60.4-2 ANFAutomorphism
‣ ANFAutomorphism( F, k )( function )

Let F be an abelian number field and k be an integer that is coprime to the conductor (see Conductor (18.1-7)) of F. Then ANFAutomorphism returns the automorphism of F that is defined as the linear extension of the map that raises each root of unity in F to its k-th power.

gap> f:= CF(25);
CF(25)
gap> alpha:= ANFAutomorphism( f, 2 );
ANFAutomorphism( CF(25), 2 )
gap> alpha^2;
ANFAutomorphism( CF(25), 4 )
gap> Order( alpha );
20
gap> E(5)^alpha;
E(5)^2