Bill Allombert on Thu, 13 Jul 2017 19:49:49 +0200

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: ffgen

On Thu, Jul 13, 2017 at 05:20:34PM +0200, Eric J. Van der Velden wrote:
> Hi Bill,
> Thanks! I will try ffprimroot.
> I am sorry, I do not know the term "field generator". Do you mean like i in
> F₉, which is of order 4, but 1 and i are a vectorspace basis over F₃ of F₉?

A generator g of K is a element of K such that all subfields of K
containing g are equal to K.

If K is isomorphic to F_{p^n}, then g is a generator if and only if
1,g,...,g^(n-1) is a basis of K seen as a F_p vector space.