Bill Allombert on Wed, 14 Mar 2007 16:03:08 +0100

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Re: PARI/GP support for finite fields element

On Wed, Mar 14, 2007 at 10:03:07AM +0000, Prof. J. E. Cremona wrote:
> Dear Bill,
> That sounds excellent.  Using that, the code I have for computing group
> structures of elliptic curves over finite fields could easily be
> extended from Z/p to the general case.  I would use multiplicative order
> and primitive element, maybe also discrete log.
> One question:  How would the efficiency compare between using your new
> construction in degree 1 and using plain int_mod for Z/p?  If the new
> construction was much slower that would mean keeping two different
> implementations, for the degree 1 and degree >1 cases.

This is hard to tell, it probably depend what you are doing.

But in practice, you could just use Mod(1,p) instead of ffgen() and
everything else should work the same way. At least it is the idea.

If you do low-level libopari programming ,then you can use the Fq_*
functions family which handle both cases efficiently (you just pass 
NULL for the degree 1 polynomial).