Here's a toy example of the difficulty I'm having...
Let $K/\mathbb{Q}$ be a Galois extension of degree 3.
There are two non-trivial irreducible characters on Gal$(K/\mathbb{Q}),$ call them $\chi_1$ and $\chi_2.$
Once I've defined the number field $K$ in MAGMA, I can get these as follows:
triv, chi1, chi2 := Explode(ArtinRepresentations(K));
Now I list the elements of the Galois group of the extension:
id, phi1, phi2 := Automorphisms(K);
What I want to do now is something like "Evaluate(chi1,phi1)" but this doesn't exist...
Does anyone know how to go about this?
Many thanks!
EDIT: Here is some sample code:
_<x>:=PolynomialRing(Rationals());
K:=Subfields(CyclotomicField(9))[3,1];
triv,chi1,chi2:=Explode(ArtinRepresentations(K));
id,phi1,phi2:=Explode(Automorphisms(K));
chi1(phi1);