Implement "first_lexicographic" option for irreducible polynomials over finite fields of odd characteristic

[jpflori]

This is the default behavior in Magma.

CC: @defeo @pjbruin

Component: finite rings

Keywords: finite fields magma irreducible

Author: Jean-Pierre Flori

Branch/Commit: 2f34e15

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/16359

[jpflori]

Commit: 2f5b9e4

[jpflori]

Author: Jean-Pierre Flori

[jpflori]

Changed keywords from none to finite fields magma irreducible

[jpflori]

Branch: u/jpflori/ticket/16359

[jpflori]

comment:1

Maybe the non-prime case needs some thought.

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New commits:

2f5b9e4

Implement "first_lexicographic" option for irreducible polys over ffs.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

44d67e1

Leftover degree restriction.

[sagetrac-git]

Changed commit from 2f5b9e4 to 44d67e1

[pjbruin]

comment:3

Looks good. One question: do you really want to say "try random polynomials in lexicographic order" in the docstring?!

[jpflori]

comment:4

Nope.
Correcting that now.

[sagetrac-git]

Changed commit from 44d67e1 to 2f34e15

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2f34e15

Fix typo in finite field poly code.

[jpflori]

comment:6

Done.
Now we should make it so this is as fast as Magma's implementation.
I think refactoring the finite field poly factorization code and make it use NTL/PARI/FLINT code should be enough.

[pjbruin]

Reviewer: Peter Bruin

[vbraun]

Changed branch from u/jpflori/ticket/16359 to 2f34e15