#13670: Inversion in polynomial quotient rings could give clearer error message
when element is non-invertible
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Reporter: Bouillaguet | Owner: malb
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.5
Component: commutative algebra | Resolution:
Keywords: polynomial rings | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Charles Bouillaguet | Merged in:
Dependencies: #13671 | Stopgaps:
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Comment (by Bouillaguet):
Replying to [comment:3 mstreng]:
> compare this:
>
> > {{{
> > sage: R.<x,y> = QQ[]
> > sage: S = R.quotient_ring(R.ideal(x^2, y))
> > sage: 0/S(x)
> > 0
> > }}}
>
> to this:
>
> {{{
> sage: P.<x> = QQ[]
> sage: S = P.quotient_ring(x^2)
> sage: 0/S(x)
> ZeroDivisionError: element xbar of quotient polynomial ring not
invertible
> }}}
I would personally be more inclined to the second solution (at least
because it does not conceal the fact that we are trying to divide by
something which is non-invertible --- most likely a bug). Do we agree on
this?
However, if I understand correctly, division by non-invertible elements is
still allowed, e.g. the division of `p*q` by `q` should succeeds, even if
`q ` has no inverse...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13670#comment:4>
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