The best way to solve your problem is in two steps.
First we use the fact that GF(p^r) is a vector space over GF(p) to
express elements of GF(p^r) as vectors over GF(p) (losing the
multiplicative structure in the process). We do this by taking basis
and then using the Coefficients operation.
gap> f := GF(3,2);
GF(3^2)
gap> cb := CanonicalBasis(f);
CanonicalBasis( GF(3^2) )
gap> Coefficients(cb,Z(9)^2);
[ Z(3)^0, Z(3)^0 ]
Now we use the function IntFFE to see the equivalent elements of Z mod
pZ.
gap> List(last, IntFFE);
[ 1, 1 ]
gap>
if you want to know which basis GAP is using here, you can do:
gap> BasisVectors(cb);
[ Z(3)^0, Z(3^2) ]
You can convert back using the inner product of vectors:
gap> [2,1]*last;
Z(3^2)^7
I hope this is what you were looking for
Steve Linton
On 27 Aug 2009, at 10:22, Nasira Sindhu wrote:
Hi,
I´am trying to understand the represenation of the elments of
GF(x,y) in GAP.
I need to work with the field F_p^l. F_p^l is isomorph to (Z_p)^l .
Is there a way to translate the follwing output into a
representation of (Z_p)^l in GAP:
gap> Elements(GF(3,2));
[ 0*Z(3), Z(3)^0, Z(3), Z(3^2), Z(3^2)^2, Z(3^2)^3, Z(3^2)^5,
Z(3^2)^6,
Z(3^2)^7 ]
I need tuples to handle with them.
Which tuple representation is for example Z(3^2)^2 ?
regards,
Nasira
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