Failure of specialization over some rings

[pfili]

The following code used to fail in the specialization for polynomials over some rings:

            sage: R.<c>=RR[]
            sage: P.<z>=AffineSpace(R,1)
            sage: H=End(P)
            sage: f=H([z^2+c])
            sage: f.specialization({c:1})

should return:

            Scheme endomorphism of Affine Space of dimension 1 over Real Field with 53 bits of precision
              Defn: Defined on coordinates by sending (z) to
                    (z^2 + 1.00000000000000)

If the base ring of R was QQ, this would work, but if it was RR, it would fail. The problem was in the specialization function, which used a dictionary psi whose keys were supposed to belong to the flattened ring, but instead belonged to the unflattened polynomial ring. Over some rings the built-in coercion functions would fix this while over others they would not. The dictionary psi has been corrected so that the specialization function works as desired.

Component: algebra

Keywords: polynomials, specialization

Author: Paul Fili

Branch/Commit: 5fedbef

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/23811

[pfili]

Branch: u/paulfili/develop

[pfili]

Changed branch from u/paulfili/develop to none

[pfili]

Branch: u/paulfili/specialization-fix

[bhutz]

Changed branch from u/paulfili/specialization-fix to u/bhutz/specialization-fix

[bhutz]

New commits:

20e33eb	Fixed dictionary psi in specialization function
e447f83	23811: minor whitespace fix

[bhutz]

Commit: e447f83

[bhutz]

Changed author from paulfili to Paul Fili

[bhutz]

Reviewer: Ben Hutz

[bhutz]

comment:6

This fixes the issue. I just made a minor whitespace change.

I think this is just a minor priority since Sage is failing with an error message, we just should be able to deal with that case.

[pfili]

Changed branch from u/bhutz/specialization-fix to u/paulfili/specialization-fix

[pfili]

Changed commit from e447f83 to 5fedbef

[pfili]

comment:8

Fixed a typo where the doc test added referred to the wrong trac #, otherwise unchanged and should be good to go.

---

New commits:

5fedbef

Fixed a typo in the doc (referred to the wrong trac #)

[vbraun]

Changed branch from u/paulfili/specialization-fix to 5fedbef