60.2-4 IsCyclotomicField
‣ IsCyclotomicField( F )( property )

returns true if the field F is a cyclotomic field, i.e., an abelian number field (see IsAbelianNumberField (60.2-3)) that can be generated by roots of unity.

gap> IsNumberField( CF(9) ); IsAbelianNumberField( Field( [ ER(3) ] ) );
true
true
gap> IsNumberField( GF(2) );
false
gap> IsCyclotomicField( CF(9) );
true
gap> IsCyclotomicField( Field( [ Sqrt(-3) ] ) );
true
gap> IsCyclotomicField( Field( [ Sqrt(3) ] ) );
false