60.1-2 AbelianNumberField
‣ AbelianNumberField( n, stab )( function )
‣ NF( n, stab )( function )

For a positive integer n and a list stab of prime residues modulo n, AbelianNumberField returns the fixed field of the group described by stab (cf. GaloisStabilizer (60.2-5)), in the n-th cyclotomic field. AbelianNumberField is mainly thought for internal use and for printing fields in a standard way; Field (58.1-3) (cf. also 60.2) is probably more suitable if one knows generators of the field in question.

AbelianNumberField can be abbreviated to NF, this form is used also when GAP prints abelian number fields.

Fields constructed with NF are stored in the global list ABELIAN_NUMBER_FIELDS, so repeated calls of NF just fetch these field objects after they have been created once.

gap> NF( 7, [ 1 ] );
CF(7)
gap> f:= NF( 7, [ 1, 2 ] );  Sqrt(-7); Sqrt(-7) in f;
NF(7,[ 1, 2, 4 ])
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6
true