Enhance change_ring method on morphisms to use canonical embedding when possible, give clearer error in other cases

[HTalbott]

The following code does not work, and gives an unhelpful error message.

sage: R.<t>=QQ[]
sage: K.<v>=QuadraticField(2)
sage: K2.<w>=NumberField(t^4-2)
sage: P.<x,y>=ProjectiveSpace(QQ,1)
sage: phi=K.embeddings(K2)[0]
sage: f=DynamicalSystem_projective([x^2+3*y^2,y^2])
sage: f.change_ring(phi)

Since phi is an embedding of K into K2, and f has coefficients defined over QQ, phi cannot change the base ring of f. We add functionality to change_ring on morphisms so it uses the canonical embedding of the base ring of f into the domain of phi when such a canonical embedding exists. When such a canonical embedding does not exist, we add an error to change_ring noting the mismatch between the base ring of f and the domain of phi.

Component: number fields

Keywords: SI2019

Author: Henry Talbott

Branch/Commit: d85b712

Reviewer: Adam Towsley, Anna Chlopecki, Emily Rachfal, Juliano Levier-Gomes

Issue created by migration from https://trac.sagemath.org/ticket/28028

[juliacai05]

Branch: u/gh-juliacai05/28028

[meggrip]

New commits:

0c4e09d

Ticket #28028: enhanced change_ring function to fix domain error

[meggrip]

Commit: 0c4e09d

[sagetrac-git]

Changed commit from 0c4e09d to d85b712

[sagetrac-git]

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

d85b712

ticket #28028, updated test formatting

[sagetrac-atowsley]

Reviewer: Adam Towsley

[annanc2]

Changed reviewer from Adam Towsley to Adam Towsley, Anna Chlopecki, Emily Rachfal, Juliano Levier-Gomes

[vbraun]

Changed branch from u/gh-juliacai05/28028 to d85b712