13.11 GaloisCyc

GaloisCyc( z, k )

returns the cyclotomic obtained on raising the roots of unity in the representation of the cyclotomic z to the k-th power. If z is represented in the field Q_n and k is a fixed integer relative prime to n, GaloisCyc( ., k ) acts as a Galois automorphism of Q_n (see GaloisGroup for Number Fields); to get Galois automorphisms as functions, use GaloisGroup GaloisGroup.

    gap> GaloisCyc( E(5) + E(5)^4, 2 );
    E(5)^2+E(5)^3
    gap> GaloisCyc( E(5), -1 );           # the complex conjugate
    E(5)^4
    gap> GaloisCyc( E(5) + E(5)^4, -1 );  # this value is real
    E(5)+E(5)^4
    gap> GaloisCyc( E(15) + E(15)^4, 3 );
    E(5)+E(5)^4

GaloisCyc is an internal function.

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