Conference Papers Year : 2016

GBLA – Gröbner Basis Linear Algebra Package

Brice Boyer
  • Function : Author
  • PersonId : 977005
Jean-Charles Faugère
Sylvian Lachartre
  • Function : Author
  • PersonId : 977006
Fayssal Martani
  • Function : Author
  • PersonId : 977007

Abstract

This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea of Faug\`ere and Lachartre (GB reduction). We further exploit underlying structures in matrices generated during Gröbner basis computations in algorithms like F4 or F5 taking advantage of block patterns by using a special data structure called multilines. Moreover , we discuss a new order of operations for the reduction process. In various different experimental results we show that GBLA performs better than GB reduction or Magma in sequential computations (up to 40% faster) and scales much better than GB reduction for a higher number of cores: On 32 cores we reach a scaling of up to 26. GBLA is up to 7 times faster than GB
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Dates and versions

hal-01276346 , version 1 (19-02-2016)
hal-01276346 , version 2 (22-11-2016)

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Cite

Brice Boyer, Christian Eder, Jean-Charles Faugère, Sylvian Lachartre, Fayssal Martani. GBLA – Gröbner Basis Linear Algebra Package. 41st International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, ON, Canada. pp.135-142, ⟨10.1145/2930889.2930914⟩. ⟨hal-01276346v1⟩
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