#16983: Fix finite field modulus handling
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: finite rings | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/ticket/16983 | b6a6c669c7f8c1a2efd0da70da1f25c1d60663bc
Dependencies: #16934 | Stopgaps:
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Description changed by jdemeyer:
Old description:
> For prime finite fields, we should support a custom modulus (internally
> in Sage, we don't need to use this modulus in the backend):
> {{{
> sage: x = polygen(GF(7))
> sage: k = GF(7, modulus=x+5)
> sage: k.modulus()
> x + 6
> sage: k.gen()
> 1
> }}}
>
> We should also make the modulus monic:
> {{{
> sage: x = polygen(GF(7))
> sage: k.<a> = GF(7^2, modulus=2*x^2-3, impl="pari_ffelt")
> sage: k.modulus()
> 2*x^2 + 4
> }}}
> (the Givaro backend does this implicitly)
New description:
For prime finite fields, we should support a custom modulus (internally in
Sage, we don't need to use this modulus in the backend):
{{{
sage: x = polygen(GF(7))
sage: k = GF(7, modulus=x+5)
sage: k.modulus()
x + 6
sage: k.gen()
1
}}}
We should also make the modulus monic:
{{{
sage: x = polygen(GF(7))
sage: k.<a> = GF(7^2, modulus=2*x^2-3, impl="pari_ffelt")
sage: k.modulus()
2*x^2 + 4
}}}
(the Givaro backend does this implicitly)
The patch does the above, with lots of cleaning up.
--
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Ticket URL: <http://trac.sagemath.org/ticket/16983#comment:7>
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