*huge* bug in multivariate polynomial substitution

[williamstein]

Observe:

sage: R.<x,y> = QQ[]
sage: f = x + 2*y
sage: f.subs(x=y,y=x)
3*y
sage: var('x,y')
sage: f = x + 2*y
sage: f.subs(x=y,y=x)
2*x + y

This is really really bad. Notice in the first and second substitution that the semantics are completely wrong/inconsistent. The semantics should be as in the second one in both cases.

If you do f.subs in the first case above you'll see at the bottom code using I think libsingular that is really wrong. Probably the only way to do this right will be to construct a homomorphism and apply it (?), sort of like this:

sage: R.<x,y> = QQ[]
sage: f = x + 2*y
sage: R.hom([y,x])(f)
2*x + y

Component: commutative algebra

Issue created by migration from https://trac.sagemath.org/ticket/6873

[malb]

comment:2

This is a dupe of #6482.

I think the fix is to not check whether b in a=b is a monomial but whether it is constant. If it isn't a constant we should just fall back to fast_map.

[malb]

comment:3

Dupe of #6482