#20935: Weird crash in mod N arithmetic for medium-size N
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Reporter: davidloeffler | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.3
Component: basic arithmetic | Resolution:
Keywords: modular arithmetic | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by davidloeffler):
* keywords: => modular arithmetic
Old description:
> The following code crashes in Sage v7.2 with a !ZeroDivisionError:
> {{{
> V = FreeModule(Zmod(3^10), 1)
> v = V.gen(0)
> x = v * v
> x.valuation(3)
> }}}
> The variable x is just 1 (mod 3^10^), and if you just do {{{
> Zmod(3^10)(1).valuation(3)}}} it returns 0 (as it should), but creating
> it via linear algebra in this way seems to somehow return a broken
> object.
>
> Oddly enough, only powers of 3 between 3^10^ and 3^19^ (inclusive) seem
> to raise this error -- larger or smaller powers work fine. Similarly
> powers of 2 between 2^16^ and 2^30^, or powers of 5 between 5^7^ and
> 5^13^. This strongly suggests there is an overflow error occurring
> somewhere when the modulus is too large for a 16-bit integer but large
> enough for a 32-bit.
New description:
The following code crashes in Sage v7.2 with a !ZeroDivisionError:
{{{
V = FreeModule(Zmod(3^10), 1)
v = V.gen(0)
x = v * v
x.valuation(3)
}}}
The variable x is just 1 (mod 3^10^), and if you just do {{{
Zmod(3^10)(1).valuation(3)}}} it returns 0 (as it should), but creating it
via linear algebra in this way seems to somehow return a "broken" integer
mod object.
This error only occurs for moduli in a certain interval: between 46342
(~2^15.5^) and 2147483646 (~2^31^). Investigation suggests that {{{v *
v}}} is getting returned as an {{{IntegerMod_int}}} object where it should
be an {{{IntegerMod_int64}}}; the culprit seems to be the method
{{{_dot_product_}}} in {{{ sage/modules/vector_modn_dense.pyx}}}.
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Ticket URL: <https://trac.sagemath.org/ticket/20935#comment:1>
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