Algorithms for Large Integer Matrix Problems

  • Mark Giesbrecht
  • Michael Jr. Jacobson
  • Arne Storjohann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2227)


New algorithms are described and analysed for solving various problems associated with a large integer matrix: computing the Hermite form, computing a kernel basis, and solving a system of linear diophantine equations. The algorithms are space-efficient and for certain types of input matrices — for example, those arising during the computation of class groups and regulators — are faster than previous methods. Experiments with a prototype implementation support the running time analyses.


Class Group Hermite Form Smith Normal Form Lift Step Ring Operation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mark Giesbrecht
    • 1
  • Michael Jr. Jacobson
    • 2
  • Arne Storjohann
    • 1
  1. 1.Ontario Research Centre for Computer AlgebraUniversity of Western OntarioLondonCanada
  2. 2.Dept. of Computer ScienceUniversity of ManitobaWinnipegCanada

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