The module rings.number_field defines the following classes:
The command CyclotomicField(n) creates the n-th cyclotomic field, got by adjoing an n-th root of unity to the rational field.
sage: CyclotomicField(3) Cyclotomic Field of order 3 and degree 2 sage: CyclotomicField(18) Cyclotomic Field of order 18 and degree 6 sage: z = CyclotomicField(6).gen(); z zeta_6 sage: z**3 -1 sage: (1+z)**3 6*zeta_6 - 3
The command QuadraticExtension(a) creates the field Q(sqrt(a)).
sage: QuadraticField(3) Number Field with defining polynomial x^2 - 3 sage: QuadraticField(-4) Number Field with defining polynomial x^2 + 4
The module rings.number_field defines the following functions: