d

%______________________________________________________________25/06/07___
%|   Regular solution sub-function         |    H.C.Eng.Ali Özgül (C)(R)  |
%|_________________________________________|______________________________|
%|Sub Function Application                 |
%|                                         |
%| [Solution]=regsolution( func(R) )       |
%|_________________________________________|
% [Syntax]
%    [ssolution] = regsolution(func)
%    func = function(R-parameter)
%
%    The [ssolution] is the symbolic expression on general maple's [solve.m]
%    function. "R" parameter is selected as symbolic variable for [ssolution.m]
%    This solution sub-function outputs are returned the regular solution
%    technique with solution's roots order-degree
%
% [Example];
%    regsolution((R^10-4)*(R^2+1)^4*sin(R))   <--|
%
% *** Equation's roots && order-degree
%        0             1.0000
%        0 + 1.0000i   4.0000
%        0 - 1.0000i   4.0000
%   1.1487             1.0000
%  -1.1487             1.0000
%  -0.9293 - 0.6752i   1.0000
%   0.9293 + 0.6752i   1.0000
%  -0.3550 - 1.0925i   1.0000
%   0.3550 + 1.0925i   1.0000
%  -0.3550 + 1.0925i   1.0000
%   0.3550 - 1.0925i   1.0000
%  -0.9293 + 0.6752i   1.0000
%   0.9293 - 0.6752i   1.0000    %
%
%  *** Generaly solution with maple solve function's output
%  solution = solve((R^10-4)*(R^2+1)^4*sin(R),R)
%
%                                                                   sqrt(-1)
%                                                                   sqrt(-1)
%                                                                   sqrt(-1)
%                                                                   sqrt(-1)
%                                                                  -sqrt(-1)
%                                                                  -sqrt(-1)
%                                                                  -sqrt(-1)
%                                                                  -sqrt(-1)
%                                                                    2^(1/5)
%                                                                   -2^(1/5)
%  -((1/4*5^(1/2)-1/4+1/4*sqrt(-1)*2^(1/2)*(5+5^(1/2))^(1/2))*2^(2/5))^(1/2)
%   ((1/4*5^(1/2)-1/4+1/4*sqrt(-1)*2^(1/2)*(5+5^(1/2))^(1/2))*2^(2/5))^(1/2)
% -((-1/4*5^(1/2)-1/4+1/4*sqrt(-1)*2^(1/2)*(5-5^(1/2))^(1/2))*2^(2/5))^(1/2)
%  ((-1/4*5^(1/2)-1/4+1/4*sqrt(-1)*2^(1/2)*(5-5^(1/2))^(1/2))*2^(2/5))^(1/2)
% -((-1/4*5^(1/2)-1/4-1/4*sqrt(-1)*2^(1/2)*(5-5^(1/2))^(1/2))*2^(2/5))^(1/2)
%  ((-1/4*5^(1/2)-1/4-1/4*sqrt(-1)*2^(1/2)*(5-5^(1/2))^(1/2))*2^(2/5))^(1/2)
%  -((1/4*5^(1/2)-1/4-1/4*sqrt(-1)*2^(1/2)*(5+5^(1/2))^(1/2))*2^(2/5))^(1/2)
%   ((1/4*5^(1/2)-1/4-1/4*sqrt(-1)*2^(1/2)*(5+5^(1/2))^(1/2))*2^(2/5))^(1/2)

clc
clear

syms R real
regsolution ( (R^6-196)^10*(R-5)^4*(R^2+5));

Generaly solution equation with non-regular roots
 
ans =
 
                                     sqrt(-1)*5^(1/2)
                                    -sqrt(-1)*5^(1/2)
                                                    5
                                                    5
                                                    5
                                                    5
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                            -14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                             14^(1/3)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 
 
Generaly solution equation with regular format
 
ans =
 
                                                    5
                                                    5
                                                    5
                                                    5
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
                                             14^(1/3)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)+1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
 -(-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
  (-1/2*14^(2/3)-1/2*sqrt(-1)*3^(1/2)*14^(2/3))^(1/2)
                                     sqrt(-1)*5^(1/2)
                                    -sqrt(-1)*5^(1/2)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
                                            -14^(1/3)
 
 
Regular solution equation.s with order-degree roots

ssolution =

   5.0000             4.0000          
   2.4101            10.0000          
  -1.2051 - 2.0872i  10.0000          
   1.2051 + 2.0872i  10.0000          
  -1.2051 + 2.0872i  10.0000          
   1.2051 - 2.0872i  10.0000          
        0 + 2.2361i   1.0000          
        0 - 2.2361i   1.0000          
  -2.4101            10.0000          

Published with MATLAB® 7.1