GBLA -- Gr\"obner Basis Linear Algebra Package
Brice Boyer, Christian Eder, Jean-Charles Faug\`ere, Sylvian, Lachartre, and Fayssal Martani

TL;DR
GBLA is an open-source C library that optimizes matrix reduction in Gr"obner basis computations, achieving significant speedups and better scalability through novel data structures, operation ordering, and storage formats.
Contribution
It introduces a new data structure, operation order, and storage format for Gr"obner basis matrix reduction, improving performance and scalability over existing methods.
Findings
Up to 40% faster than GB reduction in sequential runs
Scales up to 26 times better on 32 cores
Reduces storage size by up to 4 times
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 Gr\"obner 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…
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Taxonomy
TopicsPolynomial and algebraic computation · Numerical Methods and Algorithms · Cryptography and Residue Arithmetic
