GBLA – Gröbner Basis Linear Algebra Package

Abstract : This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea [7] of Faugère 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 reduction. Further, we compare different parallel schedulers GBLA can be used with. We also developed a new advanced storage format that exploits the fact that our matrices are coming from Gröbner basis computations, shrinking storage by a factor of up to 4. A huge database of our matrices is freely available with GBLA.
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https://hal.inria.fr/hal-01276346
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Submitted on : Tuesday, November 22, 2016 - 5:06:34 PM
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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-01276346v2⟩

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