The Gfan Homepage

Software package written by Anders Nedergaard Jensen


Abstract

Gfan is a software package whose main function is to enumerate all reduced Gröbner bases of a polynomial ideal. The reduced Gröbner bases yield the maximal cones in the Gröbner fan of the ideal. Several subcomputations can be done and additional tools are included. Among these the highlights are:
  • gfan_interactive which allows interactive walks on the edge graph of the state polytope of an ideal, and
  • commands for graphical renderings of Gröbner fans and monomial ideals.



If you do not know what Gfan is you can read a presentation of it in pdf-format or in postscript-format. If you would like to know more you can also view the manual as a pdf-file or a postscript-file. CaTS is another program for computing Gröbner fans working for toric and lattice ideals only.

Download

Citations

@Misc{gfan,
     author = {Jensen, Anders N.},
     title = {Gfan, a software system for {G}r{\"o}bner fans},
     howpublished = {Available at \href{http://home.imf.au.dk/ajensen/software/gfan/gfan.html}}
}

References

  • David Avis and Komei Fukuda. A basis enumeration algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete Computational Geometry, 8:295--313, 1992.
  • Stéphane Collart, Michael Kalkbrener, and Daniel Mall. Converting bases with the Gröbner walk. J. Symb. Comput., 24(3/4):465--469, 1997.
  • Komei Fukuda. cddlib reference manual, cddlib Version 093b. Swiss Federal Institute of Technology, Lausanne and Zürich, Switzerland, 2003. http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html .
  • Komei Fukuda, Anders Jensen, and Rekha Thomas. Computing Gröbner fans. In preparation.
  • Torbjörn Granlund et al. GNU multiple precision arithmetic library 4.1.2, December 2002. http://swox.com/gmp/.
  • Birkett Huber and Rekha R. Thomas. Computing Gröbner fans of toric ideals. Experimental Mathematics, 9(3/4):321--331, 2000.
  • Anders Jensen. CaTS, a software system for toric state polytopes. Available at http://www.soopadoopa.dk/anders/cats/cats.html.
  • Anders Jensen. A non-regular Gröbner fan. 2005. math.CO/0501352.
  • Teo Mora and Lorenzo Robbiano. The Gröbner fan of an ideal. J. Symb. Comput., 6(2/3):183--208, 1988.
  • Jörg Rambau. Topcom: Triangulations of point configurations and oriented matroids. ZIB report, 02-17, 2002.
  • Bernd Sturmfels. Gröbner bases and Convex Polytopes, volume 8 of University Lecture Series. American Mathematical Society, 1996.