#13303: is_unit and __invert__ for Polynomial Quotient Rings
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Reporter: caruso | Owner:
AlexGhitza
Type: defect | Status:
positive_review
Priority: major | Milestone:
sage-5.6
Component: algebra | Resolution:
Keywords: inversion quotient polynomial rings | Work issues:
Report Upstream: N/A | Reviewers: Travis
Scrimshaw
Authors: Xavier Caruso | Merged in:
Dependencies: | Stopgaps:
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Changes (by caruso):
* status: needs_review => positive_review
Old description:
> 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.
New description:
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]
--
Comment:
Thanks. I merged your review into my patch.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13303#comment:8>
Sage <http://www.sagemath.org>
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