Computation of integral solutions of a special type of systems of quadratic equations

  • Michael Pohst
Algorithms — Computational Number Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 162)


Let S,T be n×n integral matrices and one of them positive definite. We develop a method to decide whether a solution X∈ℤn×n of XtrSX=T exists and, if the answer is affirmative, an algorithm for the computation of X. Some applications in algebraic number theory and lattice construction are presented.


Basis Vector Type Frequency Reduction Theory Elementary Divisor Vector Type 
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  1. [1]
    G. Havas and L. Sterling, "Integer matrices and Abelian groups", Symbolic and Algebraic Computation (E. W. Ng, ed.), Lecture Notes in Computer Science 72, Springer Verlag (1979), 431–451.Google Scholar
  2. [2]
    W. Plesken and M. Pohst, "Constructing integral lattices with prescribed minimum I", to appear.Google Scholar
  3. [3]
    M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications", ACM SIGSAM Bulletin vol. 15, no. 1 (1981), 37–44.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Michael Pohst
    • 1
  1. 1.Mathematisches InstitutUniversität Düsseldorf4 DüsseldorfFRG

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