On effective computation of fundamental units. II

Introduction. In part I of this paper we described the theoretical improvements of our method of computing fundamental units in algebraic number fields which we achieved in the last few years. Those improvements were of considerable influence on the corresponding computer program. Since its first 1976 [2] implementation it was completely rewritten and changed in so many details that a new presentation cannot be avoided. In Sections 1 and 2 of this paper we describe the applications of part I [6] to the algorithm for constructing fundamental units. Section 3 contains a complete list of numerical examples concerning algebraic number fields of small degree and small absolute discriminant. Besides the fundamental units the tables contain much information about fields of degree five and six which was so far unknown. The determination of those fields (and their subfields) is described in [3]. Besides the fundamental units we also listed the order of the torsion subgroup TUF of the unit group U, whenever it is different from 2. It was computed by the methods of Section 2 of [5]. All computations were carried out on the Control Data Cyber 76 of the Computer Center of the University of Cologne.