Comment #12 on issue 2022 by smichr: inconsistent behaviour of subs when
using non-commutative symbols
http://code.google.com/p/sympy/issues/detail?id=2022
Yes, the extraction happens internally. You don't/won't know it's happening
except that you see exp(4*x).subs(exp(2*x), y) become y**2.
Regarding "all", we can make some progress if we can agree on what to try.
What is the objective to do when doing subs? If you mean "given
expr.subs(f(x), f(y)) try replace f(x) as a full argument somewhere, but if
you can't then see if you can replace it extractively, and if you can't
then solve f(x)=f(y), solve for x and then, if there is a single
relationship between them, replace x" we can do that:
all=True possible results
(3*x+2).subs(3*x, y) -> y + 2 because of exact arg matching
(3*x+2).subs(3*x+1, y) -> y + 1 because of extractive matching
(6*x+2).subs(3*x+1, y) -> 2*y because of extractive matching
(3*x+2).subs(3*x+5, y) ->y - 3 because of algebraic matching
(3*x+2).subs(sin(x), y) -> 3*asin(y)+2 because of algebraic matching.
(3*x+2).subs(x**2, y) -> no change because there is no single relationship
between x and y
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