K.gen() where K = GF(p) returns 1, not a primitive element

[sagetrac-jxxcarlson]

sage: k = GF(7)
sage: k.gen()
1

Component: number theory

Keywords: galois field

Issue created by migration from https://trac.sagemath.org/ticket/3045

[aghitza]

comment:1

This is actually the correct behaviour. The function that returns a primitive element is K.multiplicative_generator(), not K.gen(). There was some inconsistency in the docstrings of the various types of finite fields, which is fixed by the attached patch.

[kedlaya]

comment:2

This otherwise deserves a positive review, except that I couldn't verify the claim in the doctest that the outputs of gen() and multiplicative_generator() can vary between runs. Is that really true?

[aghitza]

comment:3

Attachment: trac_3045.patch.gz

Kiran, I tried to find some examples and couldn't. I think the point of the warning in the docstring is that we are not guaranteeing that the finite fields code wouldn't change in the future in such a way that other generators would be returned; or, for that matter, that the same version of Sage running on wildly different architectures won't return different generators. I modified the docstrings a bit to (hopefully) make that more clear.

Note that multiplicative_generator() calls pari's znprimroot(), so whatever fuzziness there is in pari's finding a generator gets automatically inherited by Sage.

[roed314]

comment:4

Looks good to me. I think the docstrings are clear enough.

[sagetrac-mabshoff]

comment:5

Merged in Sage 3.3.alpha2.

Cheers,

Michael