Fwd: [GAP Forum] Finite field defined with an irreducible polynomial

[Erik Postma]

On Fri, Aug 22, 2008 at 10:25 PM, Anvita <anvita21 at gmail.com> wrote:
> Dear Forum,
>
> When a finite field is defined using an irreducible polynomial, there seems
> to be a problem
> finding the coefficients of the field's elements in the natural power bases.
> (...)
> Is there any way around this problem?

Hmmm. One way around it is to define the subspace generated by what we
know is a basis. That will work:

gap> G := Subspace(F, b);
<vector space over GF(5), with 7 generators>
gap> Dimension(G);
7
gap> Basis(G, b);
Basis( <vector space of dimension 7 over GF(5)>, [ !Z(5)^0, (a),
(a^2), (a^3), (a^4),
 (a^5), (a^6) ] )

All the best,
Erik.