#14832: Unified construction of irreducible polynomials over finite fields
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Reporter: pbruin | Owner: cpernet
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-5.12
Component: finite rings | Resolution:
Keywords: polynomials | Work issues:
Report Upstream: N/A | Reviewers: Jean-Pierre Flori
Authors: Peter Bruin | Merged in:
Dependencies: #14817, #14818 | Stopgaps:
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Description changed by pbruin:
Old description:
> Currently, every finite field implementation (integers mod ''p'', Givaro,
> NTL, PARI) has its own code for constructing an irreducible polynomial
> when given a string as the `modulus` keyword. This ticket does the
> following:
>
> - implement a new class `PolynomialRing_dense_finite_field`
> - create methods
> `PolynomialRing_dense_{finite_field,mod_p}.irreducible_element(n,
> algorithm=None)`.
>
> In a separate ticket (#14833), the `FiniteField` constructor is adapted
> to call the new function.
>
> The default choice is now deterministic: Conway polynomials if available,
> otherwise lexicographically first (via NTL/GF2E) in characteristic 2,
> Adleman-Lenstra (via PARI) in characteristic > 2.
>
> Since it uses PARI's `ffinit`, this depends on #14818.
>
> Apply:
> * [attachment:trac_14832-PolynomialRing_dense_finite_field.patch],
> * [attachment:trac_14832-irreducible_polynomial.patch],
> * [attachment:trac_14832-reviewer.patch].
New description:
Currently, every finite field implementation (integers mod ''p'', Givaro,
NTL, PARI) has its own code for constructing an irreducible polynomial
when given a string as the `modulus` keyword. This ticket does the
following:
- implement a new class `PolynomialRing_dense_finite_field`
- create methods
`PolynomialRing_dense_{finite_field,mod_p}.irreducible_element(n,
algorithm=None)`.
In a separate ticket (#14833), the `FiniteField` constructor is adapted to
call the new function.
The default choice is now deterministic: Conway polynomials if available,
otherwise lexicographically first (via NTL/GF2E) in characteristic 2,
Adleman-Lenstra (via PARI) in characteristic > 2.
Since it uses PARI's `ffinit`, this depends on #14818.
Apply:
* [attachment:trac_14832-PolynomialRing_dense_finite_field.patch]
* [attachment:trac_14832-irreducible_polynomial.patch]
* [attachment:trac_14832-reviewer.patch]
* [attachment:trac_14832-doctest.patch]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14832#comment:15>
Sage <http://www.sagemath.org>
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