60.1-1 CyclotomicField
‣ CyclotomicField ( [subfield, ]n ) | ( function ) |
‣ CyclotomicField ( [subfield, ]gens ) | ( function ) |
‣ CF ( [subfield, ]n ) | ( function ) |
‣ CF ( [subfield, ]gens ) | ( function ) |
The first version creates the n-th cyclotomic field . The second version creates the smallest cyclotomic field containing the elements in the list gens. In both cases the field can be generated as an extension of a designated subfield subfield (cf. 60.3).
CyclotomicField
can be abbreviated to CF
, this form is used also when GAP prints cyclotomic fields.
Fields constructed with the one argument version of CF
are stored in the global list CYCLOTOMIC_FIELDS
, so repeated calls of CF
just fetch these field objects after they have been created once.
gap> CyclotomicField( 5 ); CyclotomicField( [ Sqrt(3) ] );
CF(5)
CF(12)
gap> CF( CF(3), 12 ); CF( CF(4), [ Sqrt(7) ] );
AsField( CF(3), CF(12) )
AsField( GaussianRationals, CF(28) )