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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.
Keywords :
Gr\obner basis
Linear algebra
Cited literature [12 references]
https://hal.inria.fr/hal-01276346
Contributor : Jean-Charles Faugère <>
Submitted on : Tuesday, November 22, 2016 - 5:06:34 PM
Last modification on : Friday, January 8, 2021 - 5:44:01 PM
Long-term archiving on: : Monday, March 20, 2017 - 6:06:16 PM
Contributor : Jean-Charles Faugère <>
Submitted on : Tuesday, November 22, 2016 - 5:06:34 PM
Last modification on : Friday, January 8, 2021 - 5:44:01 PM
Long-term archiving on: : Monday, March 20, 2017 - 6:06:16 PM
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groblin.pdf
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