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.
Returns the associative structure constant algebra which is isomorphic to the cyclotomic field K as an algebra over J. Also returns the isomorphism from K to the algebra mapping w^i to the i + 1st unit vector of the algebra where w is the generator of K.If a sequence S is given it is taken to be a basis of K over J and the isomorphism will map the ith element of S to the ith unit vector of the algebra.
The vector space isomorphic to the cyclotomic field K as a vector space over J and the isomorphism from K to the vector space. The isomorphism maps w^i to the i + 1st unit vector of the vector space.If S is given, the isomorphism will map the ith element of S to the ith unit vector of the vector space.
The smallest n such that the field K is contained in Q(zeta_n); 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(zeta_m). Note that this will be the m with which the cyclotomic field was created.[Next][Prev] [Right] [Left] [Up] [Index] [Root]