For a set S of cyclotomics,
DefaultField( S ) = CF( S )
is the smallest cylotomic field
containing S (see DefaultField), the so--called conductor of S;
Field( S ) = NF( S )
is the smallest field containing S (see
Field).
gap> DefaultField( [ E(5) ] ); DefaultField( [ E(3), ER(6) ] ); CF(5) CF(24) gap> Field( [ E(5) ] ); Field( [ E(3), ER(6) ] ); CF(5) NF(24,[ 1, 19 ])
DefaultField
and Field
are used by functions that specify the field
for which some cyclotomics are regarded as elements (see DefaultField,
Field), e.g., Trace
with only one argument will compute the trace of
this argument (which must be a cyclotomic) with respect to its default
field.
GAP 3.4.4