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Gfan

swMATH ID: 4698
Software Authors: Anders Nedergaard Jensen
Description: Gfan is a software package for computing Gröbner fans and tropical varieties. These are polyhedral fans associated to polynomial ideals. The maximal cones of a Gröbner fan are in bijection with the marked reduced Gröbner bases of its defining ideal. The software computes all marked reduced Gröbner bases of an ideal. Their union is a universal Gröbner basis. The tropical variety of a polynomial ideal is a certain subcomplex of the Gröbner fan. Gfan contains algorithms for computing this complex for general ideals and specialized algorithms for tropical curves, tropical hypersurfaces and tropical varieties of prime ideals. In addition to the above core functions the package contains many tools which are useful in the study of Gröbner bases, initial ideals and tropical geometry. The full list of commands can be found in Appendix B of the manual. For ordinary Gröbner basis computations Gfan is not competitive in speed compared to programs such as CoCoA, Singular and Macaulay2.
Homepage: http://home.imf.au.dk/jensen/software/gfan/gfan.html
Programming Languages: The program is written in C++ and can be compiled with gcc 3.3.3.
Operating Systems: Linux, Mac OS X and other UNIX variants. It is likely thatthe program will also run on Microsoft Windows systems through Cygwin.
Dependencies: gcc 3.3.3. Thefollowing libraries are required: gmp (arithmetics) and cddlib (LP-solving).
Keywords: {\tt Gfan}
Related Software: SINGULAR; Macaulay2; polymake; SageMath; cdd; PHCpack; Maple; TOPCOM; CoCoA; gmp; 4ti2; Normaliz; SoPlex; DEMiCs; MixedVol; Magma; gfanlib; CoCoALib; tropical.lib; TropLi
Referenced in: 122 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
A presentation of the Gfan software. Zbl 1230.13026
Jensen, Anders N.
2006
all top 5

Referenced by 146 Authors

15 Sturmfels, Bernd
14 Jensen, Anders Nedergaard
7 Joswig, Michael
7 Thomas, Rekha R.
7 Verschelde, Jan
6 Cueto, María Angélica
6 Ren, Yue
6 Yu, Josephine
4 Bigatti, Anna Maria
4 Maclagan, Diane
4 Markwig, Thomas
3 Bogart, Tristram
3 Chan, Melody
3 Görlach, Paul
3 Hampton, Marshall
3 Morrison, Ralph
3 Ren, Qingchun
3 Schönemann, Hans
3 Takayama, Nobuki
2 Abbott, John A.
2 Adrovic, Danko
2 Bliss, Nathan
2 Boocher, Adam
2 Brodsky, Sarah B.
2 Chen, Tianran
2 Fukuda, Komei
2 Herrmann, Sven
2 Kastner, Lars
2 Keicher, Simon
2 Kileel, Joe
2 Leykin, Anton
2 Markwig, Hannah
2 Maruri-Aguilar, Hugo
2 Panizzut, Marta
2 Rincón, Felipe
2 Sáenz de Cabezón Irigaray, Eduardo
2 Sam, Steven V.
2 Sommars, Jeff
2 Speyer, David E.
2 Stapledon, Alan
2 Swinarski, David
2 Tillmann, Stephan
2 Tran, Ngoc Mai
2 Vaccon, Tristan
2 Wynn, Henry P.
2 Zhang, Leon
1 Aholt, Chris
1 Altıntaş Sharland, Ayşe
1 Ardila, Federico
1 Aroca, Fuensanta
1 Bahloul, Rouchdi
1 Balletti, Gabriele
1 Barkhordar, Marzieh
1 Brandt, Madeline
1 Brouwer, Andries Evert
1 Cartwright, Dustin A.
1 Çevık, G.
1 Chan, Andrew J.
1 Conca, Aldo
1 Corey, Daniel
1 Craw, Alastair
1 De Loera, Jesús A.
1 De Negri, Emanuela
1 Dehghani Darmian, Mahdi
1 Deopurkar, Anand
1 Dickenstein, Alicia M.
1 Dimitrova, Elena S.
1 Donten-Bury, Maria
1 Draisma, Jan
1 Dück, Natalia
1 Epure, Raul
1 Eröcal, Burçin
1 Eur, Christopher
1 Fedorchuk, Maksym
1 Feichtner, Eva Maria
1 Frenk, Bart J.
1 Gimenez, Philippe
1 Gómez-Morales, Mirna
1 Goodman, Jacob Eli
1 Gross, Elizabeth
1 Guilloux, Antonin
1 Häbich, Mathias
1 Hampe, Simon
1 Hartshorne, Robin
1 Hashemi, Amir
1 Hausen, Jürgen
1 Hemmecke, Raymond
1 Hibi, Takayuki
1 Hofmann, Tommy
1 Hoşten, Serkan
1 Hu, Jingzhen
1 Iglesias, Andrés
1 Jordan, Charles
1 Katz, Eric
1 Kaya, Gülay
1 Kukelova, Zuzana
1 Lella, Paolo
1 Liang, Qingzhong
1 Lin, Shaowei
1 Márquez-Corbella, Irene
...and 46 more Authors
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Referenced in 53 Serials

9 Journal of Symbolic Computation
7 Journal of Algebra
5 Experimental Mathematics
4 Linear Algebra and its Applications
3 Mathematics of Computation
3 Discrete & Computational Geometry
3 Journal of Algebraic Combinatorics
3 Research in the Mathematical Sciences
2 Advances in Mathematics
2 Journal of Combinatorial Theory. Series A
2 Mathematische Annalen
2 Advances in Applied Mathematics
2 Applicable Algebra in Engineering, Communication and Computing
2 Foundations of Computational Mathematics
2 ACM Communications in Computer Algebra
2 The Journal of Software for Algebra and Geometry
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Mathematical Biology
1 Rocky Mountain Journal of Mathematics
1 Bulletin of Mathematical Biology
1 Beiträge zur Algebra und Geometrie
1 Annals of the Institute of Statistical Mathematics
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
1 Hokkaido Mathematical Journal
1 Le Matematiche
1 Mathematische Zeitschrift
1 Proceedings of the American Mathematical Society
1 Programming and Computer Software
1 Journal of the American Mathematical Society
1 SIAM Journal on Discrete Mathematics
1 Forum Mathematicum
1 International Journal of Algebra and Computation
1 IMRN. International Mathematics Research Notices
1 Celestial Mechanics and Dynamical Astronomy
1 Computational Complexity
1 The Electronic Journal of Combinatorics
1 Selecta Mathematica. New Series
1 Mathematical Research Letters
1 Qualitative Theory of Dynamical Systems
1 Advances in Geometry
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Hacettepe Journal of Mathematics and Statistics
1 Graduate Studies in Mathematics
1 The IMA Volumes in Mathematics and its Applications
1 Lecture Notes in Computer Science
1 Lecture Notes in Mathematics
1 Algorithms and Computation in Mathematics
1 Mathematics in Computer Science
1 Albanian Journal of Mathematics
1 Journal of Geometric Mechanics
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Discrete Mathematics and its Applications

Referencing Publications by Year