Efficient computation of maximal orders in radical (including Kummer) extensions

We describe an algorithm, linear in the degree of the field, for computing a (pseudo) basis for P-maximal orders of radical (which includes Kummer) extensions of global arithmetic fields. We construct our basis in such a way as to further improve maximal order computations in these radical extensions. Using this algorithm for the similar problem of computing maximal orders of class fields is discussed. We give examples of both function fields and number fields comparing the running time of our algorithm to that of the Round 2 or 4 and Fraatz (2005).