‣ GaloisStabilizer ( F ) | ( attribute ) |
Let F be an abelian number field (see IsAbelianNumberField
(60.2-3)) with conductor , say. (This means that the -th cyclotomic field is the smallest cyclotomic field containing F, see Conductor
(18.1-7).) GaloisStabilizer
returns the set of all those integers in the range such that the field automorphism induced by raising -th roots of unity to the -th power acts trivially on F.
gap> r5:= Sqrt(5); E(5)-E(5)^2-E(5)^3+E(5)^4 gap> GaloisCyc( r5, 4 ) = r5; GaloisCyc( r5, 2 ) = r5; true false gap> GaloisStabilizer( Field( [ r5 ] ) ); [ 1, 4 ]