Magma currently has three main categories corresponding to number fields: general number fields, quadratic fields, and cyclotomic number fields. It should be noted, that quadratic fields and cyclotomic fields are in fact number fields that allow special algorithms in some situations, e.g., for class group computation, continued fractions for fundamental units,
Facilities for general number fields have been developed in a joint project with the KANT group in Berlin. The core consists of machinery for performing arithmetic with arbitrary orders and their ideals. The major capabilities include facilities to determine the maximal order (round 2 and 4 algorithms), class group, unit group, Galois group (up to degree 23) and the computation of defining equations for ray class fields.