FGb

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. Courtois, Nicolas; Goubin, Louis; Meier, Willi; Tacier, Jean-Daniel: Solving underdefined systems of multivariate quadratic equations (2002)
  2. Dumas, Jean-Guillaume; Roch, Jean-Louis: On parallel block algorithms for exact triangularizations (2002)
  3. Faugère, Jean-Charles: A new efficient algorithm for computing Gröbner bases without reduction to zero ((F_5)). (2002)
  4. Foursov, Mikhail V.; Moreno Maza, Marc: On computer-assisted classification of coupled integrable equations (2002)
  5. Galligo, André; Rupprecht, David: Irreducible decomposition of curves (2002)
  6. Mourrain, Bernard; Ruatta, Olivier: Relations between roots and coefficients, interpolation and application to system solving (2002)
  7. Sodan, Angela C.: Applications on a multithreaded architecture: A case study with EARTH--MANNA (2002)
  8. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Symmetric functions applied to decomposing solution sets of polynomial systems (2002)
  9. Faugère, Jean-Charles: Finding all the solutions of cyclic 9 using Gröbner basis techniques (2001)
  10. Norton, Graham H.; Sălăgean, Ana: Strong Gröbner bases for polynomials over a principal ideal ring. (2001)
  11. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical decomposition of the solution sets of polynomial systems into irreducible components (2001)
  12. Thiéry, Nicolas M.: Computing minimal generating sets of invariant rings of permutation groups with SAGBI-Gröbner basis (2001)
  13. Aubry, Philippe; Valibouze, Annick: Using Galois ideals for computing relative resolvents (2000)
  14. Courtois, Nicolas; Klimov, Alexander; Patarin, Jacques; Shamir, Adi: Efficient algorithms for solving overdefined systems of multivariate polynomial equations (2000)
  15. Rouillier, F.; Roy, M.-F.; Safey El Din, M.: Finding at least one point in each connected component of a real algebraic set defined by a single equation (2000)
  16. Sommese, Andrew J.; Verschelde, Jan: Numerical homotopies to compute generic points on positive dimensional algebraic sets (2000)
  17. Sottile, Frank: Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro (2000)
  18. Thiéry, Nicolas M.: Algebraic invariants of graphs; a study based on computer exploration (2000)
  19. Bikker, P.; Uteshev, A. Yu.: On the Bézout construction of the resultant (1999)
  20. Faugère, Jean-Charles: A new efficient algorithm for computing Gröbner bases ((F_4)) (1999)

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