M4RI is a library for fast arithmetic with dense matrices over F2. It was started by Gregory Bard, is maintained by Martin Albrecht. Several people contributed to it (see below). The name M4RI comes from the first implemented algorithm: The “Method of the Four Russians” inversion algorithm published by Gregory Bard. This algorithm in turn is named after the “Method of the Four Russians” multiplication algorithm which is probably better referred to as Kronrod’s method. M4RI is used by the Sage mathematics software and the PolyBoRi library. M4RI is available under the General Public License Version 2 or later (GPLv2+).

This software is also referenced in ORMS.

References in zbMATH (referenced in 20 articles )

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  1. Beierle, Christof; Derbez, Patrick; Leander, Gregor; Leurent, Gaëtan; Raddum, Håvard; Rotella, Yann; Rupprecht, David; Stennes, Lukas: Cryptanalysis of the GPRS encryption algorithms GEA-1 and GEA-2 (2021)
  2. Berthomieu, Christian Eder, Mohab Safey El Din: msolve: A Library for Solving Polynomial Systems (2021) arXiv
  3. Bardet, Magali; Briaud, Pierre; Bros, Maxime; Gaborit, Philippe; Neiger, Vincent; Ruatta, Olivier; Tillich, Jean-Pierre: An algebraic attack on rank metric code-based cryptosystems (2020)
  4. Cannon, John J.; Steel, Allan K.; Unger, William R.: Construction of the irreducible modular representations of a finite group (2020)
  5. Li, Ting; Sun, Yao; Huang, Zhenyu; Wang, Dingkang; Lin, Dongdai: Speeding up the GVW algorithm via a substituting method (2019)
  6. Meel, Kuldeep S.; Shrotri, Aditya A.; Vardi, Moshe Y.: Not all FPRASs are equal: demystifying FPRASs for DNF-counting (2019)
  7. Zamarashkin, N. L.; Zheltkov, D. A.: GPU acceleration of dense matrix and block operations for Lanczos method for systems over (\mathrmGF(2)) (2019)
  8. Cenk, Murat; Hasan, M. Anwar: On the arithmetic complexity of Strassen-like matrix multiplications (2017)
  9. Dzyuba, Vladimir; van Leeuwen, Matthijs; De Raedt, Luc: Flexible constrained sampling with guarantees for pattern mining (2017)
  10. Sun, Yao; Huang, Zhenyu; Lin, Dongdai; Wang, Dingkang: On implementing the symbolic preprocessing function over Boolean polynomial rings in Gröbner basis algorithms using linear algebra (2016)
  11. Sun, Yao; Huang, Zhenyu; Wang, Dingkang; Lin, Dongdai: An improvement over the GVW algorithm for inhomogeneous polynomial systems (2016)
  12. Berthomieu, Jérémy; Faugère, Jean-Charles; Perret, Ludovic: Polynomial-time algorithms for quadratic isomorphism of polynomials: the regular case (2015)
  13. Bertolazzi, Enrico; Rimoldi, Anna: Fast matrix decomposition in (\mathbbF_2) (2014)
  14. Ullah, E.; Abbas Khan, S.: Computing border bases using mutant strategies (2014)
  15. Jeannerod, Claude-Pierre; Pernet, Clément; Storjohann, Arne: Rank-profile revealing Gaussian elimination and the CUP matrix decomposition (2013)
  16. Albrecht, Martin R.: The M4RIE library for dense linear algebra over small fields with even characteristic (2012)
  17. Albrecht, Martin; Bard, Gregory; Hart, William: Algorithm 898: Efficient multiplication of dense matrices over GF(2) (2010)
  18. Bodrato, Marco: A Strassen-like matrix multiplication suited for squaring and higher power computation (2010)
  19. Bulygin, Stanislav; Brickenstein, Michael: Obtaining and solving systems of equations in key variables only for the small variants of AES (2010)
  20. Mohamed, Mohamed Saied Emam; Mohamed, Wael Said Abd Elmageed; Ding, Jintai; Buchmann, Johannes: MXL2: Solving polynomial equations over (\textGF(2)) using an improved mutant strategy (2008)