‣ 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