GBLA -- Gr\"obner Basis Linear Algebra Package

Understand

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.