Computing a lattice basis from a system of generating vectors

  • Johannes Buchmann
  • Michael Pohst
Applications And Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 378)


In this paper we describe how the LLL-algorithm can be used to compute a basis of a lattice L in R n from a system of k generating vectors and a lower bound for the lengths of the non zero vectors in L. The algorithm which we present is proved to be polynomial time in n + k and the size of the input data. The algorithm is applied to the problem of finding multiplicative relations between units of algebraic number fields. Numerical results show that our method works very efficiently.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Johannes Buchmann
    • 1
  • Michael Pohst
    • 1
  1. 1.Mathematisches InstitutUniversität DüsseldorfDüsseldorfFRG

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