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FGb

swMATH ID: 286
Software Authors: J.-C. Faugère
Description: 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)
Homepage: http://www-polsys.lip6.fr/~jcf/FGb/index.html
Programming Languages: C, C++
Operating Systems: Windows (32 and 64 bits), Linux (32 and 64 bits), Mac (Universal ppc/intel 32/64 bits) and Sun Solaris.
Related Software: Magma; SINGULAR; Maple; ISOLATE; Kronecker; FLASH; RAGlib; SageMath; PolyBoRi; Macaulay2; MiniSat; PHCpack; slimgb; Mathematica; SPECTRA; QEPCAD; CoCoA; NTL; RegularChains; CGAL
Cited in: 247 Publications
Further Publications: http://www-polsys.lip6.fr/~jcf/Publications/index.html

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
FGb: a library for computing Gröbner bases. Zbl 1294.68156
Faugère, Jean-Charles
2010
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Cited by 338 Authors

45 Faugère, Jean-Charles
20 Safey El Din, Mohab
19 Perret, Ludovic
12 Ding, Jintai
9 Courtois, Nicolas T.
9 Yang, Bo-Yin
8 Mourrain, Bernard
7 Joux, Antoine
6 Bettale, Luk
6 Lazard, Daniel
6 Naldi, Simone
6 Rouillier, Fabrice
5 Buchmann, Johannes A.
5 Bulygin, Stanislav V.
5 Chen, Jiun-Ming
5 Preneel, Bart
5 Salvy, Bruno
4 Albrecht, Martin R.
4 Bardet, Magali
4 Brickenstein, Michael
4 Cid, Carlos Frederico
4 Gerdt, Vladimir Petrovich
4 Henrion, Didier
4 Lazard, Sylvain
4 Spaenlehauer, Pierre-Jean
4 Verschelde, Jan
4 Wolf, Christopher A.
3 Capco, Jose
3 Giné, Jaume
3 Mou, Chenqi
3 Murphy, Sean
3 Petzoldt, Albrecht
3 Pouget, Marc
3 Renault, Guénaël
3 Romanovskiĭ, Valeriĭ Georgievich
3 Schicho, Josef
3 Schost, Éric
3 Sommese, Andrew John
3 Tsigaridas, Elias P.
3 Wang, Dongming
3 Weinmann, Ralf-Philipp
2 Abłamowicz, Rafał
2 Bard, Gregory V.
2 Blinkov, Yuri A.
2 Bouillaguet, Charles
2 Boussaada, Islam
2 Chen, Xingwu
2 Cheng, Jinsan
2 Chouikha, Abd Raouf
2 Clough, Crystal Lee
2 Debraize, Blandine
2 Dubois, Vivien
2 Everett, Hazel
2 Ferčec, Brigita
2 Fouque, Pierre-Alain
2 Gaudry, Pierrick
2 Giusti, Marc
2 Goubin, Louis
2 Gower, Jason E.
2 Granboulan, Louis
2 Granger, Robert A.
2 Grasegger, Georg
2 Hodges, Timothy J.
2 Hong, Hoon
2 Horáček, Jan
2 Hu, Lei
2 Huot, Louise
2 Kang, Seok-Jin
2 Kotsireas, Ilias S.
2 Koutschan, Christoph
2 Kreuzer, Martin
2 Lecerf, Grégoire
2 Lee, Dong-Il
2 Levy-dit-Vehel, Françoise
2 Liang, Ye
2 Maniatis, Markos
2 Mora, Teo
2 Moreno Maza, Marc
2 Muller, Frédéric
2 Nakahara, Jorge jun.
2 Nie, Xuyun
2 Niu, Wei
2 Norton, Graham H.
2 Otmani, Ayoub
2 Pan, Victor Yakovlevich
2 Park, Hyungju
2 Patarin, Jacques
2 Paterson, Maura Beth
2 Paul, Souradyuti
2 Pearce, Roman
2 Peñaranda, Luis Mariano
2 Pyshkin, Andrei
2 Raddum, Håvard
2 Ruatta, Olivier
2 Sălăgean, Ana Maria
2 Schilling, Thorsten Ernst
2 Schmidt, Dieter S.
2 Semaev, Igor A.
2 Sepehrdad, Pouyan
2 Shamir, Adi
...and 238 more Authors
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Cited in 55 Serials

28 Journal of Symbolic Computation
6 Mathematics in Computer Science
5 Journal of Mathematical Cryptology
4 Programming and Computer Software
4 Designs, Codes and Cryptography
3 Journal of Algebra
3 Theoretical Computer Science
3 Parallel Computing
3 Journal of Complexity
3 Experimental Mathematics
3 Foundations of Computational Mathematics
2 SIAM Journal on Numerical Analysis
2 Discrete & Computational Geometry
2 Applicable Algebra in Engineering, Communication and Computing
2 SIAM Journal on Optimization
2 Tatra Mountains Mathematical Publications
2 Finite Fields and their Applications
2 Bulletin des Sciences Mathématiques
2 Annals of Mathematics and Artificial Intelligence
1 International Journal of Modern Physics A
1 Bulletin of the Australian Mathematical Society
1 Communications in Algebra
1 Computers & Mathematics with Applications
1 Journal of Mathematical Analysis and Applications
1 Applied Mathematics and Computation
1 Journal of Combinatorial Theory. Series A
1 Journal of Pure and Applied Algebra
1 Mathematics and Computers in Simulation
1 SIAM Journal on Computing
1 SIGSAM Bulletin
1 Cryptologia
1 Advances in Applied Mathematics
1 Acta Applicandae Mathematicae
1 Journal of Cryptology
1 Discrete Mathematics and Applications
1 Linear Algebra and its Applications
1 SIAM Journal on Applied Mathematics
1 Journal of Mathematical Sciences (New York)
1 Advances in Applied Clifford Algebras
1 The Electronic Journal of Combinatorics
1 Multibody System Dynamics
1 Mechanism and Machine Theory
1 Revista Matemática Complutense
1 Journal of the European Mathematical Society (JEMS)
1 Journal of High Energy Physics
1 Journal of Systems Science and Complexity
1 The European Physical Journal C. Particles and Fields
1 Lecture Notes in Computer Science
1 Algorithms and Computation in Mathematics
1 International Journal of Algebra
1 Journal of Physics A: Mathematical and Theoretical
1 ACM Transactions on Algorithms
1 Mathematics
1 SIAM Journal on Applied Algebra and Geometry
1 Undergraduate Texts in Mathematics

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