GBLA – Gröbner Basis Linear Algebra Package

International audienceThis is a system paper about a new GPLv2 open source C libraryGBLA implementing and improving the idea [7] of Faugère andLachartre (GB reduction). We further exploit underlying structuresin matrices generated during Gröbner basis computations in algorithmslike F4 or F5 taking advantage of block patterns by using aspecial data structure called multilines. Moreover, we discuss a neworder of operations for the reduction process. In various differentexperimental results we show that GBLA performs better than GBreduction or Magma in sequential computations (up to 40% faster)and scales much better than GB reduction for a higher number ofcores: On 32 cores we reach a scaling of up to 26. GBLA is upto 7 times faster than GB reduction. Further, we compare differentparallel schedulers GBLA can be used with. We also developed anew advanced storage format that exploits the fact that our matricesare coming from Gröbner basis computations, shrinking storage bya factor of up to 4. A huge database of our matrices is freely availablewith GBLA