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Computing a lattice basis from a system of generating vectors

  • Applications And Systems
  • Conference paper
  • First Online:
Eurocal '87 (EUROCAL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 378))

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Abstract

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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References

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Authors and Affiliations

  1. Mathematisches Institut, Universität Düsseldorf, 4000, Düsseldorf, FRG

    Johannes Buchmann & Michael Pohst

Authors
  1. Johannes Buchmann
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  2. Michael Pohst
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Editor information

James H. Davenport

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© 1989 Springer-Verlag Berlin Heidelberg

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Buchmann, J., Pohst, M. (1989). Computing a lattice basis from a system of generating vectors. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_89

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  • DOI: https://doi.org/10.1007/3-540-51517-8_89

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51517-3

  • Online ISBN: 978-3-540-48207-9

  • eBook Packages: Springer Book Archive

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