map_coefficients (of multivariate polynomial ring) cannot change base_ring

[dkrenn]

The map_coefficients() function of a multivariate polynomial ring cannot change the base ring. Sometimes this would be nice, e.g.

sage:  R.<r> = GF(9); S.<s> = GF(81)
sage:  h = Hom(R,S)[0]; h
Ring morphism:
  From: Finite Field in r of size 3^2
  To:   Finite Field in s of size 3^4
  Defn: r |--> 2*s^3 + 2*s^2 + 1
sage: T.<X,Y> = R[]   
sage:  f = r*X+Y
sage:  f.map_coefficients(h)  
Traceback (most recent call last)
...
NotImplementedError: 

NotImplementedError comes, because R(2*s^3 + 2*s^2 + 1) is not possible; it should be S(2*s^3 + 2*s^2 + 1).

Component: algebra

Keywords: map coefficients, multivariate polynomial ring, base ring, sd35

Author: Daniel Krenn

Reviewer: Julian Rueth

Merged: sage-5.0.beta3

Issue created by migration from https://trac.sagemath.org/ticket/11981

[dkrenn]

comment:1

Attachment: trac_11981_map_coefficients_multi.patch.gz

Now there is an additional parameter. If given, then the base ring of the polynomial ring is changed.
Example from above continued:

sage: f.map_coefficients(h,S)
(-s^3 - s^2 + 1)*X + Y

[dkrenn]

Author: Daniel Krenn

[saraedum]

tries to improve the docstring

[saraedum]

Changed keywords from map coefficients, multivariate polynomial ring, base ring to map coefficients, multivariate polynomial ring, base ring, sd35

[saraedum]

comment:3

Attachment: trac_11981_review.patch.gz

I found the docstring somewhat confusing. I tried to improve it. If you're happy with my changes, feel free to set it to positive_review.

[saraedum]

Reviewer: Julian Rueth

[jdemeyer]

Merged: sage-5.0.beta3