EjRzIYDHNz88mTJ58/fx7bvaSqqsre3j4kJOTMmTNsNpvBYLDZ7ISEBLmNGAsLC7lcrrm5eev4iYtEerceAb7kPmyyK2UDZQO9PwDI+IxdfkA7vv7668OHDwcHByclJU2bNm3MmDEDBw4ktTWAYN++ffr6+kuXLiWTyYcOHQoKCiKRSFOnTpUeQCaTAwICrKysDhw48P33348cOdLExGTlypW7du1ydnZ2dnY2NjZuamoKDQ09ceIEk8n09/cXCATx8fE+Pj7x8fFGRkYIgmDbBw4cOHDDhg0IgsTFxVVUVHxon2SRSLRkyZLs7Gw3NzdsU2V/f38URW1sbKTHpKen379/f8OGDZWVlUwms6CgYP78+X369PH19TUxMSkoKEhKSgoKCtLW1maz2dKn8Hi8qVOnWllZJScnh4WFPX36NCwsDHu0rKzM19fX1dV1zpw5169fT05OLi8vj4+Pp9FoXfO/pGvJ7pZFkAWTYNEBFQKZCgBE1bnvph29SSjkVYYMGXLixImVK1dev349KysLQRAtLS1HR8f58+dbW1vLpizDhg2Li4vT1tZGEOSrr76aO3cudjuXHkAmk9lstkgkwg5wcnJCEOTt27fYPsYTJ05EEITH4yUnJ3/zzTebN2/Geog4HI6vr29kZOS2bdsaGxsPHjw4aNAgaeLi5OTk4+Pzobk2GRkZN27cWLFiha+vL4lEcnd3t7KyCpe9ESKIWCxet26d/X9f3Hfu3NmrV6+YmJihQ4ciCOLq6spms/38/PLz86WZyps3b37++WdsnI2rq+vatWtTUlI8PDywpyAIsnnzZk9PTwRBpkyZoqmpefr06dLSUiaT2aF3XkFCQ9/rapk/H+dkRW6MPKQpSg4yFQCIqnNzuTt6h+jEq3Sq8kSn05OSkgQCQWZm5pUrV3g83tmzZ1NTU728vEJDQ6UjTsaPH4+lKQiCGBkZmZmZlZeXi0QiKpX66a+Vlpamrq4+c+ZM6WmtrKwcHByys7PLy8tra2ufPXvm5+eHpSnYC7m7u8fGxrY+lUQiuXDhgpGR0dSpU7GMikQiubi4yM0z0tfXt7S0lP64bNmyZcuWyR6go6MjV7Nhs9kO/91ByWTyzJkzU1NT8/PzsUzF0NBQmtOQSCQ7O7uEhASsYPPp74PiYOPQZcsqoaHv7aGhYND1o1ogUwGgB3N07MyzPuMOpKen5+np6enpiaLokydPVq9effz4cTs7O2nVREPjvT9KamodHkvX0NDA5/O1tLSKiopkyyTNzc1CobC2tlYgEIhEIgsLC9lnyf0oJRaLa2pqDAwMZLtdKBSKjo6O7GEGBgZ9+vSRe259ff2jR4/++uuvmzdv5uTkCIVC2Ud1dXUpFIr0x/79+1Op1MePH2M/qqmpyb4VSjB2WK6sEh6OZ1kFun5UC2QqAKiQjt4bFLKqDTa2dMyYMREREdJGEolkaWm5adOm1v07nwlFUYlE8vLly7Vt7dwkEAi66oVkyWVUZWVlISEheXl5CIL06tXLzMxs1KhRV65c+eh5lCAj+RDilFXkun5gR3TlB5kKAET13+DKDujoSjCdeImO09XV1dLSunv3rkAgkFs3RVNTs3fv3l17e6ZSqSYmJi9evEhMTGxz3+MHDx7QaLT8/HxsjAvm+fPnbZ5NU1NTR0fn4cOHQqFQ2gP19u3bV69e9e/fv82nNDY2bty4sbi4OCYmZuzYsb1798ZeNDMzU/awV69evXnzBnsUQZDKysq6urrBgwd3/DcmjMOHCVFWkd2sA5ZHUgmQqQBAVApYKlchq/Hq6Oi4ublFRkZGRESEhYX17dsXa29sbIyLi6urqxs3btxnvoS6urqGhoZEIsF+HDNmTHJy8tmzZ7ExsAiCCIXCJUuW8Pn8gwcPmpqaDh48+Pz581wu19jYGEGQ2traCxcutHlmDQ2NSZMmXbx48cyZM9KzXb9+vaio6KuvvmrzKUKhsLCw0MzMjM1mY4lIc3Mzj8cTCoWVlZXSw/Ly8h49ejRy5EgEQZqamv7888++fftyOJzPfCtwhntZpbT0vfwb+n1UAmQqAIBuN2fOnIKCgj/++OPcuXMsFmvQoEEvX77Mzs5+/fq1l5eXbG2jc3R1dalU6rlz54yNje3s7JydnW/cuLFly5br1697eHjU19efOHGisLBw1apVpqamJBJp/fr1vr6+s2bNwtZlaX+WsqOj4+jRo7du3VpYWIjNUk5PT//QwQiC6OjoWFtbnz17duXKlRMnTqyvr09OTn7y5AmJRJIdqiIUCn18fBYsWGBiYnLkyJH79++vWrVqyJAhn7+HEZ5wL6vIdWhC149KgJXfAADdjkajRUVFRUdHDxs2LC8v78SJEzweb9iwYbGxseHh4Z/f+6Onp+fr61tWVhYcHHzz5k0ymbx+/foNGzb8/fffISEhP/30E4Igu3bt+u6777CiiLW19a+//jpo0KBNmzZFRESMGDECW1ilTVQqdffu3fPmzbt48WJISMjjx4+3bdsmO9NHjoaGRlhYGJfLzczMDA4O3rFjx8iRI9PS0uzs7EpKSqTJiq2t7Zo1a44fPx4SEtLQ0CAbnnKTLWnExyt6hy/Zrh8YS6sqSCgxFwztoKioKARBAgMD8Q5EFbx48cLAwEBuCgboBLFYLBAIBg0a9NEj4QOsXKqqqmbMmMFisWS3Iuro042MjGJiYjo0+7pNnfjwdPs1LptvTZqEpKV11wvJuXr1velsGRndnal8+jUOPqqdTzLUVAAAoD2xsbHOzs7Pnj2Ttty8ebOiokK5R792K9myyoULiiuryG01CgUVVQHfmwEAoD2jR4+OiYlZuHDhggULdHV1b9269fvvv9PpdDc3N7xDIypsbRXp8muOjorY7UtucrJCRosDxYCaCuhJCLJ3GlAqw4cP37t3r76+fkREhL+//x9//DFjxoyTJ0+2OQUa/EtuIK0CLj3ZSUYwOVm1QE0FEAaJhJSUdOOcRmwX+Ph4gm7mDAiMxWIlJiZ21dm++OILHo/XVWcjKGw0q7TIER+PeHt3e3cMdmmTSNDvo2KgpgIIgET6dwje+7u+daXS0nff6kgkhE7vrhcCAGDkyioKyx5QlBCbOYOuA5kKwFtQ0Lt/d9+cxqtX3zszVIYB6G6mpu+G1kIhE3wG6P0BeAsMRHbufPdjeHjXf/eSLaggCGJqSsDRdjk5OXiHAJRSTk6OdNdlwgkNJeC1BpQO1FQA3mS/eCEIcvXqe2tcfj65NAXp+DZ+3c/Ozo64NxtiEIvFYrEY7yiIiM1m29nZ4R0FAN0IaiqAAOTmNM6f35W9M0eOyPf7EG+0HZvNhkylfa9evUIQ5EObAgIAVBjUVAAxdNOcxvj49wo2pqYELKgAAABoB2QqgBjkdujokqG1rYenZGR87jkBAAAoFmQqgDDkqh2fOWO5tPS9HUAQBIcN6AEAAHw2yFQAYch1zchtNtYhWDVFOvAFQZCwMJiZDAAAyggyFUAkcsNdO5esYNUU2c4jBweYKgkAAEoKMhVAMHJ9QB1NVrA0RbaaAqNoAVAZspc26DEgUwEEY2qKlJS81/LpycrVqwidLp+mdOteQgAARTpy5N+dN0BPApkKIJ7Wk3Q+cR6Q3EIpMNkHAGVRWoqEh7dXMsHKpdiiA5Cs9DCQqQBCcnB4L8mQq7K0Q7q9CFRTAFAWpaUInY6EhSF0ehv5Cpaj0OnvfWOBTUZ7EshUAFHJJisdSjhQFPHx6UByAwDAl2zageUrcv/JVVVNTWEqX48Cq+kDAnNw6OQWrDCEFgBl0ebKSe10A7UeygZUHdRUAAAA4Cc0FCkpeW/Xiw/BdjOFNKXngUwFAAAArkxNP5KvSHMUWBipR8IzUxGJRN7e3suXL2/9EJ/P9/f3t7CwYDAYHA4nISGhqalJ8RH2TJWVlXiHoCIqKirwDkF1wJvZhQh6jWP5CooiKIpkZLz7D0UJm6PAx1IxcMtUmpubjx49mpWV1fqhR48eeXp6pqWljRo1ytPTUyKRhIWFhYaGQrKiGMHBwXD5dYmKioo5c+bgHYWKuHDhwpEjR/COQkUowTWObVkqt3Ep8cA1rhj4jKhtbGzcvn17XFwc2mq8ZFNT0759++rq6nbt2uXi4oIgiFAoXLJkyalTp1xcXMaOHYtHvAAAAADABw41ladPn86ePTsuLs7S0lJTU1Pu0eLi4pycHDab7fBfKk2j0QIDA3v16pWSktI6swEAAACAClN0piISicLCwgoKCoKCgsLDw8lkstwBjx8/fvnypY2NDYVCkTbS6XRjY+OHDx/W1tYqNl4AAAAA4AmHmsrw4cNTU1OXLl3aq1ev1o9ivacWFhayjb169erfv39dXZ1IJFJQlAAAAAAgAEWPU6FSqWvXrm3ngL/++qt1o5aWlr6+/sOHD+vq6rotNAAAAAAQDuHWqG1zgg+JRFJT+0j5Jycnp3si6nHKysqSk5PxjkIVlJWVlZWVRUVF4R2IKoALvAvBNd5V4BrvQtgQ1TYfIlym0nrkCoIgKIq2tLS08yw7O7tui6jHCQwMxDsEFWFsbAxvZlf50J8w0AnwsewqcI13ITab/aFbeXdlKunp6X5+frItMTExTk5OH32iiYlJ68aGhoaKigoqldqvX782n8Vms+EPGQAAAKB6CLeaPpapPH/+XLbx7du3r1696tevH5VKxSkuAAAAAOCgu2oqTk5OxcXFnXji4MGDdXV1c3JyvL29pROVi4qKSktLXV1dtbW1uzRMAAAAABAa4WoqxsbG1tbWOTk56enp2DpvQqFw9+7dLS0tbm5uJBIJ7wABAAAAoDiEG1FLoVB++OGHu3fvBgcHHz9+3NDQMCsrq6qqisvlwkgUAAAAoKchXE0FQRBra+uTJ0/a29vfuXPn1KlTGhoaYWFhbS5oCwAAAADVRoKddAAAAABAWESsqQAAAAAAYCBTAQAAAABxQaYCAAAAAOJSzUzlzJkzQ4cO3b9/P96BKKv6+votW7awWCwGg2FhYTFr1qzc3FwY0vTpnj59yuVyzc3NzczMJk6ceP78eXj3OgdF0dzc3BkzZpibmzMYjDFjxmzZsqW+vh7vuJSeUCjkcrn29vZVVVV4x6KU+Hz+6tWrmUwmg8FgsVjwsew02WvczMzM0dExJSWlublZ9hgVzFRKSkq2bNnS5k6H4FPw+fxvvvnmwIEDffv2nTlz5qhRo+7cufPtt9+mpaXhHZpySE9P/+abb/Lz8x0dHSdPnlxRUbF06dLY2FhIVjoKRdHY2FgvL68HDx44Ojp6enq2tLQcOHBg6dKlQqEQ7+iUGIqiMTExubm5eAeirAoKCry8vJKSkhgMxsyZM/v27Qsfy05LTEycM2cOdo17eHgIhcJly5atX7/+vZs4qlpev37t6+tLp9PpdPq+ffvwDkf5tLS0hIeHMxiMvXv3SiQSrPHWrVs2NjYcDufvv//GNzziq6mpmTZtmo2Nzd27d7GWsrIyJycnW1vbwsJCfGNTOoWFhba2ttiC11jL69evV69eTafTd+zYgW9sSu3atWtDhw6l0+njxo2rrKzEOxwlg91lhg4dmpKS0tLSgqLo27dv16xZQ6fTjx07hnd0Sqa8vNzBwUH2D2ZNTc2sWbOYTOatW7ekh6laTeXUqVNZWVkeHh54B6KsqqureTyeubn59OnT1dXVscavvvpqypQpfD6/sLAQ3/CI7/79+48ePXJ1dbWyssJajIyMAgICqqurr1y5gm9sSiczM1MgEMybN49Op2MtFAplwYIFurq6ubm5IpEI3/CUlEAgiIiIsLS0/N///od3LErp9u3bPB6Py+VOmTIFWzadTCZ7eXnRaLR79+7JdVuA9lVXV9fU1IwdO1b6B1NbW9vBwUEkEuXn50sPU6lMpaCgYOfOnZ6enp+yaTNoU3V1tZqamrm5udwWSwMGDMArJOWSl5fX1NRkZ2cnu/ODhYXFgAEDbt269ebNGxxjUzoVFRW6urqWlpayjVpaWr1798YrJGUnkUiioqIEAsGaNWtoNBre4Sil/Px8dXV1V1dX2WucyWTeu3cvMjJS+gUPfAp1dXUNDY2amhqxWCxtxL6EyN50VCdTEQqFkZGRAwYM+OGHH2A1206ztLS8dOnS7t27NTTe7bQgFAozMjJoNNrAgQNxjE0pVFRU0Gg0Y2Nj2cZ+/fpRKJSXL1/KXo3go3788cfc3FwWiyXbePv27fLyciMjIy0tLbwCU16XLl06deqUn5/fsGHD8I5FKaEoWlxcPGDAgIEDByYkJHA4HBhR+znMzc0nTZqUmZm5d+9ekUjU3NyclpZ29OjRIUOG2NraSg8j3L4/nYOi6PHjx2/dunXgwAFDQ8NHjx7hHZHqwN7b/Pz8yZMnW1hY4B0OoTU0NLQ5k6JPnz4GBgb//PMP1FQ+E5/P37Vrl5aW1vTp02G/0o7i8/nbt2/ncDhz586FTorOaWhoqKioaGpq2rBhQ05ODovFYrPZWVlZBw4cePjwYXR0NFSqOoRMJq9fv37AgAEHDhyIjo7GGidOnLh+/XpDQ0PpYSqSqdy7dy82NpbL5XI4HLxjUSkoiiYnJ2/fvp3BYKxevRqKVe1DUVQikbT5kJqa6tQv8SIQCEJCQoqLi1etWiX7fQt8iqampujo6Pr6+uXLl1MoFBjl8zmqqqqam5tPnDhhbW2NIEhjY+PGjRsTExMPHTq0bNkyvKNTJs3NzSdPnoyPj9fU1LS3t+/du3dWVtalS5doNFpoaCiVSsUOU4W/nkKh8Oeff9bT01u8eDF8zepCzc3NsbGxa9asMTIy2rt3r5GREd4RER2JRJLtNZPV0tKi4GBUTElJibe3d15enr+///z58+FK76i0tLRTp04FBAQMGTIEXuQr8wAABnBJREFU71hUgb+/P5amIAhCoVAWL15sYGDA4/Hq6urwDUy5XLx4cfPmzdbW1jweb/fu3b/88ktGRsbMmTOTk5MPHDiA/reyg5JlKvv372fIsLKyun//fkxMzKNHj0JDQ/X09PAOUJm0fjMfPHggfVQkEq1evXrLli3Dhw8/evSoubk5jqEqCy0trS+++KJ1++vXr//55x8dHR0YCto52dnZXC63uLg4NDQ0MDAQansdha0yNWHChJkzZ+Idi3LDvo2QyWQGgyHbrqOjY2JiUlNTAz28n04ikaSmpqqrqwcEBEjncFAolODg4CFDhly+fLm2thZrVPreH7FYfPv2bZFI5OXlJfdQZGRkZGTkypUrFy1ahEtsyksgEPj7++fm5rq4uGzatEluHhBoh6mpqVAorKysZDKZ0sa6urrGxsYBAwZoamriGJsywvof161b17t37z179owfPx6qKZ1QVFRUXl5eXl6empoq9xCbzR40aFBSUlKbSTaQo6WlZWRkJJFIWi8uCnXTjhKLxTU1NWQyWe4PI4VC0dHR4fP50s50JctUFi1aJJd2vHnzxtHR0dTUVLaRz+dnZmZaWVlZWloOHTpUoSEqj9ZvJkYoFIaEhOTl5S1cuHDFihXw/bVDrK2tyWRyVlaW7D314cOH1dXVNjY2UFPpqLS0tHXr1n3xxRd79+4dPnw43uEoK319fS6XK9vS1NR07dq1xsZGJyengQMHQg796ezs7BITE3k8noODg/Qa5/P5RUVF5ubmffr0wTc8JaKpqamjo4PlK7LtjY2NNTU1Ghoa776WKHpFOoW4dOkSrFHbOdhii3Jr1IJPV1VV5eLiYmNjI11gEdao7bS7d+/a2NjIrlELuopQKPTy8oI1ajuhrKxs/PjxNjY2mZmZWAu2dDKDwYA1ajsqJSWFwWDMnTu3pqYGa3n79u2OHTsYDEZ4eDi2BDCKokpWUwHd7f79+2fPnkUQ5MiRI8ePH5d7dPPmzTC7qn16enr+/v5BQUFz5swZN25c7969eTxeQ0PDqlWrYKxPh0gkksOHD2OL0Hh7e8s9am1tHRERAUuqAMUzMjJau3ZtUFDQ/PnzWSyWoaFhVlZWVVWVo6Oju7s73tEpGWdnZy8vr+PHj48bN27MmDE0Gi0nJ6e8vNzKymrhwoXSmgpkKuA9eXl52PTFNtcFgYXLPoWLi4uurm5kZGRGRkZLS4uZmVlQUJCzszMMsOiQmpoabDnthoaGhoYGuUeNjY1R2PER4OTrr79OSkraunVrTk5OTk6OoaFhaGjozJkzKRQK3qEpGTKZHB4ePnr06Ojo6CtXrjQ3NxsaGq5Zs8bLy0s6RRlBEBJc7QAAAAAgLCWbpQwAAACAHgUyFQAAAAAQF2QqAAAAACAuyFQAAAAAQFyQqQAAAACAuCBTAQAAAABxQaYCAAAAAOKCTAUAAAAAxAWZCgAAAACICzIVAAAAABAXZCoAAAAAIC7IVAAAAABAXJCpAAAAAIC4IFMBAAAAAHFBpgIAICKhUMjlchkMxrp16yQSibT91KlTZmZmEyZM4PP5OIYHAFAYyFQAAEREo9FWrVpFo9F+//33GzduYI1lZWXR0dFkMjk4ONjIyAjfCAEAigGZCgCAoKytrb/99tu3b99GR0cLhcKmpqaoqKiSkhJPT08nJye8owMAKIgG3gEAAEDbSCTSggULsrKy8vLyUlJS+vbtm5KSYmZmtmTJEjKZjHd0AAAFIaEoincMAADwQZmZmb6+vlQqVU1Nrb6+fseOHS4uLngHBQBQHOj9AQAQGofDmT17dk1NTXV19fTp0ydMmIB3RAAAhYJMBQBAaCQSicVikclkEolkYmKioQF91gD0LJCpAAAITSAQ7N69WyKRqKurHzx48OnTp3hHBABQKMhUAADEhaLovn37njx54uHh4ePjIxAIfvnll8bGRrzjAgAoDmQqAADiys3N/f333/X09Pz8/Hx9fS0sLC5fvnz+/Hm84wIAKA5kKgAAgqqtrf35558bGhoWLlw4ZMgQPT09f39/DQ2N7du3l5SU4B0dAEBBIFMBABARiqInTpy4d+8ei8XicrlYo5OT08SJE8vLy/fu3dvU1IRvhAAAxYBMBQBARPfu3YuLi6NSqUFBQTQaDWskk8n+/v56enpnzpxJT0/HN0IAgGLAym8AAAAAIC6oqQAAAACAuP4fefWbIg8TYlsAAAAASUVORK5CYII=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57560,"title":"Hermite Polynomials","description":"Problem 1304 deals with Hermite polynomial of the physicist's type.\r\nIn this problem, Return the n-th Hermite polynomial of the probabilist' type.\r\nAssume that n is a non-negative finite integer.\r\nExamples:\r\n hermite_poly(0)\r\n ans = \r\n 1\r\n\r\n hermite_poly(1)\r\n ans = \r\n 1 0\r\n\r\n hermite_poly(2)\r\n ans = \r\n 1 0 -1\r\n\r\nNeither string operations nor interpolations are allowed!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 406.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 203.383px; transform-origin: 407px 203.383px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1304\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 1304\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116.5px 8px; transform-origin: 116.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with Hermite polynomial of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ephysicist\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's type.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5px 8px; transform-origin: 85.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, Return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.5px 8px; transform-origin: 8.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hermite_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHermite polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22px 8px; transform-origin: 22px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eprobabilist\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e' type.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39px 8px; transform-origin: 39px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a non-negative finite integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 224.767px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 112.383px; transform-origin: 404px 112.383px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(0)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 -1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 8px; transform-origin: 24.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNeither \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.5px 8px; transform-origin: 60.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estring operations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e nor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einterpolations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are allowed!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hermite_poly(n)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hermite_poly.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, 'interp') || contains(filetext, '2str') || ...\r\n contains(filetext, 'str2'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [1 0 -1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [1 0 -3 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [1 0 -6 0 3];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [1 0 -10 0 15 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [1 0 -15 0 45 0 -15];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [1 0 -21 0 105 0 -105 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [1 0 -28 0 210 0 -420 0 105];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [1 0 -36 0 378 0 -1260 0 945 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1 0 -45 0 630 0 -3150 0 4725 0 -945];\r\nassert(isequal(hermite_poly(n),P_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":223089,"edited_by":223089,"edited_at":"2023-01-20T06:47:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-18T07:24:00.000Z","updated_at":"2026-01-26T13:48:46.000Z","published_at":"2023-01-18T07:24:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1304\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 1304\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with Hermite polynomial of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ephysicist\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e's type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, Return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hermite_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHermite polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprobabilist\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e' type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ hermite_poly(0)\\n ans = \\n 1\\n\\n hermite_poly(1)\\n ans = \\n 1 0\\n\\n hermite_poly(2)\\n ans = \\n 1 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44260,"title":"Multivariate polynomials - convert monomial form to array","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials Problem 44259\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\r\n\r\n# Defining a polynomial is an indexing headache, with a high probability of errors. \r\n# Polynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\r\n\r\nHere, we will represent a polynomial as a sum of monomials. For example, the polynomial |p(x,y) = 2*x^5*y + 3*x*y^5| is the sum of two monomials in |x| and |y|. We will represent this by |exponents|, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector |coefficients| for the coefficient of each monomial. For |p(x,y)|, these are\r\n\r\n exponents = [5 1; 1 5];\r\ncoefficients = [2; 3];\r\n\r\nLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\r\n\r\n function c = coeffArray(exponents,coefficients)\r\n\r\nthat inputs the exponents and coefficients and returns an array as defined in Problem 44259.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials\"\u003eProblem 44259\u003c/a\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\u003c/p\u003e\u003col\u003e\u003cli\u003eDefining a polynomial is an indexing headache, with a high probability of errors.\u003c/li\u003e\u003cli\u003ePolynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eHere, we will represent a polynomial as a sum of monomials. For example, the polynomial \u003ctt\u003ep(x,y) = 2*x^5*y + 3*x*y^5\u003c/tt\u003e is the sum of two monomials in \u003ctt\u003ex\u003c/tt\u003e and \u003ctt\u003ey\u003c/tt\u003e. We will represent this by \u003ctt\u003eexponents\u003c/tt\u003e, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector \u003ctt\u003ecoefficients\u003c/tt\u003e for the coefficient of each monomial. For \u003ctt\u003ep(x,y)\u003c/tt\u003e, these are\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [5 1; 1 5];\r\ncoefficients = [2; 3];\r\n\u003c/pre\u003e\u003cp\u003eLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction c = coeffArray(exponents,coefficients)\r\n\u003c/pre\u003e\u003cp\u003ethat inputs the exponents and coefficients and returns an array as defined in Problem 44259.\u003c/p\u003e","function_template":"function c = coeffArray(exponents,coefficients)\r\nc = 0;\r\nend","test_suite":"%% test coeffArray\r\nfiletext = fileread('coeffArray.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% No variables\r\nexponents = 0;\r\ncoefficients = randi(1000);\r\ncA = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% Single variable\r\ncoefficients = randi(1000,[10 1]);\r\nexponents = (9:-1:0)';\r\ncA = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% a*x^2+b*y\r\na = randi(1000);\r\nb = randi(1000);\r\nexponents = [2 0; 0 1];\r\ncoefficients = [a; b];\r\ncA = [0 a; 0 0; b 0];\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% a*x^2+b*y^2+c*z^2+d\r\na = randi(1000);\r\nb = randi(1000);\r\nc = randi(1000);\r\nd = randi(1000);\r\nexponents = [2 0 0; 0 2 0; 0 0 2; 0 0 0];\r\ncoefficients = [a; b; c; d];\r\ncA = zeros([3 3 3]);\r\ncA(1,3,3) = a;\r\ncA(3,1,3) = b;\r\ncA(3,3,1) = c;\r\ncA(3,3,3) = d;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% Many variables\r\ncoefficients = randi(1000);\r\nnVars = randi(20)+1;\r\nexponents = ones(1,nVars);\r\ncA = zeros(2*ones(1,nVars));\r\ncA(1) = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-13T16:16:41.000Z","updated_at":"2025-12-22T13:09:01.000Z","published_at":"2017-07-13T16:26:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44259\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefining a polynomial is an indexing headache, with a high probability of errors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePolynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, we will represent a polynomial as a sum of monomials. For example, the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y) = 2*x^5*y + 3*x*y^5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the sum of two monomials in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. We will represent this by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the coefficient of each monomial. For\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, these are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [5 1; 1 5];\\ncoefficients = [2; 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function c = coeffArray(exponents,coefficients)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethat inputs the exponents and coefficients and returns an array as defined in Problem 44259.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1476,"title":"Radial Zernike polynomials","description":"Given an integer _n_ \u0026ge; 0 and an integer _m_ \u0026ge; 0, generate the \u003chttp://en.wikipedia.org/wiki/Zernike_polynomials radial Zernike polynomial\u003e of radial degree _n_ and azimuthal degree _m_. You may assume that |mod(n-m,2)==0| and _m_ \u0026le; _n_.\r\n\r\n*Examples*:\r\n\r\n radialZernike(0,0)\r\n ans =\r\n 1\r\n\r\n radialZernike(1,1)\r\n ans =\r\n 1 0\r\n\r\n radialZernike(2,0)\r\n ans =\r\n 2 0 -1\r\n\r\n radialZernike(2,2)\r\n ans =\r\n 1 0 0\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0 and an integer \u003ci\u003em\u003c/i\u003e \u0026ge; 0, generate the \u003ca href = \"http://en.wikipedia.org/wiki/Zernike_polynomials\"\u003eradial Zernike polynomial\u003c/a\u003e of radial degree \u003ci\u003en\u003c/i\u003e and azimuthal degree \u003ci\u003em\u003c/i\u003e. You may assume that \u003ctt\u003emod(n-m,2)==0\u003c/tt\u003e and \u003ci\u003em\u003c/i\u003e \u0026le; \u003ci\u003en\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e radialZernike(0,0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e radialZernike(1,1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e radialZernike(2,0)\r\n ans =\r\n 2 0 -1\u003c/pre\u003e\u003cpre\u003e radialZernike(2,2)\r\n ans =\r\n 1 0 0\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = radialZernike(n,m)\r\n P = n*m;\r\nend","test_suite":"%%\r\nuser_solution = fileread('radialZernike.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nm = 0;\r\nP_correct = [1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 1;\r\nm = 1;\r\nP_correct = [1 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 2;\r\nm = 0;\r\nP_correct = [2 0 -1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 2;\r\nm = 2;\r\nP_correct = [1 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 3;\r\nm = 1;\r\nP_correct = [3 0 -2 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 3;\r\nm = 3;\r\nP_correct = [1 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 0;\r\nP_correct = [6 0 -6 0 1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 2;\r\nP_correct = [4 0 -3 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 4;\r\nP_correct = [1 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 1;\r\nP_correct = [10 0 -12 0 3 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 3;\r\nP_correct = [5 0 -4 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 5;\r\nP_correct = [1 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 0;\r\nP_correct = [20 0 -30 0 12 0 -1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 2;\r\nP_correct = [15 0 -20 0 6 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 4;\r\nP_correct = [6 0 -5 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 6;\r\nP_correct = [1 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 1;\r\nP_correct = [35 0 -60 0 30 0 -4 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 3;\r\nP_correct = [21 0 -30 0 10 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 5;\r\nP_correct = [7 0 -6 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 7;\r\nP_correct = [1 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 0;\r\nP_correct = [70 0 -140 0 90 0 -20 0 1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 2;\r\nP_correct = [56 0 -105 0 60 0 -10 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 4;\r\nP_correct = [28 0 -42 0 15 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 6;\r\nP_correct = [8 0 -7 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 8;\r\nP_correct = [1 0 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 1;\r\nP_correct = [126 0 -280 0 210 0 -60 0 5 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 3;\r\nP_correct = [84 0 -168 0 105 0 -20 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 5;\r\nP_correct = [36 0 -56 0 21 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 7;\r\nP_correct = [9 0 -8 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 9;\r\nP_correct = [1 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2013-04-30T13:10:33.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T13:05:27.000Z","updated_at":"2026-04-08T15:23:08.000Z","published_at":"2013-04-30T13:10:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0 and an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Zernike_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradial Zernike polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of radial degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and azimuthal degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. You may assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emod(n-m,2)==0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≤\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ radialZernike(0,0)\\n ans =\\n 1\\n\\n radialZernike(1,1)\\n ans =\\n 1 0\\n\\n radialZernike(2,0)\\n ans =\\n 2 0 -1\\n\\n radialZernike(2,2)\\n ans =\\n 1 0 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61145,"title":"Translating even-degree polynomial by its vertex to the origin","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint. Compare to the Problem 61143.\r\ninput: p\r\noutput: [d, v, h]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 157.587px; transform-origin: 408px 157.594px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed (d\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the shifting distance of the above translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Compare to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61143\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[d, v, h]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_vertex(p)\r\n d = x;\r\n v = x;\r\n h = x;\r\nend","test_suite":"%%\r\np = [1 0 0 0 -1];\r\nd_correct = 1;\r\nv_correct = 'up';\r\nh_correct = '';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [1/4 -1/3 -2.5 -3 16.25];\r\nd_correct = 5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.25 -1 0.5 -3 15.25];\r\nd_correct = 5;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_vertex.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 54];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nd_correct = 2;\r\nv_correct = '';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-0.5 -2.4 3 22 -4.5 -54 -25.4];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-04T13:00:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-26T17:29:02.000Z","updated_at":"2026-03-26T10:19:33.000Z","published_at":"2026-01-04T13:00:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Compare to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[d, v, h]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55270,"title":"Cyclotomic Polynomials","description":"Given a Natural number (N), return the corresponding Cyclotomic Polynomial.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171px 8px; transform-origin: 171px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a Natural number (N), return the corresponding \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Cyclotomic_polynomial\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCyclotomic Polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = cyclcopoly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('cyclcopoly.m');\r\nassert(isempty(strfind(filetext, 'assignin')))\r\nassert(isempty(strfind(filetext, 'switch')))\r\nassert(isempty(strfind(filetext, 'else')))\r\n\r\n%%\r\nx = 1;\r\ny = [1 -1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 6;\r\ny = [1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 7;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 8;\r\ny = [1 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 9;\r\ny = [1 0 0 1 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 10;\r\ny = [1 -1 1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 12;\r\ny = [1 0 -1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 14;\r\ny = [1 -1 1 -1 1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 15;\r\ny = [1 -1 0 1 -1 1 0 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 16;\r\ny = [1 0 0 0 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 18;\r\ny = [1 0 0 -1 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 24;\r\ny = [1 0 0 0 -1 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 25;\r\ny = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 27;\r\ny = [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 28;\r\ny = [1 0 -1 0 1 0 -1 0 1 0 -1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 105;\r\ny = [1 1 1 0 0 -1 -1 -2 -1 -1 0 0 1 1 1 1 1 1 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 0 1 1 1 1 1 1 0 0 -1 -1 -2 -1 -1 0 0 1 1 1]; \r\nassert(isequal(cyclcopoly(x),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-12T05:04:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-01T15:05:58.000Z","updated_at":"2026-01-25T13:40:43.000Z","published_at":"2022-08-01T15:05:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a Natural number (N), return the corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Cyclotomic_polynomial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCyclotomic Polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44262,"title":"Multivariate polynomials - overload multiplication","description":"Problems \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array 44260\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials 44261\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix |exponents| with a row of exponents for each monomial, and a column vector |coefficients| with a coefficient for each monomial.\r\n\r\nIt would be nice to define polynomials so they can be multiplied using simple notation:\r\n\r\n p = p1*p2;\r\n\r\nThis can be done by \u003chttps://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html defining a class\u003e |mPoly| with two properties, |exponents| and |coefficients|, and two methods: a \u003chttps://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html constructor\u003e with the syntax\r\n\r\n p = mPoly(exponents, coefficients)\r\n\r\nand a method \u003chttps://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026s_tid=doc_srchtitle mtimes\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\r\n","description_html":"\u003cp\u003eProblems \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array\"\u003e44260\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials\"\u003e44261\u003c/a\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix \u003ctt\u003eexponents\u003c/tt\u003e with a row of exponents for each monomial, and a column vector \u003ctt\u003ecoefficients\u003c/tt\u003e with a coefficient for each monomial.\u003c/p\u003e\u003cp\u003eIt would be nice to define polynomials so they can be multiplied using simple notation:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = p1*p2;\r\n\u003c/pre\u003e\u003cp\u003eThis can be done by \u003ca href = \"https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html\"\u003edefining a class\u003c/a\u003e \u003ctt\u003emPoly\u003c/tt\u003e with two properties, \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and two methods: a \u003ca href = \"https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html\"\u003econstructor\u003c/a\u003e with the syntax\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = mPoly(exponents, coefficients)\r\n\u003c/pre\u003e\u003cp\u003eand a method \u003ca href = \"https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026s_tid=doc_srchtitle\"\u003emtimes\u003c/a\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\u003c/p\u003e","function_template":"classdef mPoly \r\n %MPOLY Class of multivariate polynomials\r\n \r\n properties\r\n exponents\r\n coefficients\r\n end\r\n \r\n methods\r\n function p = mPoly(ex,co)\r\n end\r\n function p = mtimes(p1,p2)\r\n end\r\n end\r\n \r\nend\r\n","test_suite":"%% Test polyMult\r\nfiletext = fileread('mPoly.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% p1 = A, p2 = B\r\nc1 = randi(1000); c2 = randi(1000);\r\ne = 0;\r\np1 = mPoly(e,c1);\r\np2 = mPoly(e,c2);\r\np = p1*p2;\r\nassert(isequal(c1*c2,p.coefficients))\r\nassert(isequal(e,p.exponents))\r\n\r\n%% p1 = y-x^2, p2 = x-2\r\ne1 = [2 0; 0 1];\r\nc1 = [-1; 1];\r\ne2 = [1 0; 0 0];\r\nc2 = [1; -2];\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 1; 1 1; 2 0; 3 0]))\r\nassert(isequal(c,[-2; 1; 2; -1]))\r\n\r\n%% p1 = y-x^2, p2 = z-2\r\ne1 = [0 1 0; 2 0 0];\r\nc1 = [1; -1];\r\ne2 = [0 0 1; 0 0 0];\r\nc2 = [1; -2];\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 1 0; 0 1 1; 2 0 0; 2 0 1]))\r\nassert(isequal(c,[-2; 1; 2; -1]))\r\n\r\n\r\n%% p1 = z-x^3, p2 = x^2+y^2+z^2-1\r\ne1 = [0 0 1; 3 0 0];\r\nc1 = [1; -1];\r\ne2 = [2 0 0; 0 2 0; 0 0 2; 0 0 0];\r\nc2 = [1; 1; 1; -1];\r\n\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 0 1; 0 0 3; 0 2 1; 2 0 1; 3 0 0; 3 0 2; 3 2 0; 5 0 0]))\r\nassert(isequal(c,[-1 1 1 1 1 -1 -1 -1]'))\r\n\r\n%% Commutative\r\nc1 = randi(1000,[2 1]);\r\ne1 = randi(1000,[2 2]);\r\nc2 = randi(1000,[3 1]);\r\ne2 = randi(1000,[3 2]);\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np12 = p1*p2;\r\np21 = p2*p1;\r\n[e12,i12] = unique(p12.exponents,'rows');\r\n[e21,i21] = unique(p21.exponents,'rows');\r\nc12 = p12.coefficients(i12);\r\nc21 = p21.coefficients(i21);\r\nassert(isequal(e12,e21))\r\nassert(isequal(c12,c21))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T04:04:05.000Z","updated_at":"2025-12-22T13:16:38.000Z","published_at":"2017-07-14T04:04:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44260\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44261\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with a row of exponents for each monomial, and a column vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with a coefficient for each monomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt would be nice to define polynomials so they can be multiplied using simple notation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = p1*p2;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis can be done by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edefining a class\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with two properties,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and two methods: a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econstructor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with the syntax\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = mPoly(exponents, coefficients)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand a method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026amp;s_tid=doc_srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emtimes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60996,"title":"Dickson Polynomials","description":"Return the coefficients of nth (n\u003e=0) Dickson polynomial of the 1st kind as follows - \r\n1st row of the output will be the coefficients of x, and, 2nd row of the output will be the coefficients of alpha.\r\n\r\nWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \r\n%Examplesa\r\nn=2;\r\nD2(x, alpha) = x^2 - 2*alpha\r\nOutput = [1 0 -2; 0 -2 1]\r\n\r\nn=3;\r\nD3(x, alpha) = x^3 - 3*x*alpha\r\nOutput = [1 0 -3 0; 0 0 -1 1]\r\n\r\nn=5;\r\nD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\r\n% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\r\n% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\r\n% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\r\nOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]\r\n\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 539.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 269.75px; transform-origin: 408px 269.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.2167px 8px; transform-origin: 79.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8417px 8px; transform-origin: 33.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enth (n\u0026gt;=0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Dickson_polynomial\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDickson polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.3917px 8px; transform-origin: 84.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the 1st kind as follows - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1st row of the output will be the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.783px 8px; transform-origin: 164.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and, 2nd row of the output will be the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ealpha\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.608px 8px; transform-origin: 375.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 306.5px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 153.25px; transform-origin: 405px 153.25px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examplesa\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD2(x, alpha) = x^2 - 2*alpha\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -2; 0 -2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.5px; tab-size: 4; transform-origin: 115.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD3(x, alpha) = x^3 - 3*x*alpha\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -3 0; 0 0 -1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 177.1px 8.5px; tab-size: 4; transform-origin: 177.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 327.25px 8.5px; tab-size: 4; transform-origin: 327.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.45px 8.5px; tab-size: 4; transform-origin: 219.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 311.85px 8.5px; tab-size: 4; transform-origin: 311.85px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.167px 8px; transform-origin: 262.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = dicksonpoly(n)\r\n y = n^2;\r\nend","test_suite":"%%\r\nfiletext = fileread('dicksonpoly.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\ny = [1 0; 0 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 2;\r\ny = [1 0 -2; 0 -2 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 3;\r\ny = [1 0 -3 0; 0 0 -3 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 4;\r\ny = [1 0 -4 0 2; 0 0 2 -4 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 5;\r\ny = [1 0 -5 0 5 0; 0 0 0 5 -5 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 6;\r\n%D6(x, alpha) = x^6 - 6*alpha*x^4 + 9*alpha^2*x^2 - 2*alpha^3\r\ny = [1 0 -6 0 9 0 -2; 0 0 0 -2 9 -6 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 9;\r\n%D9(x, alpha) = x^9 - 9*alpha*x^7 + 27*alpha^2*x^5 - 30*alpha^3*x^3 + 9*alpha^4*x\r\ny = [1 0 -9 0 27 0 -30 0 9 0; 0 0 0 0 0 9 -30 27 -9 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 10;\r\n%D10(x, alpha) = x^10 - 10*alpha*x^8 + 35*alpha^2*x^6 - 50*alpha^3*x^4 + 25*alpha^4*x^2 - 2*alpha^5\r\ny = [1 0 -10 0 35 0 -50 0 25 0 -2; 0 0 0 0 0 -2 25 -50 35 -10 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-10T16:35:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-07T17:01:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-07T15:27:35.000Z","updated_at":"2026-01-26T13:57:28.000Z","published_at":"2025-09-07T15:27:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enth (n\u0026gt;=0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Dickson_polynomial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDickson polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the 1st kind as follows - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1st row of the output will be the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and, 2nd row of the output will be the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ealpha\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examplesa\\nn=2;\\nD2(x, alpha) = x^2 - 2*alpha\\nOutput = [1 0 -2; 0 -2 1]\\n\\nn=3;\\nD3(x, alpha) = x^3 - 3*x*alpha\\nOutput = [1 0 -3 0; 0 0 -1 1]\\n\\nn=5;\\nD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\\n% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\\n% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\\n% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\\nOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2163,"title":"Evaluate Polynomial","description":"Given a polynomial equation coefficients in a vector p, you have to return its value at x.\r\n\r\nExample:\r\n\r\nFor inputs p and x\r\n\r\n p = [1 0 1]\r\n x = [1 4]\r\n\r\nOutput y is [1*1^2 + 1, 1*4^2 + 1] or \r\n\r\n y = [2 17]","description_html":"\u003cp\u003eGiven a polynomial equation coefficients in a vector p, you have to return its value at x.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003eFor inputs p and x\u003c/p\u003e\u003cpre\u003e p = [1 0 1]\r\n x = [1 4]\u003c/pre\u003e\u003cp\u003eOutput y is [1*1^2 + 1, 1*4^2 + 1] or\u003c/p\u003e\u003cpre\u003e y = [2 17]\u003c/pre\u003e","function_template":"function y = polynomial(p,x)\r\n y = 0;\r\nend","test_suite":"%%\r\np = [1 0 -8 -7 5];\r\nx = [ 5 7 9 ];\r\ny_correct = [ 395 1965 5855];\r\nassert(isequal(polynomial(p,x),y_correct))\r\n\r\n%%\r\np = [1 0 -10 0 0 0 11 -50];\r\nx = [3 7 4 5];\r\ny_correct = [-260 655500 6138 46880]\r\nassert(isequal(polynomial(p,x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":147,"test_suite_updated_at":"2014-02-07T15:58:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T05:50:19.000Z","updated_at":"2026-03-09T18:42:08.000Z","published_at":"2014-02-07T05:50:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a polynomial equation coefficients in a vector p, you have to return its value at x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor inputs p and x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = [1 0 1]\\n x = [1 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput y is [1*1^2 + 1, 1*4^2 + 1] or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 17]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43617,"title":"Calculate the values of a polynomial.","description":"Calculate the values of a polynomial.Input parameter p - vector of polynomial coefficients, x - matrix of the argument values.\r\n\r\nExample \r\n\r\np=[-1 1]\r\n\r\nx=[1 2;3 4]\r\n\r\nresult=[ 0 -1; -2 -3]","description_html":"\u003cp\u003eCalculate the values of a polynomial.Input parameter p - vector of polynomial coefficients, x - matrix of the argument values.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ep=[-1 1]\u003c/p\u003e\u003cp\u003ex=[1 2;3 4]\u003c/p\u003e\u003cp\u003eresult=[ 0 -1; -2 -3]\u003c/p\u003e","function_template":"function y = SolvePoly(p,x)\r\n y = x;\r\nend","test_suite":"%%\r\np=[-1 1]\r\nx=[1 2;3 4]\r\ny_correct=[ 0 -1; -2 -3]\r\nassert(isequal(SolvePoly(p,x),y_correct))\r\n%%\r\np=[-2 0 1 -1 3 2]\r\nx=[5 6 11; 2 13 7; 4 9 21]\r\ny_correct=[-6133 -15352 -320857;\r\n -52 -740517 -33297;\r\n -1986 -117421 -8159317]\r\nassert(isequal(SolvePoly(p,x),y_correct)) ","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":87,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T22:55:06.000Z","updated_at":"2026-02-25T20:49:54.000Z","published_at":"2016-10-24T22:55:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the values of a polynomial.Input parameter p - vector of polynomial coefficients, x - matrix of the argument values.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[-1 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[1 2;3 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[ 0 -1; -2 -3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43621,"title":"Get derivarive of polynomial given as vector array.","description":"Get derivarive of polynomial given as vector array.\r\n\r\nExample \r\n\r\np=[ 1 2 0 5 0 3 ];\r\n\r\nresult=[ 5 8 0 10 0 ];","description_html":"\u003cp\u003eGet derivarive of polynomial given as vector array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ep=[ 1 2 0 5 0 3 ];\u003c/p\u003e\u003cp\u003eresult=[ 5 8 0 10 0 ];\u003c/p\u003e","function_template":"function y = PolyPol(x)\r\n y = x;\r\nend","test_suite":"%%\r\np = [ 1 2 0 5 0 3 ];\r\ny_correct = [ 5 8 0 10 0 ];\r\nassert(isequal(PolyPol(p),y_correct))\r\n%%\r\np = [ 3 2 5 1 0 2];\r\ny_correct = [ 15 8 15 2 0 ];\r\nassert(isequal(PolyPol(p),y_correct))\r\n%%\r\np = [ 15 8 15 2 0 ];\r\ny_correct = [ 60 24 30 2 ];\r\nassert(isequal(PolyPol(p),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":84,"test_suite_updated_at":"2016-10-25T09:14:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T09:10:39.000Z","updated_at":"2026-04-07T19:10:13.000Z","published_at":"2016-10-25T09:14:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGet derivarive of polynomial given as vector array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep=[ 1 2 0 5 0 3 ];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[ 5 8 0 10 0 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24;\r\nassert(isequal(PolSol(a,b),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-25T18:45:55.000Z","updated_at":"2026-02-10T11:32:57.000Z","published_at":"2016-10-25T18:45:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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array.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ex=[1 2 0 5 0 3]\u003c/p\u003e\u003cp\u003eresult=[-2.7267 ; \r\n 0.4784 + 1.0983i;\r\n 0.4784 - 1.0983i;\r\n -0.1150 + 0.8680i;\r\n -0.1150 - 0.8680i]\u003c/p\u003e","function_template":"function y = PolRoot(x)\r\n y=x\r\nend","test_suite":"%%\r\nx = [1 2 0 5 0 3];\r\ny_correct = [-2.7267 + 0.0000i ;0.4784 + 1.0983i ;0.4784 - 1.0983i ;-0.1150 + 0.8680i ;-0.1150 - 0.8680i];\r\ny=PolRoot(x)\r\nassert(abs(y(1)-y_correct(1))\u003c10^(-4))\r\nassert(abs(y(2)-y_correct(2))\u003c10^(-4))\r\nassert(abs(y(3)-y_correct(3))\u003c10^(-4))\r\nassert(abs(y(4)-y_correct(4))\u003c10^(-4))\r\n%%\r\nx = [3 2 5 1 0 2];\r\ny_correct = [-0.3205 + 1.2968i; -0.3205 - 1.2968i; -0.7915 + 0.0000i; 0.3829 + 0.5704i; 0.3829 - 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version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate roots of polynomial given as vector array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[1 2 0 5 0 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[-2.7267 ; 0.4784 + 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540];\r\nassert(isequal(multiply(a,b),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":138,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T06:42:09.000Z","updated_at":"2026-02-16T16:29:25.000Z","published_at":"2014-02-07T06:42:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply two polynomial equation.Given polynomial coefficients a and b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1183,"title":"Polynomial division","description":"Divide a polynomial u by polynomial v and return the quotients only.\r\n\r\nExample:\r\n\r\n u = x^4+3*x^3+5*x+3\r\n v = x^2+1\r\n\r\nAnswer:\r\n\r\n x^3+2*x+3","description_html":"\u003cp\u003eDivide a polynomial u by polynomial v and return the quotients only.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e u = x^4+3*x^3+5*x+3\r\n v = x^2+1\u003c/pre\u003e\u003cp\u003eAnswer:\u003c/p\u003e\u003cpre\u003e x^3+2*x+3\u003c/pre\u003e","function_template":"function y = poly_div(u,v)\r\n y = x;\r\nend","test_suite":"%%\r\nu = [1 3 5 3]; v = [1,1];\r\ny_correct = [1 2 3];\r\nassert(isequal(poly_div(u,v),y_correct));\r\n%%\r\nu=[4 -2 -14 -3 17 21 9]; v = [1 2 1];\r\ny_correct = [4 -10 2 3 9];\r\nassert(isequal(poly_div(u,v),y_correct));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":9752,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":107,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T04:43:36.000Z","updated_at":"2026-02-17T08:53:45.000Z","published_at":"2013-01-07T04:43:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide a polynomial u by polynomial v and return the quotients only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ u = x^4+3*x^3+5*x+3\\n v = x^2+1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnswer:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x^3+2*x+3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43618,"title":"Multiply two polynomials p and q given in in vector representation.","description":"Multiply two polynomials p and q given in vector representation.\r\nExample \r\np=[-2 0 1 -1 3 2]\r\n\r\nq=[1 0 -1 2 4]\r\n\r\nresult=[-2 0 3 -5 -6 5 -1 0 16 8]","description_html":"\u003cp\u003eMultiply two polynomials p and q given in vector representation.\r\nExample \r\np=[-2 0 1 -1 3 2]\u003c/p\u003e\u003cp\u003eq=[1 0 -1 2 4]\u003c/p\u003e\u003cp\u003eresult=[-2 0 3 -5 -6 5 -1 0 16 8]\u003c/p\u003e","function_template":"function y = MulPoly(p,q)\r\n y = x;\r\nend","test_suite":"%%\r\np=[-2 0 1 -1 3 2]\r\nq=[1 0 -1 2 4]\r\ny_correct =[-2 0 3 -5 -6 5 -1 0 16 8];\r\nassert(isequal(MulPoly(p,q),y_correct))\r\n%%\r\np=[-2 0 1 0 -3 1]\r\nq=[-1 0 -1 2 2]\r\ny_correct =[2 0 1 -4 -2 1 5 -7 -4 2];\r\nassert(isequal(MulPoly(p,q),y_correct))\r\n%%\r\np=[1 2 0 5 0 3]\r\nq=[3 2 5 1 0 2]\r\ny_correct =[3 8 9 26 12 36 15 15 13 0 6];\r\nassert(isequal(MulPoly(p,q),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T23:09:36.000Z","updated_at":"2026-02-17T14:22:13.000Z","published_at":"2016-10-24T23:09:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply two polynomials p and q given in vector representation. Example p=[-2 0 1 -1 3 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq=[1 0 -1 2 4]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eresult=[-2 0 3 -5 -6 5 -1 0 16 8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2164,"title":"Roots","description":"Find out the roots of a given polynomial equation.Given are the coefficients of the equation.","description_html":"\u003cp\u003eFind out the roots of a given polynomial equation.Given are the coefficients of the equation.\u003c/p\u003e","function_template":"function y = return_root(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 5 8 9 7 4 5];\r\ny_correct = roots(x); \r\nassert(isequal(return_root(x),y_correct))\r\n\r\nx = [1 0 0 48 50];\r\ny_correct = roots(x); \r\nassert(isequal(return_root(x),y_correct))\r\n\r\nx = [11 55 4 6 ];\r\ny_correct = roots(x)\r\nassert(isequal(return_root(x),y_correct))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":11900,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":424,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-02-07T06:11:07.000Z","updated_at":"2026-02-17T09:14:55.000Z","published_at":"2014-02-07T06:11:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out the roots of a given polynomial equation.Given are the coefficients of the equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44659,"title":"Nth root of a number","description":"Given an input and a number N, find the Nth root of the number(s)","description_html":"\u003cp\u003eGiven an input and a number N, find the Nth root of the number(s)\u003c/p\u003e","function_template":"function y = rootN(a,N)\r\n y = x;\r\nend","test_suite":"%%\r\na = 1;\r\nN = 100\r\ny_correct = 1;\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = [1 64 216];\r\nN = 3\r\ny_correct = [1 4 6];\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = 1/100;\r\nN = 2\r\ny_correct = 1/10;\r\nassert(isequal(rootN(a,N),y_correct))\r\n\r\n%%\r\na = 826^10;\r\nN = 10\r\ny_correct = 826;\r\nassert(isequal(rootN(a,N),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2018-05-29T13:54:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-29T13:48:03.000Z","updated_at":"2026-02-20T14:32:58.000Z","published_at":"2018-05-29T13:48:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3px; transform-origin: 404px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; 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border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = diff_poly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2 3 4];\r\ny_correct = [3 4 3];\r\nassert(isequal(diff_poly(x),y_correct))\r\n\r\n%%\r\nc=randi(100);\r\nx = [c randi(100)];\r\ny_correct = c;\r\nassert(isequal(diff_poly(x),y_correct))\r\n\r\n%%\r\nx = [6 5 3 4];\r\ny_correct = [18 10 3];\r\nassert(isequal(diff_poly(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":14267,"edited_by":223089,"edited_at":"2022-12-11T07:09:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":240,"test_suite_updated_at":"2022-12-11T07:09:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-05T23:15:12.000Z","updated_at":"2026-03-05T12:22:34.000Z","published_at":"2013-06-05T23:15:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ in = [ 1\\n 1\\n 1 ]\\n\\n out = [ 2\\n 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44847,"title":"Say type of roots in quadratic equation","description":"Given the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\r\n \r\n \r\n ","description_html":"\u003cp\u003eGiven the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n y = '';\r\nend","test_suite":"%%\r\nx = [1 1 1];\r\ny_correct = 'Complex';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [1 3 1];\r\ny_correct = 'RealDifferent';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [1 -4 4];\r\ny_correct = 'RealEqual';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":274816,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":"2019-02-13T20:27:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-02-13T20:26:09.000Z","updated_at":"2026-03-11T08:52:01.000Z","published_at":"2019-02-13T20:26:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the coefficients of a quadratic equation, write a function that gives the output y='RealDifferent' if the roots are real and different, y='RealEqual' if the roots are real and equal, and y='Complex' if the roots are complex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42775,"title":"Raise a polynomial to a power","description":"In Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\r\n\r\nIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)","description_html":"\u003cp\u003eIn Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\u003c/p\u003e\u003cp\u003eIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)\u003c/p\u003e","function_template":"function q = polypow(p,N)\r\n q = p^N; \r\nend","test_suite":"%%\r\np=[2];\r\nN=8;\r\ny_correct=256;\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=[1 1];\r\nN=1;\r\ny_correct=[1 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=[1 1];\r\nN=5;\r\ny_correct=[1 5 10 10 5 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=1:5;\r\nN=3;\r\ny_correct=[1 6 21 56 126 234 369 504 594 574 465 300 125];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=5:-1:1;\r\nN=3;\r\ny_correct=[125 300 465 574 594 504 369 234 126 56 21 6 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n\r\n%%\r\np=5:-1:1;\r\nN=1;\r\ny_correct=[5 4 3 2 1];\r\nassert(isequal(polypow(p,N),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8580,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":97,"test_suite_updated_at":"2016-03-16T17:46:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-16T17:30:45.000Z","updated_at":"2026-04-03T02:46:51.000Z","published_at":"2016-03-16T17:44:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Matlab, polynomials are represented by a vector of coefficients. For example, the polynomial p=a*x^2 + b*x + c is represented by the vector p=[a, b, c].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you will be given a polynomial p and a power N. We would like you to return the vector q that represents the polynominal p^N, the Nth power of p. If p = (x + 1), for instance, you will be returning the coefficients of (x+1)^N. (N will be a positive integer greater than 0.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44259,"title":"Product of two multivariate polynomials","description":"MATLAB \u003chttps://www.mathworks.com/help/matlab/polynomials.html has a few functions\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as |y-x^2| or |x^2+y^2+z^2-1|. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if |p(x) = A + B x^3|, then the coefficients are\r\n\r\n c = [B 0 0 A].\r\n\r\nNote this is same order as used by the builtin functions. A couple more examples: if |p(x,y) = x - y^2|, then\r\n\r\n c = [0 -1; 0 0; 1 0].\r\n\r\nIf |p(x,y,z) = z-2|, then |c| has dimensions |[1 1 2]| with |c(:,:,1) = 1| and |c(:,:,2) = -2|.\r\n\r\nThe challenge is to create a function |polyMult| that takes two arrays of coefficients for polynomials |p1| and |p2| and returns the coefficients for |p1*p2|. See the tests for examples.","description_html":"\u003cp\u003eMATLAB \u003ca href = \"https://www.mathworks.com/help/matlab/polynomials.html\"\u003ehas a few functions\u003c/a\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as \u003ctt\u003ey-x^2\u003c/tt\u003e or \u003ctt\u003ex^2+y^2+z^2-1\u003c/tt\u003e. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if \u003ctt\u003ep(x) = A + B x^3\u003c/tt\u003e, then the coefficients are\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ec = [B 0 0 A].\r\n\u003c/pre\u003e\u003cp\u003eNote this is same order as used by the builtin functions. A couple more examples: if \u003ctt\u003ep(x,y) = x - y^2\u003c/tt\u003e, then\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ec = [0 -1; 0 0; 1 0].\r\n\u003c/pre\u003e\u003cp\u003eIf \u003ctt\u003ep(x,y,z) = z-2\u003c/tt\u003e, then \u003ctt\u003ec\u003c/tt\u003e has dimensions \u003ctt\u003e[1 1 2]\u003c/tt\u003e with \u003ctt\u003ec(:,:,1) = 1\u003c/tt\u003e and \u003ctt\u003ec(:,:,2) = -2\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe challenge is to create a function \u003ctt\u003epolyMult\u003c/tt\u003e that takes two arrays of coefficients for polynomials \u003ctt\u003ep1\u003c/tt\u003e and \u003ctt\u003ep2\u003c/tt\u003e and returns the coefficients for \u003ctt\u003ep1*p2\u003c/tt\u003e. See the tests for examples.\u003c/p\u003e","function_template":"function c = polyMult(c1,c2)\r\n y = c1*c2;\r\nend","test_suite":"%% Test polyMult\r\nfiletext = fileread('polyMult.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% p1 = A*x, p2 = B*y\r\nc1 = randi(1000); c2 = randi(1000);\r\nassert(isequal(c1*c2,polyMult(c1,c2)))\r\n\r\n%% p1 = y-x^2, p2 = x-2\r\nc1 = [0 -1; 0 0; 1 0];\r\nc2 = [1; -2];\r\nc = [0 -1; 0 2; 1 0; -2 0];\r\nassert(isequal(c,polyMult(c1,c2)))\r\n\r\n%% p1 = y-x^2, p2 = z-2\r\nc1 = [0 -1; 0 0; 1 0];\r\nc2 = reshape([1; -2],[1 1 2]);\r\nc = reshape([0 0 1 -1 0 0 0 0 -2 2 0 0],[3 2 2]);\r\nassert(isequal(c,polyMult(c1,c2)))\r\n\r\n%% p1 = z-x^3, p2 = y-x^2, p3 = x^2+y^2+z^2-1, p4 = z-2\r\nc1 = reshape([0 0 0 1 -1 0 0 0],[4 1 2]);\r\nc2 = [0 -1; 0 0; 1 0];\r\nc3 = zeros([3 3 3]);\r\nc3([9 21 25]) = [1 1 1];\r\nc3(27) = -1;\r\nc4 = reshape([1; -2],[1 1 2]);\r\nc = zeros(8,4,5);\r\nc([56 91 104 118 126 139 149 153]) = -2*ones(1,8);\r\nc([30 53 78 88 92 101 115 123]) = -1*ones(1,8);\r\nc([24 59 72 86 94 107 117 121]) = 1*ones(1,8);\r\nc([62 85 110 120 124 133 147 155]) = 2*ones(1,8);\r\nassert(isequal(c,polyMult(c1,polyMult(c2,polyMult(c3,c4)))))\r\n\r\n%% Commutative\r\nc1 = randi(1000,[2 3 4]);\r\nc2 = randi(1000,[4 5 1]);\r\nassert(isequal(polyMult(c1,c2),polyMult(c2,c1)))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-11T22:41:35.000Z","updated_at":"2025-12-22T12:43:34.000Z","published_at":"2017-07-11T22:43:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/polynomials.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehas a few functions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for creating and manipulating single-variable polynomials, but outside of the Symbolic Math Toolbox there is nothing for multivariate polynomials such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey-x^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex^2+y^2+z^2-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Generalizing the approach for one variable, we can define an array of coefficients with one dimension for each variable. We will index them in decreasing order, for example if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = A + B x^3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then the coefficients are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = [B 0 0 A].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote this is same order as used by the builtin functions. A couple more examples: if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y) = x - y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[c = [0 -1; 0 0; 1 0].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y,z) = z-2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has dimensions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[1 1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(:,:,1) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec(:,:,2) = -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe challenge is to create a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolyMult\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that takes two arrays of coefficients for polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and returns the coefficients for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep1*p2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. See the tests for examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46726,"title":"[Thermodynamics] Polynomial fitting of heat capacity data","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 295.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147.95px; transform-origin: 407px 147.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.867px 8px; transform-origin: 378.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn easy way to describe the temperature-dependence of the ideal gas heat capacity is by use of polynomials. Given are a vector of temperatures \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.825px 8px; transform-origin: 175.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in Kelvin) and a vector if corresponding heat capacities \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eCP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.283px 8px; transform-origin: 102.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some substance (in J/mol K).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.292px 8px; transform-origin: 171.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function should perform a polynomial fit of degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.817px 8px; transform-origin: 147.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and return a function handle to that polynomial.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.9667px 8px; transform-origin: 64.9667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample (hydrogen):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 91.95px; transform-origin: 404px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 288.75px 8px; transform-origin: 288.75px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 219.45px 8px; transform-origin: 219.45px 8px; \"\u003eT = [300 400 500 600 700 800 900 1000]; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 69.3px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 69.3px 8px; \"\u003e% temperature in K\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 319.55px 8px; transform-origin: 319.55px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 219.45px 8px; transform-origin: 219.45px 8px; \"\u003eCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2]; \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 100.1px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 100.1px 8px; \"\u003e% heat capacity in J/mol K\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 319.55px 8px; transform-origin: 319.55px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 138.6px 8px; transform-origin: 138.6px 8px; \"\u003eFUN = cpFitting(T,CP,2); \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); perspective-origin: 180.95px 8px; text-decoration: none; text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); transform-origin: 180.95px 8px; \"\u003e% polynomial fitting and create function handle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8px; transform-origin: 42.35px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; FUN(350)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 29.0074\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8px; transform-origin: 42.35px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; FUN(940)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 29.9943\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function cpfun = cpFitting(T,CP,N)\r\n % T ... vector of temperatures in K\r\n % CP .. vector of heat capacities in J/mol K\r\n % N ... degree of the desired polynomial\r\n cpfun = @(t) t;\r\nend","test_suite":"%%\r\nT = 300:100:1000; % hydrogen @ 300K \u003c T \u003c 1000K\r\nCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2];\r\ncpfun = cpFitting(T,CP,2);\r\nassert(abs(cpfun(350)-29.0074) \u003c 1e-3 \u0026\u0026 abs(cpfun(550)-29.2505) \u003c 1e-3 \u0026\u0026 abs(cpfun(940)-29.9943) \u003c 1e-3);\r\n%%\r\nT = 500:100:1500; % water/steam @ 500K \u003c T \u003c 1500K\r\nCP = [35.22 36.22 37.5 38.74 40 41.27 42.52 43.75 44.94 46.06 47.11];\r\ncpfun = cpFitting(T,CP,3);\r\nassert(abs(cpfun(560)-35.842) \u003c 1e-3 \u0026\u0026 abs(cpfun(1000)-41.26) \u003c 1e-3 \u0026\u0026 abs(cpfun(1400)-46.0668) \u003c 1e-3);\r\n%%\r\nT = 100:100:1000; % methane @ 100K \u003c T \u003c 1000K\r\nCP = [33.28 33.51 35.76 40.63 46.63 52.74 58.6 64.08 69.14 73.75];\r\ncpfun = cpFitting(T,CP,3);\r\nassert(abs(cpfun(290)-35.993) \u003c 1e-3 \u0026\u0026 abs(cpfun(630)-54.1682) \u003c 1e-3 \u0026\u0026 abs(cpfun(950)-71.6749) \u003c 1e-3);\r\n%%\r\nstr = fileread('cpFitting.m'); % sorry, no regexp hacks :-)\r\nassert(isempty(regexp(str,'regexp')));","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":11486,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-11T12:11:15.000Z","updated_at":"2026-04-14T14:05:02.000Z","published_at":"2020-10-11T12:26:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eAn easy way to describe the temperature-dependence of the ideal gas heat capacity is by use of polynomials. Given are a vector of temperatures \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e (in Kelvin) and a vector if corresponding heat capacities \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e for some substance (in J/mol K).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYour function should perform a polynomial fit of degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and return a function handle to that polynomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eExample (hydrogen):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[T = [300 400 500 600 700 800 900 1000]; % temperature in K\\nCP = [28.85 29.18 29.26 29.32 29.44 29.62 29.88 30.2]; % heat capacity in J/mol K\\nFUN = cpFitting(T,CP,2); % polynomial fitting and create function handle\\n\u003e\u003e FUN(350)\\nans =\\n 29.0074\\n\u003e\u003e FUN(940)\\nans =\\n 29.9943]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44274,"title":"Calculate the sum of two polynomials","description":"Calculate the sum of two polynomials if they are written in notation with their coefficients.\r\nexample:\r\n() + () = \r\na=[3 4 5];\r\nb=[1 4 7 6];\r\n\r\noutput =[1 7 11 11];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 172.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86.3667px; transform-origin: 407px 86.3667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276.5px 8px; transform-origin: 276.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the sum of two polynomials if they are written in notation with their coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eexample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.5px 8px; transform-origin: 2.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 79px; height: 19px;\" width=\"79\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) + (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 108.5px; height: 19px;\" width=\"108.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) = \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 123.5px; height: 19px;\" width=\"123.5\" height=\"19\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 40px 8.5px; tab-size: 4; transform-origin: 40px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ea=[3 4 5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eb=[1 4 7 6];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eoutput =[1 7 11 11];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = rwpadd(a,b)\r\n p= a+b;\r\nend","test_suite":"%%\r\na=[3 4 5];\r\nb=[1 4 7 6];\r\ny_correct = [1 7 11 11];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=[1 1 1 3 -2];\r\nb=[1 3];\r\ny_correct = [1 1 1 4 1];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=[1];\r\nb=[1 2 3];\r\ny_correct = [1 2 4];\r\nassert(isequal(rwpadd(a,b),y_correct))\r\n\r\n%%\r\na=randi(10,1,5);\r\nb=[];\r\nassert(isequal(rwpadd(a,b),a))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":38144,"edited_by":223089,"edited_at":"2022-12-12T05:56:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":"2022-12-12T05:56:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-02T18:19:55.000Z","updated_at":"2026-04-07T18:12:52.000Z","published_at":"2017-08-02T18:19:55.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the sum of two polynomials if they are written in notation with their coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3x^2+4x+5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) + (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+4x^2+7x+6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) = \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^3+7x^2+11x+11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[a=[3 4 5];\\nb=[1 4 7 6];\\n\\noutput =[1 7 11 11];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0 0 1 1 2 2 3 3]\r\n y = [ 0 1 0 1 0 1 0 1]\r\n z = [-4 -1 -3 -2 0 -1 5 2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0 0 1 1 2 2 3 3]\r\n y = [ 0 1 0 1 0 1 0 1]\r\n z = [-4 -1 -3 -2 0 -1 5 2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n cxx=0;\r\n cxy=0;\r\n cyy=0;\r\n c00=0;\r\n c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":46,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2025-12-07T17:59:24.000Z","published_at":"2012-03-19T09:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0 0 1 1 2 2 3 3]\\n y = [ 0 1 0 1 0 1 0 1]\\n z = [-4 -1 -3 -2 0 -1 5 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":543,"title":"deconvolution","description":"* Suppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\r\n* In this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\r\n* Suppose there is another vector w like [1 -1].\r\n* In this example, the second polynomial is (x-1).\r\n* If x is any integer then the polynomial represented by (v/w) is integer?\r\n ","description_html":"\u003cul\u003e\u003cli\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/li\u003e\u003cli\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/li\u003e\u003cli\u003eSuppose there is another vector w like [1 -1].\u003c/li\u003e\u003cli\u003eIn this example, the second polynomial is (x-1).\u003c/li\u003e\u003cli\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/li\u003e\u003c/ul\u003e","function_template":"function yesno = integ(v,w)\r\n yesno=1==1/1; % yes\r\n yesno=1==1/2; % no\r\nend","test_suite":"%%\r\nv=[1 0 0 -1];\r\nw=[1 -1];\r\nassert(integ(v,w))\r\n%%\r\nv=[2 9 6 -1 16 -5];\r\nw=[2 3 -1 5];\r\nassert(integ(v,w))\r\n%%\r\nv=[1 4 10 20 35 50 58 58 49 30];\r\nw=1:6;\r\nassert(integ(v,w))\r\n%%\r\nv=1:10;\r\nw=1:6;\r\nassert(~integ(v,w))\r\n%%\r\nv=3:12;\r\nw=-3:2;\r\nassert(~integ(v,w))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-03-31T22:38:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-31T22:38:54.000Z","updated_at":"2025-12-08T23:40:32.000Z","published_at":"2012-03-31T22:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is a vector v like [1 0 0 -1], representing polynomial coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the polynimial is 1*x^3+0*x^2+0*x-1 or (x^3-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose there is another vector w like [1 -1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this example, the second polynomial is (x-1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf x is any integer then the polynomial represented by (v/w) is integer?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43619,"title":"Divide polynomial p1 by p2.","description":"Divide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\r\n\r\nExample\r\n\r\np1=[3 2 5 1 0 2 ] \r\n\r\np2=[1 2 0 5 0 3]\r\n\r\nThen q=[3] r=[0 -4 5 -14 0 -7]","description_html":"\u003cp\u003eDivide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003ep1=[3 2 5 1 0 2 ]\u003c/p\u003e\u003cp\u003ep2=[1 2 0 5 0 3]\u003c/p\u003e\u003cp\u003eThen q=[3] r=[0 -4 5 -14 0 -7]\u003c/p\u003e","function_template":"function [q,r] = DivPol(p1,p2)\r\n y = x;\r\nend","test_suite":"%%\r\np1=[3 2 5 1 0 2 ]\r\np2=[1 2 0 5 0 3]\r\n\r\nq_correct=[3] \r\nr_correct=[0 -4 5 -14 0 -7]\r\n[q,r]=DivPol(p1,p2)\r\n\r\nassert(isequal(q,q_correct))\r\nassert(isequal(r,r_correct))\r\n%%\r\np1=[-2 0 3 -5 -6 5 -1 0 16 8]\r\np2=[1 0 -1 2 4]\r\n\r\nq_correct=[-2 0 1 -1 3 2] \r\nr_correct=[0 0 0 0 0 0 0 0 0 0]\r\n[q,r]=DivPol(p1,p2)\r\n\r\nassert(isequal(q,q_correct))\r\nassert(isequal(r,r_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":90467,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-24T23:36:33.000Z","updated_at":"2026-04-14T13:21:38.000Z","published_at":"2016-10-24T23:36:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDivide polynomial p1 by p2 given as vectors. Return result q and r vectors which corresponds the quotient and remainder of division respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[3 2 5 1 0 2 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[1 2 0 5 0 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen q=[3] r=[0 -4 5 -14 0 -7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52303,"title":"Bessel Polynomials","description":"Return the n-th Bessel polynomial\r\nAssume that n is a non-negative finite integer.\r\n\r\nbessel_poly(0)\r\nans = 1\r\n\r\nbessel_poly(1)\r\nans = [1 1]\r\n\r\nbessel_poly(2)\r\nans = [3 3 1]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 254.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.233px; transform-origin: 407px 127.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.5px 8px; transform-origin: 8.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Bessel_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBessel\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.5px 8px; transform-origin: 35.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e polynomial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39px 8px; transform-origin: 39px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a non-negative finite integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 163.467px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 81.7333px; transform-origin: 404px 81.7333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(0)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = [1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ebessel_poly(2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans = [3 3 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bessel_poly(x)\r\n%Wear a mask\r\n%Stay home, stay safe\r\nend","test_suite":"%%\r\nx = 1;\r\ny = [1 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = [3 3 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 5;\r\ny = [945 945 420 105 15 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [105 105 45 10 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 7;\r\ny = [135135 135135 62370 17325 3150 378 28 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = [15 15 6 1];\r\nassert(isequal(bessel_poly(x),y))\r\n\r\n%%\r\nx = 0;\r\ny = 1;\r\nassert(isequal(bessel_poly(x),y))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-07-14T18:48:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-14T18:29:16.000Z","updated_at":"2026-04-14T12:40:39.000Z","published_at":"2021-07-14T18:46:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bessel_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBessel\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[bessel_poly(0)\\nans = 1\\n\\nbessel_poly(1)\\nans = [1 1]\\n\\nbessel_poly(2)\\nans = [3 3 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1633,"title":"Find the right x in a 1. order Polynomal (y = m*x+c)","description":"Given two points in a Cartesian coordinate system, find the x-value, where polynomial of 1. order (y = m*x+c) is equal to a given value c.\r\n\r\ne.g.: \r\nwe have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8;\r\nThe input is:\r\nx = [1 3], y = [2,6], c = 8.\r\n\r\nThe answer is 4.\r\n\r\nConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line. \r\n\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 102px; vertical-align: baseline; perspective-origin: 332px 102px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven two points in a Cartesian coordinate system, find the x-value on the line y = m*x+b where the y-value is equal to a given value c.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ee.g.: we have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8; The input is: x = [1 3], y = [2,6], c = 8.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe answer is 4.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = getTheRightPosition(x,y,c)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [1 2]; y = [5 6]; c = 5;\r\ny_correct = 1;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n%%\r\nx = [1 -2]; y = [1 -2]; c = 50;\r\ny_correct = 50;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 -2]; y = [1 2]; c = 50;\r\ny_correct = -146;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n\r\n%%\r\nx = [1 1]; y = [1 -2]; c = 50;\r\ny_correct = 1;\r\nassert(abs(getTheRightPosition(x,y,c)-y_correct)\u003c1e-10)\r\n%%\r\nx = [1 1]; y = [1 1]; c = 50;\r\ny_correct = NaN;\r\nassert(isequal(isnan(getTheRightPosition(x,y,c)),isnan(y_correct)))\r\n%%\r\nx = [1 2]; y = [1 1]; c = 50;\r\ny_correct = NaN;\r\nassert(isequal(isnan(getTheRightPosition(x,y,c)),isnan(y_correct)))\r\n%%\r\nx = [1 2]; y = [2 2]; c = 2;\r\ny_correct = Inf;\r\nassert(isequal(isinf(getTheRightPosition(x,y,c)),isinf(y_correct)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":12126,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-09T10:02:33.000Z","updated_at":"2025-12-29T14:46:22.000Z","published_at":"2013-06-09T10:35:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two points in a Cartesian coordinate system, find the x-value on the line y = m*x+b where the y-value is equal to a given value c.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.: we have the points P1(1,2) and P2(3,6) and we want wo know at which x-value y is equal to c = 8; The input is: x = [1 3], y = [2,6], c = 8.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe answer is 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the possibility that there isn't any solution (return NaN) of that there is an infinity amount of points (return Inf). Additionally consider that the point could represent a vertial line.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61007,"title":"Pseudo-Zernike Polynomials","description":"Problem #1476 deals with Radial Zernike Polynomials.\r\nHere, generate the Pseudo-Zernike Polynomials for a given order n and degree k -\r\n%Examples pR(n,k)\r\npR(0,0) = 1 =\u003e [1]\r\n\r\npR(1,1) = 3*r-2 =\u003e [3 -2]\r\n\r\npR(3,2) = 7*r^3 + 6*r^2 =\u003e [7 6 0 0]\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions. \r\n\r\n\t\t\r\n\t","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 304.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 152.3px; transform-origin: 408px 152.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.0083px 8px; transform-origin: 28.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProblem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1476\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#1476\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.767px 8px; transform-origin: 121.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with Radial Zernike Polynomials.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 8px; transform-origin: 60.2917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere, generate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pseudo-Zernike_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePseudo-Zernike Polynomials\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.8417px 8px; transform-origin: 54.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a given order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.21667px 8px; transform-origin: 6.21667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.675px 8px; transform-origin: 11.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.7333px 8px; transform-origin: 23.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003edegree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 61.3px; transform-origin: 405px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.5px; tab-size: 4; transform-origin: 65.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examples pR(n,k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 69.3px 8.5px; tab-size: 4; transform-origin: 69.3px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(0,0) = 1 =\u0026gt; [1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96.25px 8.5px; tab-size: 4; transform-origin: 96.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(1,1) = 3*r-2 =\u0026gt; [3 -2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 8.5px; tab-size: 4; transform-origin: 138.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003epR(3,2) = 7*r^3 + 6*r^2 =\u0026gt; [7 6 0 0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.108px 8px; transform-origin: 264.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.0667px 8px; transform-origin: 31.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 8px; transform-origin: 15.5333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pseudozernike(n,k)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('pseudozernike.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, 'str2num'); \r\n\r\n%%\r\ny = 1;\r\nassert(isequal(pseudozernike(0,0),y))\r\n\r\n%%\r\ny = [3 -2];\r\nassert(isequal(pseudozernike(1,0),y))\r\n\r\n%%\r\ny = [10 -12 3];\r\nassert(isequal(pseudozernike(2,0),y))\r\n\r\n%%\r\ny = [1 0 0 0];\r\nassert(isequal(pseudozernike(3,3),y))\r\n\r\n%%\r\ny = [84 -168 105 -20 0];\r\nassert(isequal(pseudozernike(4,1),y))\r\n\r\n%%\r\ny = [9 -8 0 0 0];\r\nassert(isequal(pseudozernike(4,3),y))\r\n\r\n%%\r\ny = [165 -360 252 -56 0 0];\r\nassert(isequal(pseudozernike(5,2),y))\r\n\r\n%%\r\ny = [11 -10 0 0 0 0];\r\nassert(isequal(pseudozernike(5,4),y))\r\n\r\n%%\r\ny = [1716 -5544 6930 -4200 1260 -168 7];\r\nassert(isequal(pseudozernike(6,0),y))\r\n\r\n%%\r\nn = randi([20 30]);\r\ny = [1 zeros(1,n)];\r\nassert(isequal(pseudozernike(n,n),y))\r\n\r\n%%\r\nn = randi([30 40]);\r\ny = [2*n+1 -2*n zeros(1,n-1)];\r\nassert(isequal(pseudozernike(n,n-1),y))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-10-24T15:17:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2025-09-21T09:16:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-21T08:30:15.000Z","updated_at":"2026-01-26T15:39:10.000Z","published_at":"2025-09-21T09:16:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1476\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#1476\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with Radial Zernike Polynomials.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, generate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pseudo-Zernike_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePseudo-Zernike Polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a given order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003edegree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examples pR(n,k)\\npR(0,0) = 1 =\u003e [1]\\n\\npR(1,1) = 3*r-2 =\u003e [3 -2]\\n\\npR(3,2) = 7*r^3 + 6*r^2 =\u003e [7 6 0 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57427,"title":"Intersection points of a polynomial","description":"Find the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\r\nInput: a polynomial represented by a vector of coefficients p .\r\nThe function returns a vector x containing the points of intersection of the polynomial with the X-axis,\r\nwhere x is sorted in ascending order and rounded to 4 digits after the decimal point.\r\nIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable y .\r\nHint: use the polynomial functions of MATLAB.\r\n\r\nExample: for the polynomial p(x) = x^2 - 3x + 1.25\r\ngiven by its vector of coefficients p = [1 -3 1.25]\r\nx = [ 0.5 \r\n 2.5 ]\r\ny = 1.25\r\n\r\n* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 411px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 205.5px; transform-origin: 407px 205.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eInput: a polynomial represented by a vector of coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function returns a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e containing the points of intersection of the polynomial with the X-axis,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is sorted in ascending order and rounded to 4 digits after the decimal point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ey \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHint: use the polynomial functions of MATLAB.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample: for the polynomial p(x) = x^2 - 3x + 1.25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003egiven by its vector of coefficients p = [1 -3 1.25]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e= [ 0.5 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e 2.5 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e = 1.25\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x y] = poly_intersection(p)\r\n x = p(1);\r\n y = 0;\r\nend","test_suite":"%%\r\np1 = [ 2 -9 1 10];\r\nx_correct =[-0.9158\r\n 1.3393\r\n 4.0765];\r\ny_correct = 10;\r\n[x y] = poly_intersection(p1)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))\r\n\r\n%%\r\np2 = [1 -3 1.25];\r\nx_correct =[0.5 ; 2.5];\r\ny_correct = 1.25;\r\n[x y] = poly_intersection(p2)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))\r\n\r\n%%\r\np3 = [ 2 -14.5 0.8 14];\r\nx_correct =[ -0.9024\r\n 1.0999\r\n 7.0525];\r\ny_correct = 14;\r\n[x y] = poly_intersection(p3)\r\n\r\nassert(isequal(y,y_correct))\r\nassert(isequal(round(x,4),x_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2710538,"edited_by":2710538,"edited_at":"2022-12-17T10:29:59.000Z","deleted_by":null,"deleted_at":null,"solvers_count":113,"test_suite_updated_at":"2022-12-17T10:26:09.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-16T22:11:02.000Z","updated_at":"2025-07-05T08:30:16.000Z","published_at":"2022-12-16T22:11:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the intersection points of a polynomial, given by its vector of coefficients with the X-axis and the Y-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: a polynomial represented by a vector of coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function returns a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e containing the points of intersection of the polynomial with the X-axis,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is sorted in ascending order and rounded to 4 digits after the decimal point.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition, the function returns the point of intersection of the polynomial with the Y-axis in the variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: use the polynomial functions of MATLAB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: for the polynomial p(x) = x^2 - 3x + 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven by its vector of coefficients p = [1 -3 1.25]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e= [ 0.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e 2.5 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e* It can be assumed that the polynomials of the tests have real values ​​at the points of intersection with the x-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61001,"title":"Stirling Numbers - I","description":"Problems #1388 \u0026 #45187 deal with Stirling numbers of the 2nd Kind.\r\nHere, generate the Stirling numbers S(n,k) of the 1st kind of a given order n, for all degree k in descending order -\r\nS(0,0) = 1;\r\n\r\nS(1,1:0) = [1 0];\r\n\r\nS(3,3:0) = [1 3 2 0];\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 97.0833px; transform-origin: 408px 97.0833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5083px 7.79167px; transform-origin: 31.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProblems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1388\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#1388\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u0026amp; \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/45187\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e#45187\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.033px 7.79167px; transform-origin: 133.033px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deal with Stirling numbers of the 2nd Kind.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2917px 7.79167px; transform-origin: 60.2917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere, generate the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind\"\u003e\u003cspan style=\"perspective-origin: 52.5167px 7.79167px; transform-origin: 52.5167px 7.79167px; \"\u003e\u003cspan style=\"\"\u003eStirling numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 19.4417px 7.79167px; transform-origin: 19.4417px 7.79167px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eS(n,k)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 45.5px 7.79167px; transform-origin: 45.5px 7.79167px; \"\u003e\u003cspan style=\"\"\u003e of the 1st kind\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5083px 7.79167px; transform-origin: 52.5083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a given order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 7.79167px; transform-origin: 4.275px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.675px 7.79167px; transform-origin: 46.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for all degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.79167px; transform-origin: 3.89167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.6917px 7.79167px; transform-origin: 67.6917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in descending order -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 42.35px 8.25px; tab-size: 4; transform-origin: 42.35px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(0,0) = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.25px; tab-size: 4; transform-origin: 0px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 65.45px 8.25px; tab-size: 4; transform-origin: 65.45px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(1,1:0) = [1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.25px; tab-size: 4; transform-origin: 0px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.916667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.916667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.916667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.916667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80.85px 8.25px; tab-size: 4; transform-origin: 80.85px 8.25px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eS(3,3:0) = [1 3 2 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.108px 7.79167px; transform-origin: 264.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = stirlingI(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('stirlingI.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\ny = 1;\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 1;\r\ny = [1 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 3;\r\ny = [1 3 2 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 4;\r\ny = [1 6 11 6 0];\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 7;\r\ny = flip([0 \t720 \t1764 \t1624 \t735 \t175 \t21 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 8;\r\ny = flip([0 \t5040 \t13068 \t13132 \t6769 \t1960 \t322 \t28 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 10;\r\ny = flip([0 \t362880 \t1026576 \t1172700 \t723680 \t269325 \t63273 \t9450 \t870 \t45 \t1]);\r\nassert(isequal(stirlingI(n),y))\r\n\r\n%%\r\nn = 14;\r\ny = [1 91 3731 91091 1474473 16669653 135036473 790943153 3336118786 9957703756 20313753096 ...\r\n 26596717056 19802759040 6227020800 0];\r\nassert(isequal(stirlingI(n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T08:00:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-13T07:58:07.000Z","updated_at":"2026-02-10T22:53:50.000Z","published_at":"2025-09-13T07:58:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1388\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#1388\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/45187\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e#45187\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deal with Stirling numbers of the 2nd Kind.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, generate the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eStirling numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eS(n,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the 1st kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of a given order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, for all degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in descending order -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[S(0,0) = 1;\\n\\nS(1,1:0) = [1 0];\\n\\nS(3,3:0) = [1 3 2 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61165,"title":"Breaking straight lines","description":"Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\r\nBreak the given line by building a piecewise linear function constituted by two branches:\r\none branch stands for the parent polynomial p;\r\nand another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).\r\nGiven (P, p), find\r\nR, the breaking point;\r\nr, the 1×2 array that represents the perpendicular line. If r violates the definition of a function, return r = ''.\r\ninput: (P, p)\r\noutput: (R, r)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 508.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 254.275px; transform-origin: 408px 254.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a point in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane and let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone branch stands for the parent polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand another branch stands for the perpendicular line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that passes by the point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the breaking point;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array that represents the perpendicular line. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e violates the definition of a function, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(R, r)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 213.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 106.9px; text-align: left; transform-origin: 384px 106.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"251\" height=\"208\" style=\"vertical-align: baseline;width: 251px;height: 208px\" 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8GFmZubw4cO7du3q5ubW3B/1SqUSna2N5eXl7d27l3tYWlpaWFjIfR+4oaEhMTFx6tSpXHd8YxcvXuSW2O7SpQvbMP5TiZHJZNw29/+RiNRqNTW/4J9Vmjutha1yAlVVVVZFT3V1dWVlpUulVRvV1NS42h0zjk3jesj2+c4Wb6P//OvlsFV43NzcxGIxr5+y+vry/n28driEsbt37549e7a5Z6dNmzZr1ix2WHZ2dkFBQf/+/UeMGGF8DBfuZBTTaWlpJqcy7ubmllWyreZOa2GrAMByts937m/PESNGcKnk5uY2fPhwIiosLOT789V2mEzDrubrmD59OhGdP39+2bJlbM+6devMHM+GThoMhuTk5IqKCrZz5MiR8fHx3CLd7c8+WwXg0Gz//dXi4mIW6y+++OKUKVOISCQSLV68OCAggIhOnjxp8yu6uA4dOhARF4Lx8fHsy8PNdafk5uYaDAaRSMT+7xBRSEjIa6+9NnXq1KioKMuv6+fn16Z289MqAODw8v3V9957b9iwYR4eHlu2bFm7dq1YLGbjnR88eOBMAyHsxJUrVwYNGjRp0qSIiAiZTBYVFcU+qIyLi5s5c2bj4/Pz89PT059++ukFCxYMGzZMrVbHxsbKZLLy8vLPPvvMkiuyLrgXXnihb9++SUlJTc5CY622twoa41ZYNZ4NGFwHL/PPXL9+fcaMGazb1MfHh4X7xYsXp02bhlmCrcJ6q+vq6swc8+677xYXF4vF4oEDB/bo0aO4uPj111+/d++eXC4fNWoUe63JGbZu3frFF18Q0YABA0aMGCGTyTIzM5csWcI+I2EdaMbdaOzlXNf5t99+W1xc7OHhMWjQIOMvVXFtNhgMxidhL2zxtOZbBa3ArbCqUpWpVGXCNgbanw1GRDR7apEoMjIyOjq6pqYmLy/v/v375o9PSkqSSqVWLS3fitXonZJEIomOjvbz88vPzy8pKWF7oqKiysrKTL79bywgIKBXr14SieT+/futmLc5NDS0tra2vLy8TU23davsXCvesTExMUVFRa0YDcIV74y7e4aLTAWsUChyc3NdavyMsXnz5mk0mp07dxKv63sYDIZbt27dunWLv0sAo9frc3NzTfbk5eWZf5VKpWIj6FuHp9mJ29gq4HDFO4NFmlwQ1ucDcEJ6vcL4W9ZYYdU1Id8BnBCKdyDkO4DzQfEODPIdwNmgeAcG+Q7gVFC8Awf5DuBUULwDB/lu15YvX368kU8//XTDhg2hoaFCt85SK1eu/P7773/7298S0Zw5c44fP7506dI2nnP69OnHjx9fsWKFLRr4q7NJJJL09PTjx49z8+w7EBTvYIzH8e/QdnK5XC6XN94ZHh6uUChmz57NzdZpz6RSqUgkcnd3JyKZTCaXy7lFYFqN3RkfHx9bNPBXZxOLxWxqHW4lAweC4h2MId8dwMWLFzdt2kREbm5uwcHBCQkJs2fPlslk8+bN27hxo9Cts87x48dLSkpu3LghdEOapdVqN2/eLBaLjaeqdwgo3sEE8t0BqNXq0tJStl1SUpKdnR0aGjp27Fi2qirj5+fXr1+/4OBgvV6vVCoLCgrY/k6dOnXv3r2goEClUo0fP76+vv7rr78eOHCgRqPJz88fOHBgbGxsRUVFZmbm7du3jS/a3AmJaOjQoQaDITMzc+DAgX369DEYDNeuXVMqldxEY56enuy1dXV1ly5dMj5teXn57du3jWdN8PT0VCgU3bp1c3d3Lykp+de//lVTU0NEbMmq8+fPc6ft06ePv7//5cuX2QGN9ejRY/DgwZ6enjk5OT/++OPjx4/Z/sGDB7u7u587d65Pnz4KhSItLc3M3z0Gg6GwsFAkEtXX11vyw5q/V+0JxTuYQL47JNY1zC3YlJCQ8MYbb/j7+3MHHD9+fOPGjXq9fuLEifPnz8/Pzw8NDfX29s7JycnJyWFrJN29e5frxK+vr9+9e/dHH33U4gk9PT3//Oc/E1FmZubgwYO5A44ePfr2228TUXBw8I4dOyIiIth+Nusvd9j06dNnzZqVnp7O/vIIDw/fvHlzZGQkd8CiRYtefvnl0tJStuTspEmTuF8Ga9eu7dat26pVqxqvdhIREfGXv/yFW9udiHQ63d/+9rePP/6YiP7yl7+IRKLLly8PHDiQiLKzs83ku6en54cffkhEv/3tb8vKysz/sObvVXOX4AOKd2jMCfO9zGGnG9wilW5tfo09Tu/evdkKq2yGztDQ0M2bN3t6ehYXF586dapz585jx45NTEzU6/Vc7w2r9O/cuXP58mXuPKGhoaxsHzJkSERExKJFi5RK5ZUrVyw5IRENHjy4sLAwIyNjyJAhPXr0mDRp0kcffVRcXPzee+9FRETodLoTJ04Q0ZgxY8x0ZG/YsCEyMrKmpubEiRNyuXzEiBE+Pj6vvfbaK6+8YtWtW758eceOHevq6v79738/fPhw+PDh3bt3X7BgwZEjRzQaDTtm4MCBNTU1N2/eZFOwWaW5H9bCe9UOULxDY06Y784nPj6eFbNisTgyMpIb13HkyBEiWrhwoaenZ3l5+ezZs1mW5eXlLV68eMyYMcZLmScnJx88eJCIuMr6zJkzq1evJiIfH58DBw507tx55syZq1evNn9CbjrfixcvLl++XKfTyWSy1NRUb2/vqKioiIgIVoyvWrWKTRN28uTJbdu2NflzjRw5Mjo6mog2bdp05swZIvrNb36zfv363r17N/5U2Ty2Bsirr77KFu/++uuvP/vsM7FYHBISws1wV1xcvGDBgtbNNtzkD1tcXGz+XpksUckrH5/J3AzAKN6BQb47ALlczjqjOVqtNiUlhQVo//79iej69etcZ8uPP/5IRB4eHn369GF71Gr1p59+anLaffv2cc9++eWXL7/8cteuXVs8IfcXALd+ek1NTUFBQZ8+fUJCQtjvnuzsbG4OyIyMjOvXr7McN9G3b18iKikpYeFORCdPngwODhaJRFzXuYUWLFjg5eVVWloaExPTuXNn7nYZdw199dVXrZ5Kvskfllq6Vz/88EPrLtc6bBEPlaoMxTswyHcHkJeXt3fvXu5haWlpYWEhWynFy8srKCiIiBISEkx+BxARVwVfvHixcXcwt1IuEd25c4eIOnbsaOEJich4eElVVRURGQyGsLAwMlpjnSkoKGgy31lEGs8grdfrDxw4QP9ZdNBE47VEOD4+Pi+++OKoUaPM9AV9//33zT3VoiZ/WMvvVXvCUk3AccJ8DwwIELoJNnb37t3GnygybCk+IiouLs7OzjZ5Nj8/n5XkTX7Wx/W0cOepqKho8YRNvtzkPMYfNhIRG/nemFUDzEUiUXBwcJNPhYWF7dq1y8PDQ6vVXrx4MT8//+bNm40XGW/LB55mfliy4F4BCMIJ892l1NbWqlSqgICAc+fOsT56IvL09Fy4cKFEIjG/uFK3bt24DGJdJXfu3GnLCYmouLiYiPr16+fm5tbQ0EBEbm5uTRbv9J8/Gvr3788dHB4ezsbwvPTSS+wYuVzOxs+EhoY29/tg6NCh7KmFCxdeu3aN/vOXAd/aeK8A+Ib5CRzelStXiOjJJ5/kqub58+e/8MILkydPNl+xJiUlsQq0e/fuU6ZMof+UnK0+IfdamUz29NNPsz3Tp09vbioFpVJJRHK5fNy4cUQkkUjmz5/v6empVquLi4urq6uJaOTIkUTk5ua2cuXK5i7KjRNlvzA8PT3/+Mc/sj3G/e98aMu9AuAb6neHl5KSMmzYsI4dOx48ePDKlSudO3dmoyEPHjzIDQ1s0pAhQ7788suKioouXbpIpdKSkhJWO5s/oaenp5lznjp16scff+zTp8+aNWsmTpwoEokGDBjQ3MHnzp1jY9LfeOONadOmhYaGsm73zz77jIiuXbs2ZMiQRYsWjR8/vlOnTjKZrLnzXL16lW0cPny4oKCgR48ebIIBIlq+fDmv4xRbffMB2gHqd7vGun3r6urMHFNUVLRs2bKSkhJ/f/9Ro0b16NGjrq7uk08+YYs4s9c2eYarV68GBQX17NlTKpXevXt37dq17Huh5k9YX1+v1WobGhrYeBLjdrI9K1euzM7OFolEAwcOHDBgwMOHD0+ePMk9y/7LdWe/+uqr3333nZubW58+fTp06KDVaj/++GP2paTNmzcXFxezVdpFItHx48dZH7fxT8T+q1Qq9+/f39DQ0LFjxyFDhnh7ex85coTtGTBgQFhYmFarNRgMxg02YXw29gMaDAatVtviD2v+XgEIi9+/Xq2SlJQklUqt+ofRitXonZVEIunWrVuXLl2qqqpu3LjBxng0KSIi4vDhw1qtdvTo0R07duzdu3dpaWl+fr5Jf4LlJ2zuKpGRkUVFRbdu3WJ962b4+flFRkZqNJqCggKTsjc4ODg4OPjq1atm0pk7Mioqqqqq6tq1a+xnCQ4OlslkhYWFfHeVWH6vWvGOjYmJKSoqqqystEFDXYNCocjNzXXZOzZv3jyNRrNz505C/4zT0Ov1+fn51o7ZKC0t5Wa2sckJOQUFBZZPw1JRUZGVldXkUw8ePHjw4IElJ2l8pIUvbLs23isAnqB/BgDAOaF+dzmPHz9+9OiRtV8QBQCHg3x3OQ8ePJg0aZLQrQAA3qF/xjp6vaLlgwAA7ADqd4toNKs0mle5h+7uGUQklW7BLH3QzvR6RVVVKiaZAUsg31tgkuwMW0hBp0uVSrdIpVuFaBe4KDbPO5sKGCkP5iHfzWky3E0OICL+In758uXjx4832alSqa5fv7579+67d++2eIY5c+a89NJLaWlpbB2iFnl6etbX1zc5YLxjx46HDx82XpeOiHQ6XVFR0TfffPPVV1+ZPAU2Z7JIk1qd6uMzWcD2gJ1DvjerxXDnDiPeIl4ulzeeZlYul4eHhysUitmzZ5tZZ46RyWRyudzX19eSy/Xo0eOjjz6qrKxs/EuFiDw9PZucJMDf379///5RUVHNreMBtoJFmsAqyPem6fUKS8Kd0WhW8dpLc/HixU2bNhGRm5tbcHBwQkLC7NmzZTLZvHnzWpxc5fjx4yUlJTdu3LDkQhKJhJqfzpfzyiuv3Lx5k4i8vb0jIiIWLFjQrVu33/72t4cPH7bkTwpoHaywCtZCvjfNpFCy4PhX+Yt4tVrNfcu0pKQkOzs7NDR07NixbCorJjw8fNCgQU888YRWq7127Rpbpo6IysvLb9++zS1RPXToUIPBkJmZOXDgwD59+hgMhmvXrimVSoPBEBISEh8fT0Te3t4KheLWrVvNff/zwYMHXHsKCwsLCgo++eQTIurevTvynT8o3sFayPemGRdKluC7hDfBlsHj5sWdOXPmggULjOvu8+fPr1+/vrKycvr06bNmzUpPT9+4caOnpyfrhc/MzBw8eDB38NGjR99+++0pU6bMmjWL7dm2bdu+fft2795tSWO4admlFiwODq2D4h1aAePfm2Dng9x79+7dr18/IiosLCSihISExYsXu7u7X7p06YMPPjh27JjBYBg2bBg3B3pjgwcPLiwsPHToEJsyZdKkSWFhYefPn2cTPRLRxx9/fPHiRUsa4+3tza3FwdoDfEDxDq3AS/3u7u6enp7e5NIKc+bMYUv8OB+9XsFTSRUfH8+WBxKLxZGRkax4J6IjR44Q0cKFC4no0qVLS5YsYTM13rx5c8mSJRMmTGiuAL948eLy5ct1Op1MJktNTfX29o6Kijpz5oxGoxkzZkxtbe0HH3xgpj1vvPFGRUUFEXXo0KFHjx7s74arV6+ytZPA5nQ6FO/QGrzke1hYWJcuXZp8qsXP7uxB6/7x8PdPTi6XmyzfrNVqU1JSzp07J5FIWC/8v//9b24a3mPHji1ZsoSIunXr1uQJ9+7dy6bbrampKSgo6NOnj1UL2vXu3dtkT05Ozptvvmn5GcAqJh/1o3gHC/GS7yxWampq2BzExsrKyvi4onPLy8vbu3cv97C0tLSwsLC2tpaIQkJC2N9Jly9f5g6orKwsLy/39/dvLrUfPnzIbbPJyq0aup6cnFxUVMS2dTpdYWFhi8M0odXKyvqVlfXjHqJ4B8vxku9du3Ylop9++mnfvn18nL8dSKVbrBpCw2Ys4Mndu3fPnj3b5FNisZhtGAe0l5cXGzVfUVHRqVOnxq/ilk9qne+///727dttOQNY7saNF40fongHy/Hy+Wp4eDgROXQEWJvXQv2r4wpnVLs9qwAAIABJREFU4/EwvXv3Zv1gKKsdHYbNQFvwku+sfv/Nb35z6NChzMzMc+fO7d+/37HmpJVIMiyPbAEnGqurq2NjYCZMmMCGJ7q5uT3//PNExFbda8U5JRIJRjraCQybgbbgsX739PQcNGiQj49PQEBAQkLCtm3bLJwCxU5IpVst+eck+BRju3btIqLo6OjDhw/v3Lnz4MGDo0ePJqJ9+/ZZu+7ogwcPDAaDh4fHxx9/nJiYyEtzwWIo3qGNbN//7u7uzj7Wq6urO3jwYG5ubkRExNy5c318fCZMmHDhwoVDhw4199rY2NiUlBTuIUsuM7p06cJ90McHFtxmOuL5DnfWUV5XV2fmmHPnzq1fv37lypWdOnVive11dXU7d+788ssviYiNk2Hnqa+v12q1EonEeK1q9hTbU15efuLEicTExNDQ0KioqOPHjxtfSK/XGwwGkUjU4lLXYIavr29MTIwlR169+pbxw549DwcGWvRCFxcZGVlfX19dXS10Q9rPokWLuO24uLjk5GS23cQQ9Tby8vJasmSJj49Pamoq9x2Zvn37fvLJJx4eHpcuXZoxY0aTL0xKSho+fPiePXu4Pbdu3TJ/rWnTppGVq9G3gl6v0GhWmXyjVfCy3YSXl1f37t07dep07969mzdvtiWCO3bs6O7uXlpaihy3uXnz5vn6+hq/yc27ffsntuHl9dfOndE5Y5GhQ4dev369srJS6Ia0n6ioKG47Li5Oo9GwsYu2r98fP368datp8F29evXcuXOjR4/u1auXmdcqlcqsrCybN6mNJJIMbhZW/r7E1EaPHz/Ozc3Nzc1t+6m4uWWAD1VVVZZHT0BAYExMzNmzZzw80lwqsNqipqamsrLSpW6XcWzGxcVx27bP96CgoKioqLq6OpOk7tChA7V5ZJ7g7DPcwbl16xbpUmkFtmL7fJ85c+bChQsNBsNTTz11//59tjMoKGjAgAFkQZcLAADYhO3Hz1y6dImIRCLRu+++y2ZK8fX1/dOf/sS+Zpmenm7zKwIAQGO2r9/PnTt36dKlQYMGDRkyJCMjo6yszM/Pj33NMi8v7/Dhwza/YntS6PUZEkyqDAAOwPb1u06ne/nll9PS0tg35gMDA1m4p6amzpgxg5sDy7Gs0mjKVKoylSq1qqpMpUpVq1PVaoWVo8sBANoTL6VoRUXFK6+88s477/To0cPPz+/u3bs3b9500OGoqzSaVzUak50KnY6IUnW6LVLpVj6/6mlX62t36NDhH//4R+Npn1Uq1dWrV7/44gubjN4BAFvhsavh4cOHxvMUOqImw93kACLiL+Ltan1tsVjs4+PTZCPDw8PHjBnzxhtvNDcPGgC0P3QlN6vFcOcOIz4jnuxvfe01a9ZwpTr7NuYf//hHqVQ6Y8YM5DuA/UC+N02h11sS7swqjYbXfLe39bVLSkq49pSWlt66dcvf33/BggXR0dHu7u741iuAnUC+N22VxeHOvMpzxJuwq/W1iUitVhNRfX19fX29LX4+ALABrK/dNIWVRai1vw/awq7W1yai7t27T506lYiys7MddHwUgFNC/d4Eexv4aG/ra2/cuJH7unznzp39/f2JqLq62ngRQQAQHPLdZvj76pO9ra8dGhoaGhpqslOn05WXl1t+EuDY7aR14OiQ701oXUzz971We1tfe/v27devX2fbAQEBgwcPnjp1qr+//5QpU4yn7wcLcbNPBwQECt0WcCrIdwdgb+trX7169ccff+QenjlzJiQkZPjw4exTAbCK8SJNKlWZu/svk1EDtBE+X23aFisHw2S0NGacJ3ayvjaLe5lM1j6XcyZYYRX4g3xvmrV5be3vA1uxk/W1a2pqiKjJb7eCGVhhFXiFfG9ahkRieWRvkUoFnFTSHtbX1mg0RPTEE08EBwdbdUUXp9M9ZfwQxTvYFvK9WVulUksintcpxixfX7umpqZTp06DBw+OiIioq6vbtm1bc+trNzQ0mF9fm4jY+tomF2poaGBDdBp/Q5V9YCsWi6dMmdLGH9l16PUKjWYZ9xDFO9ic7dfXbrWkpCSpVGrVYtnz5s0jntfXflWjMfPdJb7nj7Qc1td2CMbvWLU61bhzxtd3cpP5HhMTU1RUhPX5LKdQKHJzc132js2bN4/H9bWdzFapNMPdfZVGY/KNVvtJdgbrazsW9LxDO0C+tyxDIpn8n08OsX4T2ASGzUA7QP+7dRDu0HYo3qF9IN8B2huKd2gfyHeAdqXToXiHduLwvQ2xsbFsTAKA/YuNjf3+e4XxHhTvwB/Hrt+zsrKUSqWADejSpYuAV3dELn7HLlzw/uGHX4ZdoXgHXjl2/Z6VlZWVlSVgAzA22VoufsfU6sk6nTf3EMU78Mqx63cAB4JhM9DOkO8A7UQiyTCe4R3FO/DNsftnABwOi3i1OhXFO/AN9TuAALCIB7QD5DsAgHNCvgMAOCfkOwCAc0K+AwA4J+Q7AIBzQr4DADgn5DsAgHNCvgMAOKf2+P6qRCJhswbevn27HS4HAADUPvn+yiuv/P73vyeimJgY3a9XqQYAAJ7w3j+jUCh+97vf8X0VAAAwwW++BwQEbN26VSQS8XoVAHujVqeqVGVCtwJcHb/5/s477zzxxBO8XgLA3nDzvKtUZUh5EBCP+T579uzRo0cbDIb09HT+rgJgbzSaVcYP9XpFc0cC8IqvfO/Vq9fKlSuJ6MCBA//3f//H01UA7A0WaQL7wUu+e3l57dixw8PDIy8vb9u2bXxcAsA+mRTvWKQJBMTL+Mg1a9ZERUVptdoVK1ZYNSAyNjY2JSWFe7hr1y4eWmdLPXv2lMvl1dXVQjfEYTj3HSsr66dS/VK8Bwbm9u1bSRTTlnM69x3jQ2RkZH19vUvdsUWLFnHbcXFxycnJbNv2+Z6YmPj8888T0XvvvXfjxg1rX75nzx5uu6ioyJYt44FcLr93715lZaXQDXEYzn3HiovfNn4olW5p+3vYue8YH0JCQlztjhnHplKp5LZtn+8zZ85kGwqFYvjw4UQUHR3N9nzwwQcGg2H9+vX37t1r8rVKpTIrK8vmTeJPdXV1ZWWlS72T2siJ71jjnvfa2mNtP60T3zGe1NTUuNodM47NuLg4btv2+c6Ndh81apTJU2yPt7e3zS8KIDj0vIO9sX2+Hzp06OTJk8Z7YmJinn32WSJ69913tVrto0ePbH5RAGFh2AzYIdvn+7fffmuyZ9KkSSzfDxw4gPlnwCmheAc7hPmBAdoKxTvYp/bL96qqqvr6+na7HEC7QfEO9qk95gc+evTo0aNH2+FCAO0PxTvYLfTPALQJinewW8h3gNZD8Q72DPkO0HoSSUZAQCD3EMU72JX26H8HcG4s4tXqVBTvYFdQvwPYho/PZKGbAPAryHcAAOeEfAcAcE7IdwAA54R8BwBwTsh3AADn9HO+jxgxIjMz85133klISOAmcAcAAMf1y/h3Hx+f55577rnnnnvw4MGxY8f++c9/Xr9+XcCWAQBAW/xcv9fU1Gi1WrYdHBz8u9/97p///GdaWtr/+3//r1OnTsI1DwAAWunnfFcqlQkJCStWrDhx4gQX9N27d1++fPmZM2f2798/efJkDw8P4doJAADW+aV/prq6mk3k6+3tPWbMmPHjx48cOdLT01MkEiUkJCQkJKxbt+6rr7769NNP8/PzBWwxAABYoonxM7W1tUePHv3DH/6QkJCwcuXK2tpatt/Hx2fWrFlff/31vn37hg4d2r7tBAAA6zQ9PlIikYwaNeq1115bs2aNt7e3ybPDhw//6KOPFi5cyH/zAOyFWp0qdBMArPOr+SMlEsmIESMmTJjwX//1X76+vsZP3bp1KzU19datWxMnThw3bpxYLF6yZMmHH37Yvq0FEAab512lKqP/zBYJYP9+zveQkJClS5eOGTNGLpcbP/3w4cNjx46lpqZevXqV7Tl+/PgLL7ywYcMGsVjc3o0FEIjxIk0qVZmv72RMBQz27+d8j4yMfPbZZ7m91dXVJ06cSE1NPXfuXENDg8lr7t27134NBBAaFmkCB/Wr/pn6+vrvvvvu6NGjJ06c0Gg0zb3mu+++W7Nmjbu7O//NAxAeVlgFB/Vzvt+5c2fDhg3ffPONSqVq8TUNDQ2ff/45zw0DsAso3sFx/ZLvhw4dErYpAHYIxTs4LswfCdAsk+JdKn0fxTs4EOQ7QLNMind395NCtQSgFZDvAE1Dzzs4OuQ7QNPQ8w6ODvkO0AQU7+AEkO8ATUDxDk4A+Q5gCsU7OAfkO4ApFO/gHJDvAL+C4h2cBvId4FdQvIPTQL4D/IqPz2RuhncU7+DQJC0f0gbu7u6dOnVSqVTcIn8ADoFFvF6vaPFIALvFV75PmDDhd7/7XXR0tIeHBxE9fPjwk08+2bt3r5lphwHsDYp3cGi85PvkyZO3bNni5vZL509QUNCSJUt69OixdOlSPq4IAAAmeOl/X7lypZub2+PHj998883nn39+8+bNbFr5CRMmdO/enY8rAgCACdvX72FhYUFBQUS0ceNGtgzI5cuXRSLR6tWriahXr143b960+UUBAMCE7ev32NhYtvHdd99xO3Nzc9lGXV2dza8IAACN2b5+z8jImDp1KhGVlJSwPWFhYStXriSimpqas2fP2vyKAADQmO3zXaVScYu4/u1vf+vfv7+fnx97uGfPHq1Wa/MrAgBAY/yOf/f29ubCnYhCQkK8vb3NjIWPjY1NSUnhHu7atYvX5rVdz5495XJ5dXW10A1xGLhj1sIds1ZkZGR9fb1L3bFFixZx23FxccnJyWyb33xftmzZyJEj4+LiRowYERwcPHXq1MLCwt27d5t5yZ49e7jtoqIiXpvXdnK5/N69e5WVlUI3xGHgjlkLd8xaISEhrnbHjGNTqVRy27bPd3d3d4PBQER6vf7hw4eff/75559/7ufnd/To0aCgoCeffNJMviuVyqysLJs3iT/V1dWVlZUu9U5qI9wxa+GOWaumpsbV7phxbMbFxXHbth8/s3///qtXr37xxRfGOysqKrKzs4koOjra5lcEAIDGbJ/vrFOlZ8+eAQEBv1zGza1bt25EVFxcbPMrAgBAY7bPd/aXgkgk2rJli7+/v0gkGjJkyPbt29k3Vy9dumTzKwK0gl6vUKnKVKoyoRsCwBfb979/8cUX8+bN69q166hRo86fP6/VatkUY0T06NGj999/3+ZXBGgFbp53FvHcnMAATsP29bter58zZ8758+fZQ7FYzDYyMjJeeumliooKm18RwFqNF2kSsDEAPOFlfOT9+/fnzJkTFhYWGRmp0Wg8PDwKCgru3r3Lx7UAWgGLNIEr4HH8e3FxMT5NBTuEFVbBRWB9PnA5KN7BRSDfwbWgeAfXgXwH14LiHVwH8h1cCIp3cCnId3AhKN7BpSDfwVWgeAdXg3wHV4HiHVwN8h1cAop3cEHId3AJKN7BBSHfwfmheAfXhHwH56fTPWn8EMU7uAjkOzg/qfQtbvpfFO/gOvhdXxvAfrCI1+sVLR4J4BxQv4NrQfEOrgP5DgDgnJDvAADOCfkOAOCckO8AAM4J+Q4A4JyQ7wAAzgn5DgDgnJDvAADOCfkOAOCckO8AAM4J+Q4A4JyQ7+A8MHcYgDHkOzgPjWaVSlWmUpUJ3RAAu4B8BydhvEiTSlWmVqcK2x4AwSHfwUlghVUAE8h3cAZYYRWgMeQ7OAOtdoLxQxTvAIR8Byeg1yseP17EPUTxDsAg38HhoecdoEm857ufn19AQADfVwGXhZ53gOZIeDpvVFTU66+/3rdvX5lM9vjxY7FY/MMPP7z55pslJSU8XRFcE4p3gObwku/R0dH79u3jynZ3d3cieuqppwYOHPjMM888evSIj4uCC0LxDmAGL/0zSUlJLNz//ve/v/jii2vWrMnJySEif3//pUuX8nFFcE0o3gHM4KV+j4uLI6K0tLRNmzYRUVZW1pkzZ86ePSsWi4cNG8bHFcEFoXgHMM/29XvXrl1Z8X769Glu56NHj5RKJRGFhoba/IrgmlC8A5hn+/q9tLR0//79Uqk0MzOT2ymTycLCwoioqKjI5lcEF4TiHaBFts/32trazZs3G+8JCgraunVrcHAw/bqoB2g1FO8ALeJrfCRn4sSJa9euZT02hYWF77//vpmDY2NjU1JSuIe7du3iu3lt1LNnT7lcXl1dLXRDHIat7tjZs78U74GBuX37VhLFtPGc9gnvMWtFRkbW19e71B1btOiX72/HxcUlJyezbR7zvWfPnuvXrx80aBB7ePLkyTVr1tTU1Jh/1Z49e7ht++/Mkcvl9+7dq6ysFLohDsNWd6xbt0giun37JyKSSrfY/1ul1fAes1ZISIir3THj2GSfdDJ85fvMmTNXr17t4eFBRHfu3Nm8efOpU6dafJVSqczKyuKpSXyorq6urKx0qXdSG9n2jgUEBBJRba1NTman8B6zVk1NjavdMePYZMMXGV7yfcqUKevWrSOiurq65OTkvXv36vV6Pi4EAADN4SXfV61aRURarfb555+/du0aH5cAAADzbJ/vUVFR7NPUnJycwMDAESNGGD9bX19/7tw5m18UAABM2D7fuQ9UBw8ebNzrz5SXl+MrrAAA7cD2319l32MCAABh2b5+3759+/bt221+WgAAsArWbwIAcE7IdwAA54R8BwBwTsh3AADnhHwHAHBOyHcAAOeEfAe7planqlRlQrcCwCEh38F+cYs0qVRlSHkAayHfwX6ZLNKk1yuaOxIAGkO+g53CCqsAbYR8BzuFFVYB2gj5DvYIxTtA2yHfwR6heAdoO+Q72BGFXk8o3gFsBPkOwlul0ZSpVGUqVWpVVZlK9c8q9b/pqSfpNHsWxTtA6/Cy/iqAhVZpNK9qNCY7WbI/Sac30Pq33MeieAdoHdTvIJgmw93Ym7R+kySx3doD4GSQ7yCMFsPdqsMAoDHkOwhAoddbntqrkO8ArYJ8BwFYG9ko4QFaAfkOAlDodFYdjxIeoBWQ79DerA13AGgd5Ds4BvbVJwCwHPId2luGu3trXiXBdzUArIN8B8eQqlajhAewCvIdBLBFKrX2JQqdLrWqCikPYDnkOwigdV00hJQHsAbyHQSQIZFYXsI3/mWAlAewBPIdhLFVKrUk4rdIpZN9fCb7+iLlAayFfAfBtBjxW6TSrVIpEWVIJEh5AGsh30FIW6XSJlN7i1QaGBCw9dfpj5QHsArGFIMw9HoFEUkkGSy12U6FXt/iOHd2vEKvX6XRmHwVVqHTpep0Ge7uW6RSjJcHQP0OwtBoVlVVparVqSzoGctDGbU8QIuQ7yAAboVVnU5RVZWq0bzauvPYMOWNf80AOAfe810ikcjlci8vL74vBA5Eo1ll/NDdvU0r8LUl5TWaVSpVmUpVVlWVqlKVqdWmf1IAOC7e833ZsmWXLl16++23+b4QOAqd7ufinXF3z7DJCqvWpjxLdpM/HVjb2vInBYD94Dffg4KCnnvuOV4vAQ7HJDql0i02PLmFKa/RrDKf4C0eAGD/eBlj4Ofnl5iY2Lt37wkTJgQEBPBxCXBQZWX9ysr6cQ9tVbybMD/GZpDu9aPUcnazTiSpdKvNmwfQPnjJ95iYmD/96U/GewwGAx8XAodz48aLxg9tW7ybaDLlT9OT6+lNC8+g0axCvoPj4iXfb926dfz4cbY9fPhwmUzGx1XA4XDDZhieincT3Pj6VLVaodNtsDjcGY3mVUQ8OChe8v3+/fuLFy9m29988023bt34uAo4HJNhM7wW742xWv501ZNWvQolPDgujH+HdiJI8W7iDI1u5ysCCMi+vsMdGxubkpLCPdy1a5eAjbFEz5495XJ5dXW10A1xAFevvmX8sGfPw4GBMe3chrKy8KtXrX5V584vBgZe4aE5FsF7zFqRkZH19fUudccWLVrEbcfFxSUnJ7Nt+8p3ItqzZw+3XVRUJGBLLCGXy+/du1dZWSl0Q+ydTqcwGTZTW3ustrb9G9Kad5RATf0Z3mPWCgkJcbU7ZhybSqWS27avfFcqlVlZWUK3wgrV1dWVlZUu9U5qHbV6ofFDqXSLA920mLIyAWcrw3vMWjU1Na52x4xjMy4ujttG/zvwzh563jnWfqj7JJ3GbGXgoJDvwDthh82YsHaumzdpA2FOSnBMyHfgl0nxHhiYGxiYK2B7JJIMy3/BrKcNT9Jp7iFSHhwL8h34ZVK89+p1WKiWcKTSrZZEvFS65ZLvdswvD44L+Q48aqrn/TsB28NpMeKl0i1S6VasIgIOjfdRAePHj+f7EmC37Krn3YRUutXdPUOjWWX8G4j+k+zGe7AiIDgovCOBL80Mm2nv7zSZIZFk+PhMZtt6vcL8qB6kPDgc9M8AX+y5eG/MwiGb6LEBB4J8B16YFO9eXjsFHPNuc0h5cAjId+CFSfHu4XFcqJbwBykPdg75DrZnV19Y5RtSHuwW8h1sz7F63m0CKQ92CPkONuZSxbsJpDzYFeQ72JgLFu8mkPJgJ5DvYEuuXLybQMqD4JDvYEso3k0g5UFAyHewGRTvzUHKgyCQ72AzKN7NQ8pDO0O+g22geLcQUh7aDfIdbAPFu1WQ8tAOkO9gAyjeW8eSlO9XViZI28AJIN/BBlC8t4X5lE++evXj4mLU8tAKyHdoKxTvNoEeG7A55Du0FYp3G0LKgw0h36FNULzzASkPNoF8hzZB8c4flvKL+/ZFykPrIN+h9VC8t4MrgYGzwsJQy0MrIN+h9bTa8cYPUbzzBz020ArId2glvV7x+PHL3EMU7+0AKQ9WQb5DK6HnXShIebAQ8h1aAz3vgkPKQ4uQ79AaKN7tBFIezEC+g9VQvNsb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alt=\"Break line\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [R, r] = breaking(P,p)\r\n R = x;\r\n r = x;\r\nend","test_suite":"%%\r\nP = [1 1];\r\np = [2 1];\r\nR_correct = [0.2 1.4];\r\nr_correct = [-0.5 1.5];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1];\r\nR_correct = [0.8 0.6];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1.5];\r\nR_correct = [1 1];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [1 -1];\r\nR_correct = [1.5 0.5];\r\nr_correct = [-1 2];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nfiletext = fileread('breaking.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nP = [1 1];\r\np = [0 2];\r\nR_correct = [1 2];\r\nr_correct = '';\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.2 2]; \r\nR_correct = [15/13 23/13];\r\nr_correct = [5 -4];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-29T17:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-29T17:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-15T15:30:33.000Z","updated_at":"2026-04-09T10:19:31.000Z","published_at":"2026-01-26T14:18:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a point in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane and let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eone branch stands for the parent polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand another branch stands for the perpendicular line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that passes by the point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the breaking point;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array that represents the perpendicular line. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e violates the definition of a function, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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Laguerre polynomials","description":"Given an integer _n_ \u0026ge; 0 and a scalar _a_, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials Generalized Laguerre polynomial\u003e of association degree _a_.\r\n\r\nFor simplicity, assume that _a_ is a non-negative integer.\r\n\r\n*Examples*:\r\n\r\n genLaguerrePoly(0,1)\r\n ans =\r\n 1 \r\n\r\n genLaguerrePoly(1,1)\r\n ans =\r\n -1 2 \r\n\r\n genLaguerrePoly(2,1)\r\n ans =\r\n 0.5 -3 3\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0 and a scalar \u003ci\u003ea\u003c/i\u003e, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials\"\u003eGeneralized Laguerre polynomial\u003c/a\u003e of association degree \u003ci\u003ea\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eFor simplicity, assume that \u003ci\u003ea\u003c/i\u003e is a non-negative integer.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e genLaguerrePoly(0,1)\r\n ans =\r\n 1 \u003c/pre\u003e\u003cpre\u003e genLaguerrePoly(1,1)\r\n ans =\r\n -1 2 \u003c/pre\u003e\u003cpre\u003e genLaguerrePoly(2,1)\r\n ans =\r\n 0.5 -3 3\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = genLaguerrePoly(n,a)\r\n P = n*a;\r\nend","test_suite":"%%\r\nuser_solution = fileread('genLaguerrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\na = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 0;\r\nP_correct = [-1 1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 0;\r\nP_correct = [1 -4 2]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 0;\r\nP_correct = [-1 9 -18 6]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 0;\r\nP_correct = [1 -16 72 -96 24]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 0;\r\nP_correct = [-1 25 -200 600 -600 120]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 0;\r\nP_correct = [1 -36 450 -2400 5400 -4320 720]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 1;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 1;\r\nP_correct = [-1 2]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 1;\r\nP_correct = [1 -6 6]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 1;\r\nP_correct = [-1 12 -36 24]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 1;\r\nP_correct = [1 -20 120 -240 120]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 1;\r\nP_correct = [-1 30 -300 1200 -1800 720]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 1;\r\nP_correct = [1 -42 630 -4200 12600 -15120 5040]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 2;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 2;\r\nP_correct = [-1 3]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 2;\r\nP_correct = [1 -8 12]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 2;\r\nP_correct = [-1 15 -60 60]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 2;\r\nP_correct = [1 -24 180 -480 360]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 2;\r\nP_correct = [-1 35 -420 2100 -4200 2520]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 2;\r\nP_correct = [1 -48 840 -6720 25200 -40320 20160]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 3;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 3;\r\nP_correct = [-1 4]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 3;\r\nP_correct = [1 -10 20]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 3;\r\nP_correct = [-1 18 -90 120]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 3;\r\nP_correct = [1 -28 252 -840 840]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 3;\r\nP_correct = [-1 40 -560 3360 -8400 6720]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 3;\r\nP_correct = [1 -54 1080 -10080 45360 -90720 60480]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 0;\r\na = 4;\r\nP_correct = [1]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\na = 4;\r\nP_correct = [-1 5]/1;\r\nassert(isequal(round(genLaguerrePoly(n,a)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\na = 4;\r\nP_correct = [1 -12 30]/2;\r\nassert(isequal(round(genLaguerrePoly(n,a)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\na = 4;\r\nP_correct = [-1 21 -126 210]/6;\r\nassert(isequal(round(genLaguerrePoly(n,a)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\na = 4;\r\nP_correct = [1 -32 336 -1344 1680]/24;\r\nassert(isequal(round(genLaguerrePoly(n,a)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\na = 4;\r\nP_correct = [-1 45 -720 5040 -15120 15120]/120;\r\nassert(isequal(round(genLaguerrePoly(n,a)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\na = 4;\r\nP_correct = [1 -60 1350 -14400 75600 -181440 151200]/720;\r\nassert(isequal(round(genLaguerrePoly(n,a)*720),round(P_correct*720)));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":66,"test_suite_updated_at":"2013-04-28T07:10:43.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-27T14:47:51.000Z","updated_at":"2026-04-08T15:26:08.000Z","published_at":"2013-04-27T14:58:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0 and a scalar\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGeneralized Laguerre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of association degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor simplicity, assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ genLaguerrePoly(0,1)\\n ans =\\n 1 \\n\\n genLaguerrePoly(1,1)\\n ans =\\n -1 2 \\n\\n genLaguerrePoly(2,1)\\n ans =\\n 0.5 -3 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":57725,"title":"Sequence problem","description":"find the nth term of the sequence:\r\n790\r\n1303\r\n2033\r\n____\r\n4366\r\n6095\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 194.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.3125px; transform-origin: 407px 97.3125px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efind the nth term of the sequence:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 122.625px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 61.3125px; transform-origin: 391px 61.3125px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e790\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1303\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e2033\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; 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transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e4366\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e6095\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sequence(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfunctions={'polyfit','polyval'};\r\nassessFunctionAbsence(functions, 'FileName', 'sequence.m');\r\n\r\n%%\r\nx = 1;\r\ny_correct = 790;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 1303;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 6095;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 8293;\r\nassert(isequal(sequence(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 18511;\r\nassert(isequal(sequence(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2900827,"edited_by":2900827,"edited_at":"2023-02-20T05:07:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-02-20T05:07:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-02-19T16:34:33.000Z","updated_at":"2025-09-14T11:31:23.000Z","published_at":"2023-02-19T16:35:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document 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*string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Chebyshev_polynomials\"\u003eChebyshev polynomial of the 1st Kind\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e chebyshev1stKindPoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e chebyshev1stKindPoly(1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e chebyshev1stKindPoly(2)\r\n ans =\r\n 2 0 -1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = chebyshev1stKindPoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('chebyshev1stKindPoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [2 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [4 0 -3 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [8 0 -8 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [16 0 -20 0 5 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [32 0 -48 0 18 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [64 0 -112 0 56 0 -7 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [128 0 -256 0 160 0 -32 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [256 0 -576 0 432 0 -120 0 9 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [512 0 -1280 0 1120 0 -400 0 50 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [1024 0 -2816 0 2816 0 -1232 0 220 0 -11 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [2048 0 -6144 0 6912 0 -3584 0 840 0 -72 0 1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [4096 0 -13312 0 16640 0 -9984 0 2912 0 -364 0 13 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [8192 0 -28672 0 39424 0 -26880 0 9408 0 -1568 0 98 0 -1];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [16384 0 -61440 0 92160 0 -70400 0 28800 0 -6048 0 560 0 -15 0];\r\nassert(isequal(chebyshev1stKindPoly(n),P_correct));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":81,"test_suite_updated_at":"2013-04-30T12:30:22.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T11:25:32.000Z","updated_at":"2026-04-01T10:38:08.000Z","published_at":"2013-04-30T11:27:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Chebyshev_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChebyshev polynomial of the 1st Kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ chebyshev1stKindPoly(0)\\n ans =\\n 1\\n\\n chebyshev1stKindPoly(1)\\n ans =\\n 1 0\\n\\n chebyshev1stKindPoly(2)\\n ans =\\n 2 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1583,"title":"generate a matrix of Legendre polynomials","description":"input = x - the degree of the polynomial\r\noutput = matrix of Legendre polynomials","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123px 8px; transform-origin: 123px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003einput = x - the degree of the polynomial\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 126px 8px; transform-origin: 126px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eoutput = matrix of Legendre polynomials\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = leg_poly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 2;\r\ny_correct = [0 1; 1 0];\r\nassert(isequal(leg_poly(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = [0 0 1; 0 1 0; 1.5 0 -0.5];\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [0 0 0 1; 0 0 1 0; 0 1.5 0 -0.5; 2.5 0 -1.5 0];\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [0 0 0 0 0 1; 0 0 0 0 1 0; 0 0 0 1.5 0 -0.5; 0 0 2.5 0 -1.5 0; 0 4.375 0 -3.75 0 0.375; 7.875 0 -8.75 0 1.875 0]\r\nassert(all(abs(leg_poly(x)-y_correct)\u003c1e-4,'all'))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":14267,"edited_by":223089,"edited_at":"2023-02-27T05:04:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2023-02-27T05:04:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-06T13:55:33.000Z","updated_at":"2026-01-18T14:21:40.000Z","published_at":"2013-06-06T13:55:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput = x - the degree of the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput = matrix of Legendre polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43753,"title":"Laguerre Polynomials","description":"Create a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\r\n\r\n 1\t0\t0\t0\t0\t0\t0\r\n 1\t1\t0\t0\t0\t0\t0\r\n 2\t4\t1\t0\t0\t0\t0\r\n 6\t18\t9\t1\t0\t0\t0\r\n 24\t96\t72\t16\t1\t0\t0\r\n 120\t600\t600\t200\t25\t1\t0\r\n 720\t4320\t5400\t2400\t450\t36\t1\r\n\r\nSee \u003chttps://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials\u003e for more information.","description_html":"\u003cp\u003eCreate a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1\t0\t0\t0\t0\t0\t0\r\n1\t1\t0\t0\t0\t0\t0\r\n2\t4\t1\t0\t0\t0\t0\r\n6\t18\t9\t1\t0\t0\t0\r\n24\t96\t72\t16\t1\t0\t0\r\n120\t600\t600\t200\t25\t1\t0\r\n720\t4320\t5400\t2400\t450\t36\t1\r\n\u003c/pre\u003e\u003cp\u003eSee \u003ca href = \"https://en.wikipedia.org/wiki/Laguerre_polynomials\"\u003eLaguerre Polynomials\u003c/a\u003e for more information.\u003c/p\u003e","function_template":"function y = laguerre(n)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 6;\r\ny_correct = [1,0,0,0,0,0,0;1,1,0,0,0,0,0;2,4,1,0,0,0,0;6,18,9,1,0,0,0;24,96,72,16,1,0,0;120,600,600,200,25,1,0;720,4320,5400,2400,450,36,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = [1,0;1,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = [1,0,0,0;1,1,0,0;2,4,1,0;6,18,9,1];\r\nassert(isequal(laguerre(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = [1,0,0,0,0,0,0,0,0,0,0;1,1,0,0,0,0,0,0,0,0,0;2,4,1,0,0,0,0,0,0,0,0;6,18,9,1,0,0,0,0,0,0,0;24,96,72,16,1,0,0,0,0,0,0;120,600,600,200,25,1,0,0,0,0,0;720,4320,5400,2400,450,36,1,0,0,0,0;5040,35280,52920,29400,7350,882,49,1,0,0,0;40320,322560,564480,376320,117600,18816,1568,64,1,0,0;362880,3265920,6531840,5080320,1905120,381024,42336,2592,81,1,0;3628800,36288000,81648000,72576000,31752000,7620480,1058400,86400,4050,100,1];\r\nassert(isequal(laguerre(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":93456,"edited_by":223089,"edited_at":"2022-09-02T13:57:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-12-07T22:24:15.000Z","updated_at":"2026-01-02T17:37:55.000Z","published_at":"2016-12-07T22:24:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a square lower diagonal matrix containing the first n Laguerre Polynomial coefficients. For n=6, the Laguerre Matrix is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 0 0 0 0 0 0\\n1 1 0 0 0 0 0\\n2 4 1 0 0 0 0\\n6 18 9 1 0 0 0\\n24 96 72 16 1 0 0\\n120 600 600 200 25 1 0\\n720 4320 5400 2400 450 36 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLaguerre Polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more information.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44261,"title":"Multivariate polynomials - sort monomials","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array Problem 44260\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of |5*x| is 1 and the total degree of |x^3*y^5*z| is 9.\r\n\r\nWrite a function \r\n\r\n function [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\n\r\nto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\r\n\r\nExample: Consider the polynomial |p(x,y,z) = 3*x - 2 + y^2 +4*z^2|, which is represented as:\r\n\r\n exponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]\r\n\r\nThe sorted version is\r\n\r\n exponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].\r\n\r\nYou can assume that a given combination of exponents is never repeated.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array\"\u003eProblem 44260\u003c/a\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of \u003ctt\u003e5*x\u003c/tt\u003e is 1 and the total degree of \u003ctt\u003ex^3*y^5*z\u003c/tt\u003e is 9.\u003c/p\u003e\u003cp\u003eWrite a function\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\n\u003c/pre\u003e\u003cp\u003eto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\u003c/p\u003e\u003cp\u003eExample: Consider the polynomial \u003ctt\u003ep(x,y,z) = 3*x - 2 + y^2 +4*z^2\u003c/tt\u003e, which is represented as:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]\r\n\u003c/pre\u003e\u003cp\u003eThe sorted version is\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].\r\n\u003c/pre\u003e\u003cp\u003eYou can assume that a given combination of exponents is never repeated.\u003c/p\u003e","function_template":"function [coeffs,exponents] = sortMonomials(coeffs,exponents)\r\ncoeffs = 0;\r\nexponents = 0;\r\nend","test_suite":"%% Test sortMonomials\r\nfiletext = fileread('sortMonomials.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%%\r\nunsortedCoeffs = [-10 7 -10 -7 6 6 3 1 -7 2]';\r\nunsortedExponents = [5 4 2; 2 5 3; 2 1 5; 1 5 4; 1 4 3; 1 3 3; 1 2 1; 0 4 1; 0 2 1; 0 0 5];\r\n[sortedCoeffs,sortedExponents] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\nsortOrder = [1 2 4 3 5 6 8 10 7 9];\r\nassert(isequal(sortedCoeffs,unsortedCoeffs(sortOrder)))\r\nassert(isequal(sortedExponents,unsortedExponents(sortOrder,:)))\r\n\r\n%%\r\nx = randi(1000); y = randi(1000);\r\n[coeffs,exponents] = sortMonomials(x,y);\r\nassert(isequal([x y],[coeffs exponents]))\r\n\r\n%%\r\nunsortedCoeffs = randi(1000,[4 1]);\r\nough = ['hguot '; 'hguoc '; 'hguolp'; 'hguod '];\r\nunsortedExponents = ough - repmat(randi(100),size(ough));\r\nunsortedExponents = [unsortedExponents -sum(unsortedExponents,2)];\r\n[sortedCoeffs,~] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\n[~,ia] = sort(ough(:,5));\r\nassert(isequal(sortedCoeffs,flipud(unsortedCoeffs(ia))))\r\n\r\n%%\r\nz = [1 3 5+randi(10)];\r\nv1 = perms(z); \r\nv2 = perms(z+[1 0 0]);\r\nv = [v2; v1];\r\nunsortedCoeffs = randi(1000,[size(v,1) 1]);\r\nunsortedExponents = v(randperm(size(v,1)),:);\r\n[sortedCoeffs,sortedExponents] = sortMonomials(unsortedCoeffs,unsortedExponents);\r\nassert(isequal(sortedExponents,v))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-13T18:24:47.000Z","updated_at":"2017-07-15T05:42:59.000Z","published_at":"2017-07-13T18:25:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44260-multidimensional-polynomials-convert-monomial-form-to-array\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44260\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, multivariate polynomials were defined as a sum of monomial terms using|exponents|, a matrix of integers, and|coefficients|, a vector (follow the above link for an explanation). It can be useful to order the monomials. But first we need to define the total degree of a monomial as the sum of the exponents. For example, the total degree of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5*x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 and the total degree of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex^3*y^5*z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function [coeffs,exponents] = sortMonomials(coeffs,exponents)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto sort the monomials. Sort them first by descending total degree, and then for a given total degree, by lexicographical order of the exponents (by the first exponent, then the second, and so on, each in descending order). The coefficients should be sorted so they stay with the correct monomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: Consider the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y,z) = 3*x - 2 + y^2 +4*z^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [1 0 0; 0 0 0; 0 2 0; 0 0 2], coefficients = [3; -2; 1; 4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sorted version is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [0 2 0; 0 0 2; 1 0 0; 0 0 0], coefficients = [1; 3; 1; 4].]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that a given combination of exponents is never repeated.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1464,"title":"Laguerre polynomials","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre polynomial\u003e.\r\n\r\n*Examples*:\r\n\r\n laguerrePoly(0)\r\n ans =\r\n 1 \r\n\r\n laguerrePoly(1)\r\n ans =\r\n -1 1 \r\n\r\n laguerrePoly(2)\r\n ans =\r\n 0.5 -2 1\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Laguerre_polynomials\"\u003eLaguerre polynomial\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e laguerrePoly(0)\r\n ans =\r\n 1 \u003c/pre\u003e\u003cpre\u003e laguerrePoly(1)\r\n ans =\r\n -1 1 \u003c/pre\u003e\u003cpre\u003e laguerrePoly(2)\r\n ans =\r\n 0.5 -2 1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = laguerrePoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('laguerrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(laguerrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [-1 1]/1;\r\nassert(isequal(round(laguerrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [1 -4 2]/2;\r\nassert(isequal(round(laguerrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [-1 9 -18 6]/6;\r\nassert(isequal(round(laguerrePoly(n)*6),round(P_correct*6)));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [1 -16 72 -96 24]/24;\r\nassert(isequal(round(laguerrePoly(n)*24),round(P_correct*24)));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [-1 25 -200 600 -600 120]/120;\r\nassert(isequal(round(laguerrePoly(n)*120),round(P_correct*120)));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [1 -36 450 -2400 5400 -4320 720]/720;\r\nassert(isequal(round(laguerrePoly(n)*720),round(P_correct*720)));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [-1 49 -882 7350 -29400 52920 -35280 5040]/5040;\r\nassert(isequal(round(laguerrePoly(n)*5040),round(P_correct*5040)));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [1 -64 1568 -18816 117600 -376320 564480 -322560 40320]/40320;\r\nassert(isequal(round(laguerrePoly(n)*40320),round(P_correct*40320)));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [-1 81 -2592 42336 -381024 1905120 -5080320 6531840 -3265920 362880]/362880;\r\nassert(isequal(round(laguerrePoly(n)*362880),round(P_correct*362880)));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1 -100 4050 -86400 1058400 -7620480 31752000 -72576000 81648000 -36288000 3628800]/3628800;\r\nassert(isequal(round(laguerrePoly(n)*3628800),round(P_correct*3628800)));\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2013-04-28T07:10:18.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-27T14:28:54.000Z","updated_at":"2026-04-08T15:24:34.000Z","published_at":"2013-04-27T14:30:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Laguerre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLaguerre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ laguerrePoly(0)\\n ans =\\n 1 \\n\\n laguerrePoly(1)\\n ans =\\n -1 1 \\n\\n laguerrePoly(2)\\n ans =\\n 0.5 -2 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1475,"title":"Chebyshev polynomials of the 2nd Kind","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev polynomial of the 2nd Kind\u003e.\r\n\r\n*Examples*:\r\n\r\n chebyshev2ndKindPoly(0)\r\n ans =\r\n 1\r\n\r\n chebyshev2ndKindPoly(1)\r\n ans =\r\n 2 0\r\n\r\n chebyshev2ndKindPoly(2)\r\n ans =\r\n 4 0 -1\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Chebyshev_polynomials\"\u003eChebyshev polynomial of the 2nd Kind\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e chebyshev2ndKindPoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e chebyshev2ndKindPoly(1)\r\n ans =\r\n 2 0\u003c/pre\u003e\u003cpre\u003e chebyshev2ndKindPoly(2)\r\n ans =\r\n 4 0 -1\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = chebyshev2ndKindPoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('chebyshev2ndKindPoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [2 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [4 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [8 0 -4 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [16 0 -12 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [32 0 -32 0 6 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [64 0 -80 0 24 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [128 0 -192 0 80 0 -8 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [256 0 -448 0 240 0 -40 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [512 0 -1024 0 672 0 -160 0 10 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1024 0 -2304 0 1792 0 -560 0 60 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [2048 0 -5120 0 4608 0 -1792 0 280 0 -12 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [4096 0 -11264 0 11520 0 -5376 0 1120 0 -84 0 1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [8192 0 -24576 0 28160 0 -15360 0 4032 0 -448 0 14 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [16384 0 -53248 0 67584 0 -42240 0 13440 0 -2016 0 112 0 -1];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [32768 0 -114688 0 159744 0 -112640 0 42240 0 -8064 0 672 0 -16 0];\r\nassert(isequal(chebyshev2ndKindPoly(n),P_correct));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":79,"test_suite_updated_at":"2013-04-30T12:30:53.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T11:26:00.000Z","updated_at":"2026-04-08T15:02:56.000Z","published_at":"2013-04-30T11:27:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Chebyshev_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eChebyshev polynomial of the 2nd Kind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ chebyshev2ndKindPoly(0)\\n ans =\\n 1\\n\\n chebyshev2ndKindPoly(1)\\n ans =\\n 2 0\\n\\n chebyshev2ndKindPoly(2)\\n ans =\\n 4 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47578,"title":"Find a real root of a quintic function without using roots function","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGeneralized version of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47563\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 47563\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind a real root of a polynomial (5th degree) without using roots function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = noRoot(coeffs)\r\n\r\nend","test_suite":"%%\r\nfiletext = fileread('noRoot.m');\r\nassert(isempty(strfind(filetext, 'roots')))\r\n\r\n%%\r\ncoeffs = [6 8 7 9 12 467];\r\ncandidateX = noRoot(coeffs);\r\nassert(isreal(candidateX))\r\nassert(abs(sum(coeffs.*(candidateX.^(length(coeffs)-1:-1:0)))-0)\u003c0.0001)\r\n\r\n%%\r\nfor idx = 1:10\r\n coeffs = randi([3 100],1,randi([6 6]));\r\n candidateX = noRoot(coeffs);\r\n assert(isreal(candidateX))\r\n assert(abs(sum(coeffs.*(candidateX.^(length(coeffs)-1:-1:0)))-0)\u003c0.0001)\r\nend","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2020-11-23T09:07:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-20T11:22:56.000Z","updated_at":"2020-11-23T09:07:05.000Z","published_at":"2020-11-23T09:07:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGeneralized version of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47563\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 47563\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind a real root of a polynomial (5th degree) without using roots function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61006,"title":"Shapiro Polynomials","description":"Given an order n, return the coefficients of 1st Shapiro polynomials Pn(x) - \r\n\r\n%Example\r\nP1(x) = x + 1 =\u003e Output = [1 1];\r\n\r\nP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u003e Output = [1 -1 1 1 -1 1 1 1];","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 142.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 71.3667px; transform-origin: 408px 71.3667px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2333px 8px; transform-origin: 48.2333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.65px 8px; transform-origin: 91.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return the coefficients of 1st \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Shapiro_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eShapiro polynomials\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePn(x) - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 40.8667px; transform-origin: 405px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eP1(x) = x + 1 =\u0026gt; Output = [1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 315.7px 8.5px; tab-size: 4; transform-origin: 315.7px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u0026gt; Output = [1 -1 1 1 -1 1 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = shapiro(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('shapiro.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif'); \r\n\r\n%%\r\nx = 1;\r\ny = [1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = [-1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = [1 -1 1 1 -1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [-1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 1 1];\r\n\r\nassert(isequal(shapiro(x),y))\r\n\r\n%%\r\nx = 5;\r\ny = [1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 1 1];\r\nassert(isequal(shapiro(x),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-20T15:17:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-20T03:25:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-19T17:23:37.000Z","updated_at":"2026-01-26T15:34:27.000Z","published_at":"2025-09-19T17:23:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the coefficients of 1st \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Shapiro_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eShapiro polynomials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePn(x) - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nP1(x) = x + 1 =\u003e Output = [1 1];\\n\\nP3(x) = x^7 - x^6 + x^5 + x^4 - x^3 + x^2 + x + 1 =\u003e Output = [1 -1 1 1 -1 1 1 1];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60950,"title":"Find the longest runs of primes generated by polynomials","description":"Cody Problems 60942, 60943, and 60944 involve polynomials that generate primes. No polynomial can generate only prime numbers, but some can generate sizable runs of primes. For example, for = 0, 1, 2,…,10, produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For , both terms in the polynomial are divisible by 11, and the result (253) is composite. \r\nWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\r\nTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \r\nRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\r\nMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 144.3px; transform-origin: 408px 144.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60942\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60942\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60943\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60943\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60944\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e60944\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.675px 8px; transform-origin: 25.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involve \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003epolynomials that generate primes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.975px 8px; transform-origin: 92.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. No polynomial can generate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.8417px 8px; transform-origin: 12.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eonly\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.8667px 8px; transform-origin: 20.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e prime numbers, but some can generate sizable runs of primes. For example, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.9667px 8px; transform-origin: 49.9667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 0, 1, 2,…,10, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"19.5\" alt=\"f(n) = 2n^2+11\" style=\"width: 103px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.825px 8px; transform-origin: 43.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" alt=\"n = 11\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.592px 8px; transform-origin: 141.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, both terms in the polynomial are divisible by 11, and the result (253) is composite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.167px 8px; transform-origin: 374.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 61.3px; transform-origin: 392px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 358.867px 8px; transform-origin: 358.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 347.608px 8px; transform-origin: 347.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 20.4333px; text-align: left; transform-origin: 364px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 360.975px 8px; transform-origin: 360.975px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n,p] = polyPrimeRun(a)\r\n% a = vector of coefficients of the polynomial--e.g., for f(n) = 2n^2+11, a = [2 0 11]\r\n% n = length of longest run of primes (ignoring sign)\r\n% p = distinct primes in the longest run, sorted low to high \r\n q = a.*(0:1000);\r\n n = length(max(isprime(q)));\r\n p = distinct(isprime(q));\r\nend","test_suite":"%%\r\na = [1 1 0 17];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 11;\r\np_correct = [17 19 29 53 97 167 269 409 593 827 1117];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%%\r\na = [2 0 11];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 11;\r\np_correct = [11 13 19 29 43 61 83 109 139 173 211];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Honaker\r\na = [4 4 59];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 14;\r\np_correct = [59 67 83 107 139 179 227 283 347 419 499 587 683 787];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Legendre\r\na = [1 1 17];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 16;\r\np_correct = [17 19 23 29 37 47 59 73 89 107 127 149 173 199 227 257];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% A. Bruno\r\na = [3 39 37];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 18;\r\np_correct = [37 79 127 181 241 307 379 457 541 631 727 829 937 1051 1171 1297 1429 1567];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% E. Pegg Jr. \r\na = [1 0 29 0 101];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 20;\r\np_correct = [101 131 233 443 821 1451 2441 3923 6053 9011 13001 18251 25013 33563 44201 57251 73061 92003 114473 140891];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% R. Frame\r\na = [3 3 23];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 22;\r\np_correct = [23 29 41 59 83 113 149 191 239 293 353 419 491 569 653 743 839 941 1049 1163 1283 1409];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [7 -371 4871];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 24;\r\np_correct = [41 97 167 251 349 461 587 727 881 1049 1231 1427 1637 1861 2099 2351 2617 2897 3191 3499 3821 4157 4507 4871];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Legendre (1798)\r\na = [2 0 29];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 29;\r\np_correct = [29 31 37 47 61 79 101 127 157 191 229 271 317 367 421 479 541 607 677 751 829 911 997 1087 1181 1279 1381 1487 1597];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% J. Brox\r\na = [6 -342 4903];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 58;\r\np_correct = [31 43 67 103 151 211 283 367 463 571 691 823 967 1123 1291 1471 1663 1867 2083 2311 2551 2803 3067 3343 3631 3931 4243 4567 4903];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [7 -371 4871];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 24;\r\np_correct = [41 97 167 251 349 461 587 727 881 1049 1231 1427 1637 1861 2099 2351 2617 2897 3191 3499 3821 4157 4507 4871];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% F. Gobbo\r\na = [8 -488 7243];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 62;\r\np_correct = [37 43 101 139 149 181 197 251 379 523 683 859 1051 1259 1483 1723 1979 2251 2539 2843 3163 3499 3851 4219 4603 5003 5419 5851 6299 6763 7243];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% J. Brox\r\na = [43 -537 2971];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 35;\r\np_correct = [1297 1319 1361 1427 1511 1621 1747 1901 2069 2267 2477 2719 2971 3257 3881 4591 5387 6269 7237 8291 9431 10657 11969 13367 14851 16421 18077 19819 21647 23561 25561 27647 29819 32077 34421];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac\r\na = [42 270 -26436 250703];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 40;\r\np_correct = [44927 44939 48479 48767 55343 56663 65267 68879 77999 85667 93287 107279 110879 130523 133967 151967 165983 174959 199247 203579 224579 247007 250703 296519 352367 414803 484079 560447 644159 735467 834623 941879 1057487 1181699 1314767 1456943 1608479 1769627 1940639 2121767];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Euler\r\na = [1 -1 41];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 41;\r\np_correct = [41 43 47 53 61 71 83 97 113 131 151 173 197 223 251 281 313 347 383 421 461 503 547 593 641 691 743 797 853 911 971 1033 1097 1163 1231 1301 1373 1447 1523 1601];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Speiser\r\na = [103 -4707 50383];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 43;\r\np_correct = [131 503 661 971 1439 1619 1867 1873 2371 2557 2917 2953 3041 3257 3319 3391 3449 4673 5231 6599 7219 8731 9413 11069 11813 13613 14419 16363 17231 19319 20249 22481 23473 25849 26903 29423 30539 33203 34381 37189 41381 45779 50383];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Fung and Ruby\r\na = [47 -1701 10181];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 43;\r\np_correct = [379 419 577 599 1321 1451 1483 1667 2129 2273 2617 2843 2851 2969 3463 3571 3877 3989 4079 4129 4421 4493 4759 4813 5003 5039 5153 5171 5209 5231 5501 6679 6967 8221 8527 9857 10181 11587 13411 15329 17341 19447 21647];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% S.M. Ruiz\r\na = [3 -183 3318 -18757];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 47;\r\np_correct = [37 41 59 109 229 409 419 499 739 829 877 1201 1531 1597 1669 1823 1999 2389 2749 2917 3061 3271 3307 3469 3491 3529 4789 5441 6367 7691 8221 10259 10369 12829 13163 15619 16421 18757 20051 24071 28499 33353 38651];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Fung and Ruby\r\na = [36 -810 2753];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 45;\r\np_correct = [89 163 359 397 613 647 811 953 991 1153 1277 1297 1423 1531 1619 1621 1693 1747 1783 1801 1979 2357 2753 3167 4049 5003 6029 7127 8297 9539 10853 12239 13697 15227 16829 18503 20249 22067 23957 25919 27953 30059 32237 34487 36809];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Kazmenko and Trofimov (2006)\r\na = [-66 3845 -60897 251831];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 46;\r\np_correct = [811 3529 8537 8681 10613 16553 19249 23057 28211 30139 32089 32911 35027 35221 36637 38639 39301 40637 43891 57413 57593 65539 70309 77719 80651 82183 92639 92863 101281 101963 103421 107713 109789 111539 112363 131627 144889 189961 194713 251831 256049 330287 413071 504797 605861 716659];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac (2006)\r\na = [1 -99 3588 -56822 348272 -286397];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 47;\r\np_correct = [1409 2441 3517 5227 5669 7963 8209 8543 9733 10429 14243 24251 27763 29531 32411 39971 41051 52301 52561 59971 60443 62903 64811 91673 106531 156353 196003 210011 212123 270631 286397 327491 336121 355331 377021 402851 412123 424163 584411 900061 1321283 1869383 2568091 3443681 4525091 5844043 7435163];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Beyleveld (2006)\r\na = [1 -97 3294 -45458 213589];\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 50;p_correct = [109 271 541 673 1409 1873 1949 2069 2251 2341 3719 3881 4019 4451 4951 5227 5273 5449 6029 7109 7129 7789 8573 9209 9739 10223 10399 10529 10789 10889 15173 17669 25919 27449 39769 40129 56123 57149 75869 78509 99829 104323 128489 135089 162359 171329 201973 213589 247889];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Wroblewski and Meyrignac (2006)\r\na = [1 -126 6217 -153066 1987786 -13055316 34747236]/36;\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 55;\r\np_correct = [461 1091 2423 3583 4493 4549 6271 6961 7019 7933 8443 9007 9157 10429 12007 13241 13553 15443 15733 16193 20873 23993 32423 32969 35051 45737 46769 54959 56597 57397 61613 63421 64693 67993 98321 163561 166693 272563 318467 429409 552089 653687 887543 965201 1352093 1977581 2800877 3864349 5216353 6911743 9012401 11587787 14715509 18481913 22982693];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n\r\n%% Dress and Landreau (2002), Gupta (2006)\r\na = [1 -133 6729 -158379 1720294 -6823316]/4;\r\n[n,p] = polyPrimeRun(a);\r\nn_correct = 57;\r\np_correct = [383 1721 3733 3923 4259 5323 10181 12547 12659 19373 20611 23887 26539 27847 32687 33073 37571 53149 65993 70123 87977 106207 124351 134077 142019 158923 174907 189977 204331 218389 228581 232823 248587 266947 289511 318259 355049 355573 404267 467617 519643 549391 653879 729173 785923 950947 991127 1154987 1313701 1404721 1705829 1707499 2071373 2505127 3018307 3621251 4325119];\r\nassert(isequal(n,n_correct))\r\nassert(isequal(p,p_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2025-06-30T16:26:09.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-06-29T03:20:05.000Z","updated_at":"2026-02-06T13:37:00.000Z","published_at":"2025-06-29T03:20:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60942\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60942\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60943\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60943\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60944\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e60944\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involve \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003epolynomials that generate primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. No polynomial can generate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e prime numbers, but some can generate sizable runs of primes. For example, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 0, 1, 2,…,10, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(n) = 2n^2+11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(n) = 2n^2+11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e produces 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, and 211, which are all prime. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, both terms in the polynomial are divisible by 11, and the result (253) is composite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the coefficients of the polynomial in standard Matlab form (i.e., a vector with the coefficients in order of decreasing order of the terms) and returns the length of the longest run of primes as well as a sorted list (low to high) of the distinct primes in the run. Please note the following:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTake the absolute value of the output of the polynomial. For example, consider -11, -13, -19, etc. to be prime for this problem, even though negative numbers are not strictly considered to be prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRound the absolute value to the nearest integer. Although this step is not necessary when the coefficients of the polynomial are integers, it can be necessary when they are not, as in the last two tests.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake sure to list only the primes in the longest run. The polynomials will produce other primes outside of the longest run, but do not include them in the output. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1473,"title":"Legendre polynomials","description":"Given an integer _n_ \u0026ge; 0, generate the _n_-th \u003chttp://en.wikipedia.org/wiki/Legendre_polynomials Legendre polynomial\u003e.\r\n\r\n*Examples*:\r\n\r\n legendrePoly(0)\r\n ans =\r\n 1\r\n\r\n legendrePoly(1)\r\n ans =\r\n 1 0\r\n\r\n legendrePoly(2)\r\n ans =\r\n 1.5 0 -0.5\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0, generate the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Legendre_polynomials\"\u003eLegendre polynomial\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e legendrePoly(0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e legendrePoly(1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e legendrePoly(2)\r\n ans =\r\n 1.5 0 -0.5\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = legendrePoly(n)\r\n P = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('legendrePoly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1]/1;\r\nassert(isequal(round(legendrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0]/1;\r\nassert(isequal(round(legendrePoly(n)*1),round(P_correct*1)));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [3 0 -1]/2;\r\nassert(isequal(round(legendrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [5 0 -3 0]/2;\r\nassert(isequal(round(legendrePoly(n)*2),round(P_correct*2)));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [35 0 -30 0 3]/8;\r\nassert(isequal(round(legendrePoly(n)*8),round(P_correct*8)));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [63 0 -70 0 15 0]/8;\r\nassert(isequal(round(legendrePoly(n)*8),round(P_correct*8)));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [231 0 -315 0 105 0 -5]/16;\r\nassert(isequal(round(legendrePoly(n)*16),round(P_correct*16)));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [429 0 -693 0 315 0 -35 0]/16;\r\nassert(isequal(round(legendrePoly(n)*16),round(P_correct*16)));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [6435 0 -12012 0 6930 0 -1260 0 35]/128;\r\nassert(isequal(round(legendrePoly(n)*128),round(P_correct*128)));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [12155 0 -25740 0 18018 0 -4620 0 315 0]/128;\r\nassert(isequal(round(legendrePoly(n)*128),round(P_correct*128)));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [46189 0 -109395 0 90090 0 -30030 0 3465 0 -63]/256;\r\nassert(isequal(round(legendrePoly(n)*256),round(P_correct*256)));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [88179 0 -230945 0 218790 0 -90090 0 15015 0 -693 0]/256;\r\nassert(isequal(round(legendrePoly(n)*256),round(P_correct*256)));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [676039 0 -1939938 0 2078505 0 -1021020 0 225225 0 -18018 0 231]/1024;\r\nassert(isequal(round(legendrePoly(n)*1024),round(P_correct*1024)));\r\n\r\n%%\r\nn = 13;\r\nP_correct = [1300075 0 -4056234 0 4849845 0 -2771340 0 765765 0 -90090 0 3003 0]/1024;\r\nassert(isequal(round(legendrePoly(n)*1024),round(P_correct*1024)));\r\n\r\n%%\r\nn = 14;\r\nP_correct = [5014575 0 -16900975 0 22309287 0 -14549535 0 4849845 0 -765765 0 45045 0 -429]/2048;\r\nassert(isequal(round(legendrePoly(n)*2048),round(P_correct*2048)));\r\n\r\n%%\r\nn = 15;\r\nP_correct = [9694845 0 -35102025 0 50702925 0 -37182145 0 14549535 0 -2909907 0 255255 0 -6435 0]/2048;\r\nassert(isequal(round(legendrePoly(n)*2048),round(P_correct*2048)));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T10:43:53.000Z","updated_at":"2026-04-01T10:26:23.000Z","published_at":"2013-04-30T10:45:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Legendre_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLegendre polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ legendrePoly(0)\\n ans =\\n 1\\n\\n legendrePoly(1)\\n ans =\\n 1 0\\n\\n legendrePoly(2)\\n ans =\\n 1.5 0 -0.5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1068,"title":"Guess the Coefficients!","description":"Given a polynomial p known to have positive integer coefficients, deduce the values of the coefficients.\r\nFor example:\r\n p = @(x) x^2 + 2*x + 15;\r\n c = guess_the_coefficients(p);\r\noutputs\r\n c = [1 2 15]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 81.65px; transform-origin: 407px 81.65px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60px 8px; transform-origin: 60px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a polynomial\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e known to have positive integer coefficients, deduce the values of the coefficients.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 112px 8.5px; tab-size: 4; transform-origin: 112px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e p = @(x) x^2 + 2*x + 15;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 136px 8.5px; tab-size: 4; transform-origin: 136px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = guess_the_coefficients(p);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.5px 8px; transform-origin: 23.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eoutputs\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = [1 2 15]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = guess_the_coefficients(p)\r\n c = p(0);\r\nend","test_suite":"%%\r\nassert(isequal(guess_the_coefficients(@(x)3*x^2+5*x+7),[3 5 7]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)x^2+2*x+15),[1 2 15]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)2*x^3+4*x^2+6*x+8),[2 4 6 8]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval(53,x)),53))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([54 87],x)),[54 87]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([49 40 68],x)),[49 40 68]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([75 53 35 15],x)),[75 53 35 15]))\r\n\r\n%%\r\nassert(isequal(guess_the_coefficients(@(x)polyval([59 27 5 76 25],x)),[59 27 5 76 25]))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":134,"edited_by":223089,"edited_at":"2023-01-07T11:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2023-01-07T11:04:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-27T06:47:08.000Z","updated_at":"2025-11-16T14:54:18.000Z","published_at":"2012-12-05T06:28:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e known to have positive integer coefficients, deduce the values of the coefficients.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = @(x) x^2 + 2*x + 15;\\n c = guess_the_coefficients(p);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutputs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [1 2 15]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60998,"title":"Bernstein Basis Polynomials","description":"Return the coefficients of a Bernstein Basis Polynomial B(v,n) for degree n and order v - \r\n \r\n%Examples\r\nB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\r\nOutput = [-10 30 -30 10 0 0];\r\n\r\nB(3, 3) = x^3\r\nOutput = [1 0 0 0];\r\n\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 274.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 137.3px; transform-origin: 408px 137.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.05px 8px; transform-origin: 85.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the coefficients of a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Bernstein_polynomial#Bernstein_basis_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eBernstein Basis Polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eB(v,n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.7833px 8px; transform-origin: 35.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for degree \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8417px 8px; transform-origin: 33.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.21667px 8px; transform-origin: 6.21667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 61.3px; transform-origin: 405px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 34.65px 8.5px; tab-size: 4; transform-origin: 34.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 227.15px 8.5px; tab-size: 4; transform-origin: 227.15px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.5px; tab-size: 4; transform-origin: 115.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [-10 30 -30 10 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eB(3, 3) = x^3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 8.5px; tab-size: 4; transform-origin: 73.15px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 0 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.167px 8px; transform-origin: 262.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = bernstein(x)\r\n x = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('bernstein.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun') || ...\r\n contains(filetext, 'elseif') || contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 5;\r\nv = 2;\r\ny = [-10 30 -30 10 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = randi(100);\r\nv = n;\r\ny = [1 zeros(1,v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 7;\r\nv = 0;\r\ny = [-1 7 -21 35 -35 21 -7 1];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 1;\r\nv = 0;\r\ny = [-1 1];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 7;\r\nv = 3;\r\ny = [35 -140 210 -140 35 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 10;\r\nv = 4;\r\ny = [210 -1260 3150 -4200 3150 -1260 210 0 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 12;\r\nv = 10;\r\ny = [66 -132 66 zeros(1,v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 25;\r\nv = 16;\r\ny = [-2042975 18386775 -73547100 171609900 -257414850 257414850 -171609900 73547100 -18386775 2042975 zeros(1, v)];\r\nassert(isequal(bernstein(v,n),y))\r\n\r\n%%\r\nn = 13;\r\nv = 9;\r\ny = [715 -2860 4290 -2860 715 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(bernstein(v,n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:26:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-13T06:26:45.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-10T15:17:42.000Z","updated_at":"2026-01-26T14:24:46.000Z","published_at":"2025-09-10T16:33:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the coefficients of a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Bernstein_polynomial#Bernstein_basis_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eBernstein Basis Polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eB(v,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for degree \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examples\\nB(2, 5) = 10*x^2*(1-x)^3 = -10*x^5 + 30*x^4 - 30*3 + 10*x^2\\nOutput = [-10 30 -30 10 0 0];\\n\\nB(3, 3) = x^3\\nOutput = [1 0 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1304,"title":"Hermite Polynomials","description":"Return the _n_-th \u003chttp://en.wikipedia.org/wiki/Hermite_polynomials Hermite polynomial\u003e of the physicists' type.\r\n\r\nAssume that _n_ is a non-negative finite integer. \r\n\r\n*Examples*:\r\n\r\n hermite_poly(0)\r\n ans = \r\n 1\r\n \r\n hermite_poly(1)\r\n ans = \r\n 2 0\r\n\r\n hermite_poly(2)\r\n ans = \r\n 4 0 -2\r\n\r\n hermite_poly(3)\r\n ans = \r\n 8 0 -12 0\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eReturn the \u003ci\u003en\u003c/i\u003e-th \u003ca href = \"http://en.wikipedia.org/wiki/Hermite_polynomials\"\u003eHermite polynomial\u003c/a\u003e of the physicists' type.\u003c/p\u003e\u003cp\u003eAssume that \u003ci\u003en\u003c/i\u003e is a non-negative finite integer.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e hermite_poly(0)\r\n ans = \r\n 1\u003c/pre\u003e\u003cpre\u003e hermite_poly(1)\r\n ans = \r\n 2 0\u003c/pre\u003e\u003cpre\u003e hermite_poly(2)\r\n ans = \r\n 4 0 -2\u003c/pre\u003e\u003cpre\u003e hermite_poly(3)\r\n ans = \r\n 8 0 -12 0\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function p = hermite_poly(n)\r\n p = n;\r\nend","test_suite":"%%\r\nuser_solution = fileread('hermite_poly.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [2 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [4 0 -2];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [8 0 -12 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [16 0 -48 -0 12];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [32 0 -160 -0 120 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [64 0 -480 -0 720 0 -120];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [128 0 -1344 -0 3360 0 -1680 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [256 0 -3584 -0 13440 0 -13440 -0 1680];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [512 0 -9216 -0 48384 0 -80640 -0 30240 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1024 0 -23040 -0 161280 0 -403200 -0 302400 0 -30240];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 11;\r\nP_correct = [2048 0 -56320 -0 506880 0 -1774080 -0 2217600 0 -665280 -0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 12;\r\nP_correct = [4096 0 -135168 -0 1520640 0 -7096320 -0 13305600 0 -7983360 -0 665280];\r\nassert(isequal(hermite_poly(n),P_correct));","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":91,"test_suite_updated_at":"2013-04-28T07:05:09.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-02-27T09:28:44.000Z","updated_at":"2026-04-08T15:27:48.000Z","published_at":"2013-02-27T09:28:44.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Hermite_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHermite polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the physicists' type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ hermite_poly(0)\\n ans = \\n 1\\n\\n hermite_poly(1)\\n ans = \\n 2 0\\n\\n hermite_poly(2)\\n ans = \\n 4 0 -2\\n\\n hermite_poly(3)\\n ans = \\n 8 0 -12 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61179,"title":"Rotating 2d curve around a vertical axis","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the Oxz plane, around the vertical axis that passes through the vertex by an angle θ (see figures below).\r\nGiven the x-value of a point P, xP, belonging to the 2d curve, find R being the rotated point P.\r\nHint. Find critical points for their identification and behavior.\r\ninput: (p, xP, theta)\r\noutput: R\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 443.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 221.9px; transform-origin: 469px 221.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxz\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eθ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figures below).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-value of a point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003exP,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e belonging to the 2d curve, find \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e being the rotated point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Find critical points for their identification and behavior.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(p, xP, theta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 251.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 125.9px; text-align: left; transform-origin: 445px 125.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"326\" height=\"106\" style=\"vertical-align: baseline;width: 326px;height: 106px\" 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\" alt=\"Rotating 3d\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = rotate3d(p, xP, theta)\r\n R = x;\r\nend","test_suite":"%%\r\np = [3 -20 12 96 -39];\r\nxP = 4;\r\ntheta = pi/2;\r\nR_correct = [-1 5 25];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 1;\r\ntheta = pi/3;\r\nR_correct = [0 sqrt(3) 52];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [3 -20 12 96 -39];\r\nxP = 0;\r\ntheta = pi;\r\nR_correct = [-2 0 -39];\r\nassert(all(isapprox(rotate3d(p, xP, theta),R_correct), 'all'))\r\n\r\n%%\r\np = [2 0 0 0 0 0 -16];\r\nxP = sqrt(2);\r\ntheta = 3*pi/4;\r\nR_correct = [-1 1 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\nfiletext = fileread('rotate3d.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [-11/4 7 11/4 -7 0];\r\nxP = 0;\r\ntheta = 2*pi/3;\r\nR_correct = [3 -sqrt(3) 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n\r\n%%\r\np = [-1 28/11 1 -28/11 0];\r\nxP = -1;\r\ntheta = pi/2;\r\nR_correct = [2 -3 0];\r\ntolerance = 1e-13;\r\nassert(all(abs(rotate3d(p, xP, theta) - R_correct) \u003c tolerance, 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-02-14T16:56:43.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-01T12:37:27.000Z","updated_at":"2026-04-01T09:52:04.000Z","published_at":"2026-02-14T16:56:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotation of the 2d curve, which represents the polynomial graph in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxz\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane, around the vertical axis that passes through the vertex by an angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eθ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figures below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-value of a point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exP,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e belonging to the 2d curve, find \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e being the rotated point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Find critical points for their identification and behavior.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(p, xP, theta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61148,"title":"Shifting vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b], \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewith \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u0026lt;b\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe interval \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined such that the endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stand for the least and the greatest \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-values of the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep(x) = y_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_peak\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the highest local maximum of the polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see non-scale figures below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe endpoints \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they exist. Otherwise, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb = '' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see Hint 1);\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe shifting constant, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 1. An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-degree polynomial has exactly \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n a = x;\r\n b = x;\r\n k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe shifting constant, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 1. An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-degree polynomial has exactly \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b, k]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57560,"title":"Hermite Polynomials","description":"Problem 1304 deals with Hermite polynomial of the physicist's type.\r\nIn this problem, Return the n-th Hermite polynomial of the probabilist' type.\r\nAssume that n is a non-negative finite integer.\r\nExamples:\r\n hermite_poly(0)\r\n ans = \r\n 1\r\n\r\n hermite_poly(1)\r\n ans = \r\n 1 0\r\n\r\n hermite_poly(2)\r\n ans = \r\n 1 0 -1\r\n\r\nNeither string operations nor interpolations are allowed!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 406.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 203.383px; transform-origin: 407px 203.383px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://in.mathworks.com/matlabcentral/cody/problems/1304\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 1304\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116.5px 8px; transform-origin: 116.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with Hermite polynomial of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ephysicist\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's type.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.5px 8px; transform-origin: 85.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, Return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.5px 8px; transform-origin: 8.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-th\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hermite_polynomials\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHermite polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22px 8px; transform-origin: 22px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eprobabilist\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e' type.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39px 8px; transform-origin: 39px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume that\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a non-negative finite integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 224.767px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 112.383px; transform-origin: 404px 112.383px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(0)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 24px 8.5px; tab-size: 4; transform-origin: 24px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e hermite_poly(2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e ans = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 1 0 -1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 8px; transform-origin: 24.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNeither \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.5px 8px; transform-origin: 60.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003estring operations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e nor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49px 8px; transform-origin: 49px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einterpolations\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are allowed!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hermite_poly(n)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hermite_poly.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n contains(filetext, 'interp') || contains(filetext, '2str') || ...\r\n contains(filetext, 'str2'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\nP_correct = [1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 1;\r\nP_correct = [1 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 2;\r\nP_correct = [1 0 -1];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 3;\r\nP_correct = [1 0 -3 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 4;\r\nP_correct = [1 0 -6 0 3];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 5;\r\nP_correct = [1 0 -10 0 15 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 6;\r\nP_correct = [1 0 -15 0 45 0 -15];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 7;\r\nP_correct = [1 0 -21 0 105 0 -105 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 8;\r\nP_correct = [1 0 -28 0 210 0 -420 0 105];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 9;\r\nP_correct = [1 0 -36 0 378 0 -1260 0 945 0];\r\nassert(isequal(hermite_poly(n),P_correct));\r\n\r\n%%\r\nn = 10;\r\nP_correct = [1 0 -45 0 630 0 -3150 0 4725 0 -945];\r\nassert(isequal(hermite_poly(n),P_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":223089,"edited_by":223089,"edited_at":"2023-01-20T06:47:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-18T07:24:00.000Z","updated_at":"2026-01-26T13:48:46.000Z","published_at":"2023-01-18T07:24:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://in.mathworks.com/matlabcentral/cody/problems/1304\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 1304\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with Hermite polynomial of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ephysicist\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e's type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, Return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-th\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hermite_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHermite polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprobabilist\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e' type.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a non-negative finite integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ hermite_poly(0)\\n ans = \\n 1\\n\\n hermite_poly(1)\\n ans = \\n 1 0\\n\\n hermite_poly(2)\\n ans = \\n 1 0 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44260,"title":"Multivariate polynomials - convert monomial form to array","description":"In \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials Problem 44259\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\r\n\r\n# Defining a polynomial is an indexing headache, with a high probability of errors. \r\n# Polynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\r\n\r\nHere, we will represent a polynomial as a sum of monomials. For example, the polynomial |p(x,y) = 2*x^5*y + 3*x*y^5| is the sum of two monomials in |x| and |y|. We will represent this by |exponents|, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector |coefficients| for the coefficient of each monomial. For |p(x,y)|, these are\r\n\r\n exponents = [5 1; 1 5];\r\ncoefficients = [2; 3];\r\n\r\nLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\r\n\r\n function c = coeffArray(exponents,coefficients)\r\n\r\nthat inputs the exponents and coefficients and returns an array as defined in Problem 44259.","description_html":"\u003cp\u003eIn \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials\"\u003eProblem 44259\u003c/a\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\u003c/p\u003e\u003col\u003e\u003cli\u003eDefining a polynomial is an indexing headache, with a high probability of errors.\u003c/li\u003e\u003cli\u003ePolynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eHere, we will represent a polynomial as a sum of monomials. For example, the polynomial \u003ctt\u003ep(x,y) = 2*x^5*y + 3*x*y^5\u003c/tt\u003e is the sum of two monomials in \u003ctt\u003ex\u003c/tt\u003e and \u003ctt\u003ey\u003c/tt\u003e. We will represent this by \u003ctt\u003eexponents\u003c/tt\u003e, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector \u003ctt\u003ecoefficients\u003c/tt\u003e for the coefficient of each monomial. For \u003ctt\u003ep(x,y)\u003c/tt\u003e, these are\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eexponents = [5 1; 1 5];\r\ncoefficients = [2; 3];\r\n\u003c/pre\u003e\u003cp\u003eLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003efunction c = coeffArray(exponents,coefficients)\r\n\u003c/pre\u003e\u003cp\u003ethat inputs the exponents and coefficients and returns an array as defined in Problem 44259.\u003c/p\u003e","function_template":"function c = coeffArray(exponents,coefficients)\r\nc = 0;\r\nend","test_suite":"%% test coeffArray\r\nfiletext = fileread('coeffArray.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% No variables\r\nexponents = 0;\r\ncoefficients = randi(1000);\r\ncA = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% Single variable\r\ncoefficients = randi(1000,[10 1]);\r\nexponents = (9:-1:0)';\r\ncA = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% a*x^2+b*y\r\na = randi(1000);\r\nb = randi(1000);\r\nexponents = [2 0; 0 1];\r\ncoefficients = [a; b];\r\ncA = [0 a; 0 0; b 0];\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% a*x^2+b*y^2+c*z^2+d\r\na = randi(1000);\r\nb = randi(1000);\r\nc = randi(1000);\r\nd = randi(1000);\r\nexponents = [2 0 0; 0 2 0; 0 0 2; 0 0 0];\r\ncoefficients = [a; b; c; d];\r\ncA = zeros([3 3 3]);\r\ncA(1,3,3) = a;\r\ncA(3,1,3) = b;\r\ncA(3,3,1) = c;\r\ncA(3,3,3) = d;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n\r\n%% Many variables\r\ncoefficients = randi(1000);\r\nnVars = randi(20)+1;\r\nexponents = ones(1,nVars);\r\ncA = zeros(2*ones(1,nVars));\r\ncA(1) = coefficients;\r\nassert(isequal(coeffArray(exponents,coefficients),cA))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-13T16:16:41.000Z","updated_at":"2025-12-22T13:09:01.000Z","published_at":"2017-07-13T16:26:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44259-product-of-two-multidimensional-polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 44259\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e I asked you to multiply two multidimensional polynomials that were represented by an array that is a generalization of the way MATLAB handles one-variable polynomials. However, that representation has at least two problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefining a polynomial is an indexing headache, with a high probability of errors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePolynomials often have a small number of terms, so if they are higher order there will be a lot of wasted storage.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere, we will represent a polynomial as a sum of monomials. For example, the polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y) = 2*x^5*y + 3*x*y^5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the sum of two monomials in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. We will represent this by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, a matrix of integers with each row representing the exponents of one monomial (including zeros); and a column vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for the coefficient of each monomial. For\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x,y)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, these are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[exponents = [5 1; 1 5];\\ncoefficients = [2; 3];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's hedge our bets, though, and create a function that converts this form to the array form. Your task is to create a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function c = coeffArray(exponents,coefficients)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethat inputs the exponents and coefficients and returns an array as defined in Problem 44259.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1476,"title":"Radial Zernike polynomials","description":"Given an integer _n_ \u0026ge; 0 and an integer _m_ \u0026ge; 0, generate the \u003chttp://en.wikipedia.org/wiki/Zernike_polynomials radial Zernike polynomial\u003e of radial degree _n_ and azimuthal degree _m_. You may assume that |mod(n-m,2)==0| and _m_ \u0026le; _n_.\r\n\r\n*Examples*:\r\n\r\n radialZernike(0,0)\r\n ans =\r\n 1\r\n\r\n radialZernike(1,1)\r\n ans =\r\n 1 0\r\n\r\n radialZernike(2,0)\r\n ans =\r\n 2 0 -1\r\n\r\n radialZernike(2,2)\r\n ans =\r\n 1 0 0\r\n\r\nNeither *string operations* nor *interpolations* are allowed!\r\n","description_html":"\u003cp\u003eGiven an integer \u003ci\u003en\u003c/i\u003e \u0026ge; 0 and an integer \u003ci\u003em\u003c/i\u003e \u0026ge; 0, generate the \u003ca href = \"http://en.wikipedia.org/wiki/Zernike_polynomials\"\u003eradial Zernike polynomial\u003c/a\u003e of radial degree \u003ci\u003en\u003c/i\u003e and azimuthal degree \u003ci\u003em\u003c/i\u003e. You may assume that \u003ctt\u003emod(n-m,2)==0\u003c/tt\u003e and \u003ci\u003em\u003c/i\u003e \u0026le; \u003ci\u003en\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e:\u003c/p\u003e\u003cpre\u003e radialZernike(0,0)\r\n ans =\r\n 1\u003c/pre\u003e\u003cpre\u003e radialZernike(1,1)\r\n ans =\r\n 1 0\u003c/pre\u003e\u003cpre\u003e radialZernike(2,0)\r\n ans =\r\n 2 0 -1\u003c/pre\u003e\u003cpre\u003e radialZernike(2,2)\r\n ans =\r\n 1 0 0\u003c/pre\u003e\u003cp\u003eNeither \u003cb\u003estring operations\u003c/b\u003e nor \u003cb\u003einterpolations\u003c/b\u003e are allowed!\u003c/p\u003e","function_template":"function P = radialZernike(n,m)\r\n P = n*m;\r\nend","test_suite":"%%\r\nuser_solution = fileread('radialZernike.m');\r\nassert(isempty(strfind(user_solution,'regexp')));\r\nassert(isempty(strfind(user_solution,'2str')));\r\nassert(isempty(strfind(user_solution,'str2')));\r\nassert(isempty(strfind(user_solution,'interp')));\r\nassert(isempty(strfind(user_solution,'printf')));\r\nassert(isempty(strfind(user_solution,'assert')));\r\n\r\n%%\r\nn = 0;\r\nm = 0;\r\nP_correct = [1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 1;\r\nm = 1;\r\nP_correct = [1 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 2;\r\nm = 0;\r\nP_correct = [2 0 -1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 2;\r\nm = 2;\r\nP_correct = [1 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 3;\r\nm = 1;\r\nP_correct = [3 0 -2 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 3;\r\nm = 3;\r\nP_correct = [1 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 0;\r\nP_correct = [6 0 -6 0 1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 2;\r\nP_correct = [4 0 -3 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 4;\r\nm = 4;\r\nP_correct = [1 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 1;\r\nP_correct = [10 0 -12 0 3 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 3;\r\nP_correct = [5 0 -4 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 5;\r\nm = 5;\r\nP_correct = [1 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 0;\r\nP_correct = [20 0 -30 0 12 0 -1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 2;\r\nP_correct = [15 0 -20 0 6 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 4;\r\nP_correct = [6 0 -5 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 6;\r\nm = 6;\r\nP_correct = [1 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 1;\r\nP_correct = [35 0 -60 0 30 0 -4 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 3;\r\nP_correct = [21 0 -30 0 10 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 5;\r\nP_correct = [7 0 -6 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 7;\r\nm = 7;\r\nP_correct = [1 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 0;\r\nP_correct = [70 0 -140 0 90 0 -20 0 1];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 2;\r\nP_correct = [56 0 -105 0 60 0 -10 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 4;\r\nP_correct = [28 0 -42 0 15 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 6;\r\nP_correct = [8 0 -7 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 8;\r\nm = 8;\r\nP_correct = [1 0 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 1;\r\nP_correct = [126 0 -280 0 210 0 -60 0 5 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 3;\r\nP_correct = [84 0 -168 0 105 0 -20 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 5;\r\nP_correct = [36 0 -56 0 21 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 7;\r\nP_correct = [9 0 -8 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n\r\n%%\r\nn = 9;\r\nm = 9;\r\nP_correct = [1 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(radialZernike(n,m),P_correct));\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":10352,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2013-04-30T13:10:33.000Z","rescore_all_solutions":false,"group_id":25,"created_at":"2013-04-30T13:05:27.000Z","updated_at":"2026-04-08T15:23:08.000Z","published_at":"2013-04-30T13:10:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0 and an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≥ 0, generate the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Zernike_polynomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradial Zernike polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of radial degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and azimuthal degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. You may assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emod(n-m,2)==0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≤\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ radialZernike(0,0)\\n ans =\\n 1\\n\\n radialZernike(1,1)\\n ans =\\n 1 0\\n\\n radialZernike(2,0)\\n ans =\\n 2 0 -1\\n\\n radialZernike(2,2)\\n ans =\\n 1 0 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeither\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estring operations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e nor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einterpolations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are allowed!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61145,"title":"Translating even-degree polynomial by its vertex to the origin","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint. Compare to the Problem 61143.\r\ninput: p\r\noutput: [d, v, h]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 157.587px; transform-origin: 408px 157.594px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ed (d\u0026gt;0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the shifting distance of the above translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Compare to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61143\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[d, v, h]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_vertex(p)\r\n d = x;\r\n v = x;\r\n h = x;\r\nend","test_suite":"%%\r\np = [1 0 0 0 -1];\r\nd_correct = 1;\r\nv_correct = 'up';\r\nh_correct = '';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [1/4 -1/3 -2.5 -3 16.25];\r\nd_correct = 5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.25 -1 0.5 -3 15.25];\r\nd_correct = 5;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_vertex.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 54];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nd_correct = 2;\r\nv_correct = '';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-0.5 -2.4 3 22 -4.5 -54 -25.4];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-04T13:00:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-26T17:29:02.000Z","updated_at":"2026-03-26T10:19:33.000Z","published_at":"2026-01-04T13:00:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint. Compare to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[d, v, h]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55270,"title":"Cyclotomic Polynomials","description":"Given a Natural number (N), return the corresponding Cyclotomic Polynomial.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171px 8px; transform-origin: 171px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a Natural number (N), return the corresponding \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Cyclotomic_polynomial\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCyclotomic Polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = cyclcopoly(x)\r\n y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('cyclcopoly.m');\r\nassert(isempty(strfind(filetext, 'assignin')))\r\nassert(isempty(strfind(filetext, 'switch')))\r\nassert(isempty(strfind(filetext, 'else')))\r\n\r\n%%\r\nx = 1;\r\ny = [1 -1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 2;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 3;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 4;\r\ny = [1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 6;\r\ny = [1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 7;\r\ny = ones(1,x);\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 8;\r\ny = [1 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 9;\r\ny = [1 0 0 1 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 10;\r\ny = [1 -1 1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 12;\r\ny = [1 0 -1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 14;\r\ny = [1 -1 1 -1 1 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 15;\r\ny = [1 -1 0 1 -1 1 0 -1 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 16;\r\ny = [1 0 0 0 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 18;\r\ny = [1 0 0 -1 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 24;\r\ny = [1 0 0 0 -1 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 25;\r\ny = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 27;\r\ny = [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 28;\r\ny = [1 0 -1 0 1 0 -1 0 1 0 -1 0 1];\r\nassert(isequal(cyclcopoly(x),y))\r\n\r\n%%\r\nx = 105;\r\ny = [1 1 1 0 0 -1 -1 -2 -1 -1 0 0 1 1 1 1 1 1 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 0 1 1 1 1 1 1 0 0 -1 -1 -2 -1 -1 0 0 1 1 1]; \r\nassert(isequal(cyclcopoly(x),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-12T05:04:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-01T15:05:58.000Z","updated_at":"2026-01-25T13:40:43.000Z","published_at":"2022-08-01T15:05:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a Natural number (N), return the corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Cyclotomic_polynomial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCyclotomic Polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44262,"title":"Multivariate polynomials - overload multiplication","description":"Problems \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array 44260\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials 44261\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix |exponents| with a row of exponents for each monomial, and a column vector |coefficients| with a coefficient for each monomial.\r\n\r\nIt would be nice to define polynomials so they can be multiplied using simple notation:\r\n\r\n p = p1*p2;\r\n\r\nThis can be done by \u003chttps://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html defining a class\u003e |mPoly| with two properties, |exponents| and |coefficients|, and two methods: a \u003chttps://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html constructor\u003e with the syntax\r\n\r\n p = mPoly(exponents, coefficients)\r\n\r\nand a method \u003chttps://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026s_tid=doc_srchtitle mtimes\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\r\n","description_html":"\u003cp\u003eProblems \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array\"\u003e44260\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials\"\u003e44261\u003c/a\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix \u003ctt\u003eexponents\u003c/tt\u003e with a row of exponents for each monomial, and a column vector \u003ctt\u003ecoefficients\u003c/tt\u003e with a coefficient for each monomial.\u003c/p\u003e\u003cp\u003eIt would be nice to define polynomials so they can be multiplied using simple notation:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = p1*p2;\r\n\u003c/pre\u003e\u003cp\u003eThis can be done by \u003ca href = \"https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html\"\u003edefining a class\u003c/a\u003e \u003ctt\u003emPoly\u003c/tt\u003e with two properties, \u003ctt\u003eexponents\u003c/tt\u003e and \u003ctt\u003ecoefficients\u003c/tt\u003e, and two methods: a \u003ca href = \"https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html\"\u003econstructor\u003c/a\u003e with the syntax\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ep = mPoly(exponents, coefficients)\r\n\u003c/pre\u003e\u003cp\u003eand a method \u003ca href = \"https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026s_tid=doc_srchtitle\"\u003emtimes\u003c/a\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\u003c/p\u003e","function_template":"classdef mPoly \r\n %MPOLY Class of multivariate polynomials\r\n \r\n properties\r\n exponents\r\n coefficients\r\n end\r\n \r\n methods\r\n function p = mPoly(ex,co)\r\n end\r\n function p = mtimes(p1,p2)\r\n end\r\n end\r\n \r\nend\r\n","test_suite":"%% Test polyMult\r\nfiletext = fileread('mPoly.m');\r\nassert(~contains(filetext,'regexp'))\r\n\r\n%% p1 = A, p2 = B\r\nc1 = randi(1000); c2 = randi(1000);\r\ne = 0;\r\np1 = mPoly(e,c1);\r\np2 = mPoly(e,c2);\r\np = p1*p2;\r\nassert(isequal(c1*c2,p.coefficients))\r\nassert(isequal(e,p.exponents))\r\n\r\n%% p1 = y-x^2, p2 = x-2\r\ne1 = [2 0; 0 1];\r\nc1 = [-1; 1];\r\ne2 = [1 0; 0 0];\r\nc2 = [1; -2];\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 1; 1 1; 2 0; 3 0]))\r\nassert(isequal(c,[-2; 1; 2; -1]))\r\n\r\n%% p1 = y-x^2, p2 = z-2\r\ne1 = [0 1 0; 2 0 0];\r\nc1 = [1; -1];\r\ne2 = [0 0 1; 0 0 0];\r\nc2 = [1; -2];\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 1 0; 0 1 1; 2 0 0; 2 0 1]))\r\nassert(isequal(c,[-2; 1; 2; -1]))\r\n\r\n\r\n%% p1 = z-x^3, p2 = x^2+y^2+z^2-1\r\ne1 = [0 0 1; 3 0 0];\r\nc1 = [1; -1];\r\ne2 = [2 0 0; 0 2 0; 0 0 2; 0 0 0];\r\nc2 = [1; 1; 1; -1];\r\n\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np = p1*p2;\r\n\r\n[e,idx] = unique(p.exponents,'rows');\r\nc = p.coefficients(idx);\r\nassert(isequal(e,[0 0 1; 0 0 3; 0 2 1; 2 0 1; 3 0 0; 3 0 2; 3 2 0; 5 0 0]))\r\nassert(isequal(c,[-1 1 1 1 1 -1 -1 -1]'))\r\n\r\n%% Commutative\r\nc1 = randi(1000,[2 1]);\r\ne1 = randi(1000,[2 2]);\r\nc2 = randi(1000,[3 1]);\r\ne2 = randi(1000,[3 2]);\r\np1 = mPoly(e1,c1);\r\np2 = mPoly(e2,c2);\r\np12 = p1*p2;\r\np21 = p2*p1;\r\n[e12,i12] = unique(p12.exponents,'rows');\r\n[e21,i21] = unique(p21.exponents,'rows');\r\nc12 = p12.coefficients(i12);\r\nc21 = p21.coefficients(i21);\r\nassert(isequal(e12,e21))\r\nassert(isequal(c12,c21))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1011,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-14T04:04:05.000Z","updated_at":"2025-12-22T13:16:38.000Z","published_at":"2017-07-14T04:04:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblems\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44260\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44261\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e work with a monomial representation of multivariate polynomials. This has two parts, a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with a row of exponents for each monomial, and a column vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with a coefficient for each monomial.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt would be nice to define polynomials so they can be multiplied using simple notation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = p1*p2;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis can be done by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edefining a class\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emPoly\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with two properties,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexponents\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecoefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and two methods: a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econstructor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e with the syntax\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[p = mPoly(exponents, coefficients)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand a method\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes\u0026amp;s_tid=doc_srchtitle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emtimes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60996,"title":"Dickson Polynomials","description":"Return the coefficients of nth (n\u003e=0) Dickson polynomial of the 1st kind as follows - \r\n1st row of the output will be the coefficients of x, and, 2nd row of the output will be the coefficients of alpha.\r\n\r\nWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \r\n%Examplesa\r\nn=2;\r\nD2(x, alpha) = x^2 - 2*alpha\r\nOutput = [1 0 -2; 0 -2 1]\r\n\r\nn=3;\r\nD3(x, alpha) = x^3 - 3*x*alpha\r\nOutput = [1 0 -3 0; 0 0 -1 1]\r\n\r\nn=5;\r\nD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\r\n% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\r\n% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\r\n% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\r\nOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]\r\n\r\nOnly vectorized solutions will be accepted. Check the test suite for banned functions.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 539.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 269.75px; transform-origin: 408px 269.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.2167px 8px; transform-origin: 79.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8417px 8px; transform-origin: 33.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enth (n\u0026gt;=0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Dickson_polynomial\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eDickson polynomial\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.3917px 8px; transform-origin: 84.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the 1st kind as follows - \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1st row of the output will be the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.783px 8px; transform-origin: 164.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and, 2nd row of the output will be the coefficients of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ealpha\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.608px 8px; transform-origin: 375.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 306.5px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 153.25px; transform-origin: 405px 153.25px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 38.5px 8.5px; tab-size: 4; transform-origin: 38.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Examplesa\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD2(x, alpha) = x^2 - 2*alpha\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -2; 0 -2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=3;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 8.5px; tab-size: 4; transform-origin: 115.5px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD3(x, alpha) = x^3 - 3*x*alpha\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -3 0; 0 0 -1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 15.4px 8.5px; tab-size: 4; transform-origin: 15.4px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003en=5;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 177.1px 8.5px; tab-size: 4; transform-origin: 177.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 327.25px 8.5px; tab-size: 4; transform-origin: 327.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.45px 8.5px; tab-size: 4; transform-origin: 219.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 311.85px 8.5px; tab-size: 4; transform-origin: 311.85px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.167px 8px; transform-origin: 262.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = dicksonpoly(n)\r\n y = n^2;\r\nend","test_suite":"%%\r\nfiletext = fileread('dicksonpoly.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n contains(filetext, 'while') || contains(filetext, 'for ') || ...\r\n contains(filetext, 'cellfun') || contains(filetext, 'arrayfun') || ...\r\n contains(filetext, 'rowfun') || contains(filetext, 'structfun'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\ny = [1 0; 0 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 2;\r\ny = [1 0 -2; 0 -2 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 3;\r\ny = [1 0 -3 0; 0 0 -3 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 4;\r\ny = [1 0 -4 0 2; 0 0 2 -4 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 5;\r\ny = [1 0 -5 0 5 0; 0 0 0 5 -5 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 6;\r\n%D6(x, alpha) = x^6 - 6*alpha*x^4 + 9*alpha^2*x^2 - 2*alpha^3\r\ny = [1 0 -6 0 9 0 -2; 0 0 0 -2 9 -6 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 9;\r\n%D9(x, alpha) = x^9 - 9*alpha*x^7 + 27*alpha^2*x^5 - 30*alpha^3*x^3 + 9*alpha^4*x\r\ny = [1 0 -9 0 27 0 -30 0 9 0; 0 0 0 0 0 9 -30 27 -9 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n\r\n%%\r\nn = 10;\r\n%D10(x, alpha) = x^10 - 10*alpha*x^8 + 35*alpha^2*x^6 - 50*alpha^3*x^4 + 25*alpha^4*x^2 - 2*alpha^5\r\ny = [1 0 -10 0 35 0 -50 0 25 0 -2; 0 0 0 0 0 -2 25 -50 35 -10 1];\r\nassert(isequal(dicksonpoly(n),y))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-10T16:35:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2025-09-07T17:01:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-07T15:27:35.000Z","updated_at":"2026-01-26T13:57:28.000Z","published_at":"2025-09-07T15:27:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enth (n\u0026gt;=0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Dickson_polynomial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eDickson polynomial\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of the 1st kind as follows - \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1st row of the output will be the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and, 2nd row of the output will be the coefficients of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ealpha\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Examplesa\\nn=2;\\nD2(x, alpha) = x^2 - 2*alpha\\nOutput = [1 0 -2; 0 -2 1]\\n\\nn=3;\\nD3(x, alpha) = x^3 - 3*x*alpha\\nOutput = [1 0 -3 0; 0 0 -1 1]\\n\\nn=5;\\nD5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2\\n% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]\\n% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2\\n% = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]\\nOutput = [1 0 -5 0 5 0; 0 0 0 5 -5 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnly vectorized solutions will be accepted. Check the test suite for banned functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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