#12217: Finite field polynomials allow division by zero
------------------------------------+------------------------------
Reporter: johanbosman | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers: Jeroen Demeyer
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by pbruin):
* status: needs_work => needs_review
Old description:
> For prime finite fields, the following causes Sage to crash:
> {{{
> sage: P.<x> = GF(5)[]
> sage: x/0
> ------------------------------------------------------------------------
> Unhandled SIGSEGV: A segmentation fault occurred in Sage.
> This probably occurred because a *compiled* component of Sage has a bug
> in it and is not properly wrapped with sig_on(), sig_off().
> Sage will now terminate.
> ------------------------------------------------------------------------
> }}}
> The cause is a missing check for a zero denominator. This leads to
> `normalize` in `devel/sage/sage/rings/fraction_field_FpT.pyx` calling
> `nmod_poly_leading(denom)` to get the leading coefficient of the
> denominator. This crashes, since the zero polynomial doesn't have a
> leading coefficient.
>
> And non-prime finite fields don't complain at all:
> {{{
> sage: P.<x> = GF(25,'a')[]
> sage: x/5
> x
> }}}
> This is due to a missing check for division by zero in the `__invert__()`
> method of Givaro finite field elements. Inserting this check broke
> conversion of the finite field element 0 from Givaro to Gap, so this is
> also fixed.
>
> Apply: [attachment:12217-zero_division.patch]
New description:
For prime finite fields, the following causes Sage to crash:
{{{
sage: P.<x> = GF(5)[]
sage: x/0
------------------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component of Sage has a bug
in it and is not properly wrapped with sig_on(), sig_off().
Sage will now terminate.
------------------------------------------------------------------------
}}}
The cause is a missing check for a zero denominator. This leads to
`normalize` in `devel/sage/sage/rings/fraction_field_FpT.pyx` calling
`nmod_poly_leading(denom)` to get the leading coefficient of the
denominator. This crashes, since the zero polynomial doesn't have a
leading coefficient.
And non-prime finite fields don't complain at all:
{{{
sage: P.<x> = GF(25,'a')[]
sage: x/5
x
}}}
This is due to a missing check for division by zero in the `__invert__()`
method of Givaro finite field elements. Inserting this check broke
conversion of the finite field element 0 from Givaro to Gap, so this is
also fixed.
Apply: [attachment:12217-zero_division-v2.patch]
--
Comment:
For division by 0 in the polynomial ring, I decided for 'fraction has
denominator 0', but because of a different change in
`polynomial_element.pyx` (see comment:11), you will only see this message
when trying to construct fraction field elements by coercing a pair of
elements of the polynomial ring into the fraction field; see the new
doctest in `fraction_field_FpT.pyx`.
--
Ticket URL: <http://trac.sagemath.org/ticket/12217#comment:12>
Sage <http://www.sagemath.org>
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