[GAP Forum] Coefficients of basis elements for Galois field

[Ha T. Lam]

Dear GAP forum,

I built a Galois field over F2 with irreducible polynomial f

x:=Indeterminate(GF(2), "x");
> x
f:=x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0;
> x^22+x^21+x^20+x^17+x^14+x^9+x^5+x+Z(2)^0
gf:=GF(2,f);
> Field( [ a ] )
BasisVectors(Basis(gf));
> [ !Z(2)^0, a, a^2, a^3, a^4, a^5, a^6, a^7, a^8, a^9, a^10, a^11, a^12,
a^13, a^14, a^15, a^16, a^17, a^18, a^19, a^20, a^21 ]

I'm trying to get the basis elements as polynomials, in particular, I want
their coefficients, but I'm not sure how to do this. My guess is that since
they are all powers of the primitive root, if I know the coefficients
representing the primitive root, I will be able to compute their
coefficients. The next thing I tried was to extract the primitive root:

PrimitiveRoot(gf);

but I get the message "Error, no method found!"

I'm not sure what to try next, do you have any advise?

Best regards,

Ha T. Lam