Re: Primitive Polynomials

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

On Fri, Nov 04, 2022 at 09:54:37AM +0100, Martin Becker wrote:
> 
> Hello,
> 
> I would like to have an option for ffgen to return a primitive
> polynomial rather than just some random irreducible polynomial.
> Preferrably a Conway polynomial but, for many use cases,
> any will do.  Would that be hard to implement?  Pari could
> iterate through irreducible polynomials until Mod(x,candidate)
> has maximal order.  Please excuse me if that functionality is
> already present somewhere but I didn't notice.

It is indirectly possible by using ffprimroot:
minpoly(ffprimroot(ffgen([p,n])))

? minpoly(ffprimroot(ffgen([7,5])))
%1 = Mod(1,7)*x^5+Mod(2,7)*x^4+Mod(4,7)*x^3+Mod(2,7)*x^2+Mod(4,7)*x+Mod(2,7)

Cheers,
Bill.