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 ? n subscript ? 𝑛 ?_{n} . 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) )