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.
GAP 3.4.4