On Mon, Nov 26, 2012 at 04:57:38PM +0100, Inneke Van Gelder wrote:
> Dear GAP forum,
>
>
> I extend GF(2) by a primitive 19-th root of unity as follows:
>
> gap> xi:=PrimitiveRoot(GF(2^18))^((2^18-1)/19);
> z
> gap> F:=GF(GF(2),MinimalPolynomial(GF(2),xi));
> <field of size 262144>
>
> However I am interested in the subfields of this field. But this causes
> an error in GAP:
>
> Is there a way to get around this error?
Galois theory predict that the set of subfields is exactly
{GF(2^d) for all d dividing 18}
and you can even write a generator of each fields in term of a
power of PrimitiveRoot(GF(2^18)) as
PrimitiveRoot(GF(2^18))^((2^18-1)/(2^d-1)).
Cheers,
Bill.
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