Subject: computing generating elements of ZZ_p^* ?
From: Robert Dodier
Date: Tue, 22 Nov 2011 11:27:40 -0700
On 10/22/11, Oliver Kullmann <O.Kullmann at swansea.ac.uk> wrote:
> Hi Robert,
>
> unfortunately that package "gf" hasn't been updated for quite
> some time now, and quite a few of its functions are broken:
>
> load(gf);
> gf_set(131);
> gf_findprim();
>
> fasttimes: arguments must be CRE polynomials with same variables.
> #0: gf_binpower(p=x,n=131)(gf.mac line 244)
> #1: mainpowers()(gf.mac line 346)
> #2: gf_findprim()(gf.mac line 438)
> -- an error. To debug this try: debugmode(true);
>
> So finding primitive elements is broken (at least with the
> default settings).
Hmm. I see that gf can run its own test cases (gf_test and gf_hard_test)
so it's not completely broken.
Looks like gf_set(p) and gf_set(p, m(x)) are handled differently.
Help me understand what to expect from gf_findprim.
In the absence of a polynomial m(x) supplied to gf_set,
what should gf_findprim return?
Is there a meaningful default value for m(x) so that gf_set(p)
then calls gf_set(p, <suitable m(x)>) ?
best
Robert Dodier