Gfan swMATH ID: 4698 Software Authors: Jensen, Anders Nedergaard 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; TOPCOM; Maple; CoCoA; gmp; Normaliz; 4ti2; SoPlex; DEMiCs; MixedVol; GAP; DynamicPrevariety; TropLi; Magma; gfanlib Cited in: 140 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A presentation of the Gfan software. Zbl 1230.13026Jensen, Anders N. 2006 all top 5 Cited by 168 Authors 16 Sturmfels, Bernd 15 Jensen, Anders Nedergaard 8 Joswig, Michael 7 Ren, Yue 7 Thomas, Rekha R. 7 Verschelde, Jan 6 Cueto, María Angélica 6 Yu, Josephine 5 Hampton, Marshall 4 Bigatti, Anna Maria 4 Maclagan, Diane 4 Markwig, Thomas 4 Schönemann, Hans 4 Vaccon, Tristan 3 Bogart, Tristram 3 Chan, Melody 3 Görlach, Paul 3 Herrmann, Sven 3 Kastner, Lars 3 Leykin, Anton 3 Morrison, Ralph 3 Ren, Qingchun 3 Takayama, Nobuki 2 Abbott, John A. 2 Adrovic, Danko 2 Bliss, Nathan 2 Boocher, Adam 2 Brodsky, Sarah B. 2 Chen, Tianran 2 Corey, Daniel 2 Deng, Yiyang 2 Fukuda, Komei 2 Keicher, Simon 2 Kileel, Joe 2 Markwig, Hannah 2 Maruri-Aguilar, Hugo 2 Panizzut, Marta 2 Rincón, Felipe 2 Sáenz de Cabezón Irigaray, Eduardo 2 Sam, Steven V. 2 Schröter, Benjamin 2 Shaw, Kris 2 Sommars, Jeff 2 Speyer, David E. 2 Stapledon, Alan 2 Swinarski, David 2 Tillmann, Stephan 2 Tosun, Meral 2 Tran, Ngoc Mai 2 Verron, Thibaut 2 Wynn, Henry P. 2 Yokoyama, Kazuhiro 2 Zhang, Leon 1 Aholt, Chris 1 Altıntaş Sharland, Ayşe 1 Ardila, Federico 1 Aroca, Fuensanta 1 Bahloul, Rouchdi 1 Balla, George 1 Balletti, Gabriele 1 Barkhordar, Marzieh 1 Bendle, Dominik 1 Böhm, Janko 1 Bossinger, Lara 1 Brandt, Madeline 1 Brouwer, Andries Evert 1 Brysiewicz, Taylor 1 Cartwright, Dustin A. 1 Çevık, G. 1 Chan, Andrew J. 1 Conca, Aldo 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 Drummond, James M. 1 Dück, Natalia 1 Duff, Timothy 1 Eble, Holger 1 Epure, Raul 1 Eröcal, Burçin 1 Eur, Christopher 1 Fedorchuk, Maksym 1 Feichtner, Eva Maria 1 Frenk, Bart J. 1 Gimenez, Philippe 1 Glew, R. 1 Gómez-Morales, Mirna 1 Goodman, Jacob Eli 1 Greuel, Gert-Martin 1 Gross, Elizabeth 1 Guilloux, Antonin 1 Häbich, Mathias 1 Hampe, Simon 1 Hartshorne, Robin ...and 68 more Authors all top 5 Cited in 61 Serials 10 Journal of Symbolic Computation 7 Journal of Algebra 5 Experimental Mathematics 4 Discrete & Computational Geometry 4 Linear Algebra and its Applications 3 Mathematics of Computation 3 Advances in Applied Mathematics 3 Journal of Algebraic Combinatorics 3 ACM Communications in Computer Algebra 3 Research in the Mathematical Sciences 2 Advances in Mathematics 2 Journal of Combinatorial Theory. 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