function res = HasTerm(p1, p2, newTerm, vars)
% HasTerm.m
%
% A function for determining whether either of two polynomials contain a
% given term group. This function ignores coefficients of the polynomials and
% looks only at the groups of power terms.
%
% Input:
%
% p1 - First polynomial. Polynomials are described as vectors with the
% following format:
%
% [ a1 p11 p12 p13 a2 p21 p22 p23 ... an pn1 pn2 pnj ]
%
% e.g. x^2y + x + xy + 5 would be:
%
% [ 1 2 1 1 1 0 1 1 1 5 0 0 ]
%
% This vector can be of any length provided these conventions are
% observed
%
% p2 - Second polynomial in same form. This does not have to be of the
% same length as p1, but must conform to the same scheme, i.e. have
% the same number of variables.
%
% newTerm - single polynomial term in same format as the other
% polynomials terms, e.g. to find if the term x^2y in the
% previous polynomial example you would use:
%
% [1 2 1]
% As we only compare power terms the constant (1 in this case)
% will be ignored, i.e. the following examples would also give
% a positive result:
%
% [0 2 1] or [0.245646 2 1] or [1000 2 1]
%
% vars - The number of variables in the polynomials, this is 2 for the
% examples above.
%
% Output:
%
% res - Scalar, if 0, the term does not already exist. If 1, the term
% exists in the first polynomial, if 2, the term exists in the
% second polynomial. If 3, the term exists in both polynomials
%
if isempty(p1)
res(1) = 0;
else
p1 = reshape(p1',vars+1,[])';
if any(all(bsxfun(@eq, p1(:,2:end), newTerm(2:end)), 2))
res(1) = 1;
else
res(1) = 0;
end
end
if isempty(p2)
res(2) = 0;
else
p2 = reshape(p2',vars+1,[])';
if any(all(bsxfun(@eq, p2(:,2:end), newTerm(2:end)), 2))
res(2) = 2;
else
res(2) = 0;
end
end
res = sum(res);
% if size(p1,2) == 0
% res = 0;
% else
%
% res = 0;
%
% % First we reshape the polynomial vectors to (n x (vars+1)) matrix,
% % where n is the total number of terms
% p1 = reshape(p1',vars+1,[])';
% p2 = reshape(p2',vars+1,[])';
%
% % Next we remove the placeholder values at the start of each matrix
% p1(:,1) = [];
% p2(:,1) = [];
%
% % The new terms are replicated to the same size as the p1 and p2
% % matrices
% % newTerm1 = repmat(newTerm(2:end), size(p1,1), 1);
% %
% % newTerm2 = repmat(newTerm(2:end), size(p2,1), 1);
%
% % We test by
% % test1 = sum(newTerm1 == p1, 2);
% %
% % test2 = sum(newTerm2 == p2, 2);
%
% % if any(test1 == vars) && any(test2 == vars)
% % res = 3;
% % elseif any(test1 == vars)
% % res = 1;
% % elseif any(test2 == vars)
% % res = 2;
% % end
%
% test1 = 0;
% test2 = 0;
%
% for i = 1:size(p1,1)
% if sum(newTerm(2:end) == p1(i,:), 2) == vars
% test1 = 1;
% break;
% end
% end
%
% for i = 1:size(p2,1)
% if sum(newTerm(2:end) == p2(i,:), 2) == vars
% test2 = 2;
% break;
% end
% end
%
% end
end
