Computation of Independent Units in Number Fields by Dirichlet's Method

Using the basis reduction algorithm of A. K. Lenstra, H. W. Lenstra, Jr. and L. Lov&sz [8] and an idea of Buchmann [4], we describe a method for computing maximal systems of independent units in arbitrary number fields. The tables in the supplements section display such systems for the fields Q( VD) where 6 < n < 11.