Add seed parameter to GF

[roed314]

For small (p, n), we use Conway polynomials so you get the same finite field across different versions of sage. For large (p, n), the finite field you get in Sage is nondeterministic. This is a minor annoyance, but with the relative extensions we're working on in #28485 together with the changes to randomness in doctesting introduced in #29935 it will become difficult to ever show elements of relative extensions.

I propose adding a seed parameter to GF so that by default the modulus chosen is deterministic. The current behavior could be obtained by setting the seed to None.

Component: finite rings

Branch/Commit: u/roed/finite_field_seeds @ c17c2d8

Issue created by migration from https://trac.sagemath.org/ticket/33348

[roed314]

Branch: u/roed/finite_field_seeds

[sagetrac-git]

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

4b72e9e	Merge branch 'u/roed/finite_field_seeds' of https://github.com/sagemath/sagetrac-mirror into t/33348/finite_field_seeds
c17c2d8	Improve defaults, fix a doctest

[sagetrac-git]

Commit: c17c2d8

[roed314]

comment:3

Looking into this more, I don't think it's necessary for absolute extensions, since the polynomial pari generates is deterministic when the base field is prime. It will be useful for relative extensions, but I'll put this change back into #28485.