Re: primitive and irriducible polynomials

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

On Mon, May 20, 2002 at 12:23:18PM +0200, Chiara Salvini wrote:
> Hello everybody,
> I'm trying to realize a Pari program which allows to determine:
> - #(the number of){irriducible trinomials in Fp with degree=k}
> - #(the number of){primitive trinomials in Fp with degree=k}
> for p=2,....,100 and k=3,...6
> Can someone help me?

trinomial(p,k)=
{
  local(c=0,P);
  for(m=1,k-1,
    for(am=0,p-1,
      for(a0=1,p-1,/*If a0=0 we are not irreducible*/
        P=x^k+am*x^m+a0;
        c+=polisirreducible(P*Mod(1,p)))));
  c*(p-1);/*Account for non monic polynomials*/
}
count(pmax,kmax)=
{
  local(c);
  forprime(p=2,pmax,
    for(k=3,kmax,
        c=trinomial(p,k);
        print(p,":",k,":",c)));
}
count(100,6)

should be close of what you want.

For the second question, please read carefully the program of Paul van Wamelen,
in the previous post on this list.

(I hope it is not an exam question :-)

Cheers,

Bill.