In cyclotomic fields the generic ring functions are supported. The functions listed below are those functions for cyclotomic fields which are additional to those for number fields. For the list of functions applying to general number fields see Section Creation Functions and Section Structure Operations.
The smallest n such that the field K is contained in Q(ζn); for a cyclotomic field that is either the `cyclotomic order' m (see below) or half that, depending on whether m ≡ 2 mod 4. The second return value is a sequence of the ramified real places of K.
The value of m for the cyclotomic field Q(ζm). Note that this will be the m with which the cyclotomic field was created.
Returns the automorphism group of K as an abstract abelian group G and a map from G into the set of all automorphisms. Note that similar functionality is also available through AutomorphismGroup however, this function returns an abelian group and uses the fact that the automorphism group is already determined by the conductor.
Given two cyclotomic fields k⊆K a number field L/k is computed that is isomorphic to K.