#12217: Finite field polynomials allow division by zero
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Reporter: johanbosman | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old description:
> For prime finite fields, Sage (and the attached `gdb`!) 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.
> ------------------------------------------------------------------------
> }}}
> And non-prime finite fields don't complain at all:
> {{{
> sage: P.<x> = GF(25,'a')[]
> sage: x/5
> x
> }}}
New description:
For prime finite fields, Sage (and the attached `gdb`!) 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 reason is that `normalize` in
`devel/sage/sage/rings/fraction_field_FpT.pyx` calls `
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
}}}
--
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Ticket URL: <http://trac.sagemath.org/ticket/12217#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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