Re: FFELT: how to recover the field?

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sun, Dec 09, 2007 at 04:15:46PM +0100, Jeroen Demeyer wrote:
> Hello list,
> 
> Given a FFELT x in characteristic p, I would like to compute a p-th root 
> of x.  The most obvious way to do this is to compute x^(p^(n-1)), where 

Why are sqrtn(x,p) and x^(1/p) less obvious ?

> p^n is the cardinality of the field.  However, how can I recover p and n 
> given only the FFELT?  Obviously, it suffices to get the polynomial 
> defining the finite field (i.e. the argument given to ffgen()).  I tried 
> x.mod, but that doesn't work.

I think x.mod should be made to work, but I did not implement it because
I was not sure whether x.mod should return a polynomial with t_INT or
t_INTMOD coefficients (mod p).

In the mean time, you can use n=poldegree(charpoly(0*a)).

You can get p using x.p.

Thanks for your input,
Bill.