Allow evaluation of morphisms of schemes on points over different rings

[pjbruin]

In SageMath 9.3, consider the following setting:

sage: S.<x,y> = AffineSpace(ZZ, 2)
sage: T.<u,v> = AffineSpace(ZZ, 2)
sage: h = T.hom([u + v, u * v], S); h
Scheme morphism:
  From: Affine Space of dimension 2 over Integer Ring
  To:   Affine Space of dimension 2 over Integer Ring
  Defn: Defined on coordinates by sending (u, v) to
        (u + v, u*v)

The morphism h cannot be evaluated on points over F₄:

sage: F.<a> = GF(4)
sage: P = T(F)(1, a)
sage: h(P)
Traceback (most recent call last):
...
TypeError: not in prime subfield
sage: h.change_ring(F)(P)
Traceback (most recent call last):
...
TypeError: (1, a) fails to convert into the map's domain Affine Space of dimension 2 over Finite Field in a of size 2^2,but a `pushforward` method is not properly implemented

There is no error when the coordinates are in the prime field, but the coordinates of the resulting point are in Z instead of F₄:

sage: Q = T(F)(1, 0)
sage: Q.domain()
Spectrum of Finite Field in a of size 2^2
sage: h(Q)
(1, 0)
sage: h(Q).domain()
Spectrum of Integer Ring

Component: algebraic geometry

Author: Peter Bruin

Branch/Commit: d0c30c0

Reviewer: Lorenz Panny

Issue created by migration from https://trac.sagemath.org/ticket/32209

[pjbruin]

Author: Peter Bruin

[pjbruin]

Branch: u/pbruin/32209-scheme_morphisms

[pjbruin]

Commit: 608f2f4

[yyyyx4]

comment:4

With the patch, a morphism of affine schemes now happily returns values at points which clearly do not lie in its domain:

sage: S.<x,y> = AffineSpace(ZZ, 2)
sage: T.<u,v> = AffineSpace(ZZ, 2)
sage: C = Curve(x**2+y**2-1)
sage: f = C.hom([x,y],T)
sage: P = S([123,456])
sage: f.domain().defining_polynomial()(*P)
223064
sage: f(P)
(123, 456)

The following change should fix this according to my very limited testing. It is inspired by the projective case (which did already seem to detect points outside the domain).

--- b/src/sage/schemes/affine/affine_morphism.py
+++ b/src/sage/schemes/affine/affine_morphism.py
@@ -262,7 +262,7 @@ class SchemeMorphism_polynomial_affine_space(SchemeMorphism_polynomial):
         """
         from sage.schemes.affine.affine_point import SchemeMorphism_point_affine
         if check:
-            if not isinstance(x, SchemeMorphism_point_affine):
+            if not isinstance(x, SchemeMorphism_point_affine) or self.domain() != x.codomain():
                 try:
                     x = self.domain()(x)
                 except (TypeError, NotImplementedError):

[sagetrac-git]

Changed commit from 608f2f4 to d0c30c0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d0c30c0

Trac 32209: additional check

[pjbruin]

comment:7

Thanks for noticing! This looks like a good fix to me.

[yyyyx4]

Reviewer: Lorenz Panny

[vbraun]

Changed branch from u/pbruin/32209-scheme_morphisms to d0c30c0