Flint 2.8 and fq_default

[Will Youmans]

Hi all,

I see release 2.8 introduced a unified finite field module, fq_default. Are there plans for a unified module for integers mod n?

Will

[Bill Hart]

We haven't explicitly decided, but the basic idea at present is that
the code for fmpz_mod's will automatically switch to nmod's where
possible, which should have the same effect. Of course it is not quite
the same thing because it would have to recompute the precomputed
inverse for reduction mod n for every operation. We'd have to put that
in the fmpz_mod_ctx_struct if we wanted to avoid that. We haven't
taken a decision on that yet.

We will definitely eventually add fmpz_/nmod where the modulus is a
prime to fq_default of course.

Bill.

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[Will Youmans]

Thanks!

As an aside, can you say how the fq_zech modules compare in terms of performance to fq? I'm not familiar with Zech log rep. Is there a situation where they are preferred? They don't seem to be included in fq_default so I assume it is not cut and dry.

Will

[Bill Hart]

I thought fq_zech was included in fq_default. They will be faster when
the number of elements in the finite field is small, as they generate
a lookup table for addition (multiplication is trivial in that
representation).

Bill.

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[Will Youmans]

Thanks again. You are correct, I missed it.

Will