FGb/Gb libraryGb is a program (191 420 lines of C++) for computing Grobner bases, implement ”standard” algoritms. FGb (206 052 lines of C) ia an efficient program written in C for solving polynomial systems. The purpose of the FGb library is twofold. First of all, the main goal is to provide efficient implementations of state-of-the-art algorithms for computing Gröbner bases: actually, from a research point of view, it is mandatory to have such an implementation to demonstrate the practical efficiency of new algorithms. Secondly, in conjunction with other software, the FGb library has been used in various applications (Robotic, Signal Theory, Biology, Computational Geometry, . . . ) and more recently to a wide range of problems in Cryptology (for instance, FGb was explicitly used in [2, 8, 9, 4, 5] to break several cryptosystems)

References in zbMATH (referenced in 244 articles , 1 standard article )

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  1. Berthomieu, Christian Eder, Mohab Safey El Din: msolve: A Library for Solving Polynomial Systems (2021) arXiv
  2. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Exact algorithms for semidefinite programs with degenerate feasible set (2021)
  3. Mourrain, Bernard; Telen, Simon; Van Barel, Marc: Truncated normal forms for solving polynomial systems: generalized and efficient algorithms (2021)
  4. Capco, Jose; Din, Mohab Safey El; Schicho, Josef: Robots, computer algebra and eight connected components (2020)
  5. Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias: Lower bounds on the number of realizations of rigid graphs (2020)
  6. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Real root finding for low rank linear matrices (2020)
  7. Horáček, Jan; Kreuzer, Martin: On conversions from CNF to ANF (2020)
  8. Poslavsky, Stanislav: Rings: an efficient JVM library for commutative algebra (invited talk) (2019)
  9. Bender, Matías R.; Faugère, Jean-Charles; Mantzaflaris, Angelos; Tsigaridas, Elias: Bilinear systems with two supports. Koszul resultant matrices, eigenvalues, and eigenvectors (2018)
  10. Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef: The number of realizations of a Laman graph (2018)
  11. Faugère, Jean-Charles; Wallet, Alexandre: The point decomposition problem over hyperelliptic curves, Toward efficient computation of discrete logarithms in even characteristic (2018)
  12. Greenwood, Torin: Asymptotics of bivariate analytic functions with algebraic singularities (2018)
  13. Güler, Erhan; Kişi, Ömer; Konaxis, Christos: Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space (2018)
  14. Horáček, Jan; Kreuzer, Martin: 3BA: a border bases solver with a SAT extension (2018)
  15. Jiang, Yunfeng; Zhang, Yang: Algebraic geometry and Bethe ansatz. I: The quotient ring for BAE (2018)
  16. Naldi, Simone: Solving rank-constrained semidefinite programs in exact arithmetic (2018)
  17. Dong, Rina; Mou, Chenqi: Decomposing polynomial sets simultaneously into Gröbner bases and normal triangular sets (2017)
  18. Makarim, Rusydi H.; Stevens, Marc: M4GB. An efficient Gröbner-basis algorithm (2017)
  19. Rodriguez, Jose Israel; Tang, Xiaoxian: A probabilistic algorithm for computing data-discriminants of likelihood equations (2017)
  20. Awange, Joseph L.; Paláncz, Béla: Geospatial algebraic computations. Theory and applications (2016)

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Further publications can be found at: http://www-polsys.lip6.fr/~jcf/Publications/index.html