5.4.4 The option algebraic

Both has() and subs() take an optional argument to pass them extra options. This section describes what happens if you give the former the option has_options::algebraic or the latter subs_options::algebraic. In that case the matching condition for powers and multiplications is changed in such a way that they become more intuitive. Intuition says that x*y is a part of x*y*z. If you use these options you will find that (x*y*z).has(x*y, has_options::algebraic) indeed returns true. Besides matching some of the factors of a product also powers match as often as is possible without getting negative exponents. For example (x^5*y^2*z).subs(x^2*y^2==c, subs_options::algebraic) will return x*c^2*z. This also works with negative powers: (x^(-3)*y^(-2)*z).subs(1/(x*y)==c, subs_options::algebraic) will return x^(-1)*c^2*z.

Note: this only works for multiplications and not for locating x+y within x+y+z.