Computing with subfields

The algorithms presented here make use of subfield information to improve computations. For the three problems we deal with in this paper, the solution of relative norm equations, computation of independent units in the Galois closure of quartic fields and the computation of relative integral bases in quadratic extensions of number fields, we will outline the necessary algorithms that use subfield information and whenever possible we will compare the running time of each algorithm with the equivalent method not using subfield information. (C) 1997 Academic Press Limited.