#15236: Let Sage use finite fields without primality proving
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Reporter: jpflori | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.0
Component: finite rings | Resolution:
Keywords: finite fields, primality | Merged in:
proving | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Description changed by SimonKing:
Old description:
> It would be nice to be able to create finite fields without checking that
> the characteristic is actually prime.
>
> You can more or less do that for prime fields using directly the
> FiniteField_prime_modn constructor with check=False arguments.
> Unfortunately some constructions on top of this will still check that the
> characteristic is actually prime, e.g. univariate polynomial rings on top
> of it.
New description:
It would be nice to be able to create finite fields without checking that
the characteristic is actually prime.
You can more or less do that for prime fields using directly the
FiniteField_prime_modn constructor with check=False arguments.
Unfortunately some constructions on top of this will still check that the
characteristic is actually prime, e.g. univariate polynomial rings on top
of it.
Note that it already is possible to create an `IntegerModRing(n,
categogry=Fields())`. This will create a quotient ring of ZZ that believes
that it is a field. However, it will still be an integer mod ring that
does not use any of the fancy finite ''field'' implementations in sage.
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Ticket URL: <http://trac.sagemath.org/ticket/15236#comment:1>
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