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Using the basis reduction algorithm of A. K. Lenstra, H. W. Lenstra, Jr. and L. Lovász [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 ( D n ) {\mathbf {Q}}(\sqrt [n]{D})       where      6 ≤  n ≤  11 6 \leq n \leq 11      .

Computation of independent units in number fields by Dirichlet’s method