is_unit and __invert__ for Polynomial Quotient Rings

[xcaruso]

As it was noticed in ticket #13215, inversion in Polynomial Quotient Rings does not work quite well:

sage: Z16x.<x> = Integers(16)[]
sage: GR.<y> =  Z16x.quotient(x^2 + x + 1)
sage: (2*y)^(-1)
15*y + 15
sage: (2*y)*(2*y)^(-1)
2

I attach a small patch "fixing" this problem: with the patch, a NotImplemetedError is raised when the base ring is not a field.

Apply attachment: trac_13303_invert_polynomial_quotient_rings.patch

CC: @xcaruso

Component: algebra

Keywords: inversion quotient polynomial rings

Author: Xavier Caruso

Reviewer: Travis Scrimshaw

Merged: sage-5.6.beta0

Issue created by migration from https://trac.sagemath.org/ticket/13303

[jdemeyer]

comment:3

Please fill in your real name as Author.

[xcaruso]

Author: Xavier Caruso

[burcin]

Changed dependencies from #13215 to none

[tscrim]

comment:6

I've uploaded a review patch which corrects a few documentation issues. If you agree, you can set this to a positive review. Thanks.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:7

Added a proper commit message to review patch. The trailing whitespace is taken care of in there as well.

[xcaruso]

comment:8

Thanks. I merged your review into my patch.

[xcaruso]

Attachment: trac_13303_invert_polynomial_quotient_rings.patch.gz

[tscrim]

comment:9

For patchbot:

Apply only: trac_13303_invert_polynomial_quotient_rings.patch

[jdemeyer]

Merged: sage-5.6.beta0