In cyclotomic fields the generic ring functions listed below are supported. In the list below a and b are cyclotomic field elements; however, automatic coercion will ensure that +, *, -, /, eq, ne and in will also work if a or b is an integer or rational number.
A sequence of elements of the cyclotomic field K that forms an integral basis for K. The integral bases for cyclotomic fields are chosen in such a way that they are compatible with each other, that is, if K is contained in L, then its integral basis will be contained in that for L.
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 not equiv2bmod4 or m equiv2bmod4.
The (absolute) degree of K over Q. If K=Q(zeta_m) this equals phi(m).
The discriminant of the cyclotomic field 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.