New class for morphisms of polynomial rings

[jdemeyer]

Introduce a new class PolynomialRingMorphism for morphisms from a polynomial ring to any ring. It is defined by a morphism from the base ring to the codomain and by the image of the generators.

This generalizes the existing RingHomomorphism_im_gens because it also allows a non-trivial morphism on the base ring.

It is meant to be used by #25558 and possibly #26105.

CC: @saraedum @mkoeppe

Component: coercion

Reviewer: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/27034

[embray]

comment:1

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

[embray]

comment:2

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

[embray]

comment:3

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[videlec]

comment:4

This feature seems already available (ie RingHomomorphism_im_gens has a keyword base_map)

sage: K = GF(9)
sage: phi = K.frobenius_endomorphism()
sage: R = K['x,y']
sage: x,y = R.gens()
sage: f = R.hom([y,x], base_map=phi)
sage: f
Ring endomorphism of Multivariate Polynomial Ring in x, y over Finite Field in z2 of size 3^2
  Defn: x |--> y
        y |--> x
        with map of base ring
sage: f(K.gen()*x+y)
x + (-z2 + 1)*y

[videlec]

Changed author from Jeroen Demeyer to none

[videlec]

comment:5

Introducing base_map was indeed the point of #26105.

[kwankyu]

Reviewer: Kwankyu Lee