#14832: Unified construction of irreducible polynomials over finite fields
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Reporter: pbruin | Owner: cpernet
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: finite rings | Resolution:
Keywords: polynomials | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Peter Bruin | Merged in:
Dependencies: #14817 | 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. Here is a patch that
> creates methods
> `PolynomialRing_dense_{finite_field,mod_p}.irreducible_element(n,
> algorithm=None)`. In a separate ticket (#14833), the `FiniteField`
> constructor is adapted to call this 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 #14817.
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. Here is a patch that
creates methods
`PolynomialRing_dense_{finite_field,mod_p}.irreducible_element(n,
algorithm=None)`. In a separate ticket (#14833), the `FiniteField`
constructor is adapted to call this 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 #14817.
Apply: [attachment:trac_14832_make_irreducible_polynomial.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14832#comment:2>
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