Have method is_unit of QuotientRingElement and PolynomialQuotientRingElement return True in more cases

[soehms]

In the case of both classes there are examples where is_unit raises a NotImplementedError even though the answer True could easily be given:

sage: P.<x,y> = QQ[]
sage: Q = P.quo([1-x*y])
sage: Q.inject_variables()
Defining xbar, ybar
sage: ybar.is_unit()
Traceback (most recent call last):
...
NotImplementedError:

but:

sage: ~ybar
xbar

or:

sage: Z16x.<x> = Integers(16)[]
sage: S.<y> =  Z16x.quotient(x^2 + x + 1)
sage: S(3).is_unit()
Traceback (most recent call last):
...
NotImplementedError: The base ring (=Ring of integers modulo 16) is not a field

but:

sage: Z16x(3).is_unit()
True

This will be improved here. Se also this sage-devel thread.

Component: commutative algebra

Keywords: quotient ring, polynomial, is_unit, invert

Author: Sebastian Oehms

Branch/Commit: 0beccc8

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29469

[soehms]

Branch: u/soehms/is_unit_quotient_ring_elemnts_29469

[soehms]

New commits:

85afe0a

29469: initial

[soehms]

Commit: 85afe0a

[soehms]

Author: Sebastian Oehms

[sagetrac-git]

Changed commit from 85afe0a to 0beccc8

[sagetrac-git]

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

0beccc8

29469: fix doctest in matrix0

[mkoeppe]

comment:4

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[tscrim]

comment:5

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[soehms]

comment:6

Thanks!

[vbraun]

Changed branch from u/soehms/is_unit_quotient_ring_elemnts_29469 to 0beccc8