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.

References in zbMATH (referenced in 105 articles , 1 standard article )

Showing results 61 to 80 of 105.
Sorted by year (citations)
  1. Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha: A Hilbert scheme in computer vision (2013)
  2. Aroca, Fuensanta; Gómez-Morales, Mirna; Shabbir, Khurram: Torical modification of Newton non-degenerate ideals (2013)
  3. Chan, Melody; Sturmfels, Bernd: Elliptic curves in honeycomb form (2013)
  4. Cueto, María Angélica; Lin, Shaowei: Tropical secant graphs of monomial curves (2013)
  5. Hibi, Takayuki (ed.): Gröbner bases. Statistics and software systems. Transl. from the Japanese (2013)
  6. Jensen, Anders; Yu, Josephine: Computing tropical resultants (2013)
  7. Maruri-Aguilar, Hugo; Sáenz-de-Cabezón, Eduardo; Wynn, Henry P.: Alexander duality in experimental designs (2013)
  8. Nakayama, Hiromasa; Nishiyama, Kenta: Examples and exercises (2013)
  9. Ren, Qingchun; Sam, Steven V.; Schrader, Gus; Sturmfels, Bernd: The universal Kummer threefold (2013)
  10. Rincón, Felipe: Computing tropical linear spaces (2013)
  11. Bogart, Tristram; Hemmecke, Ray; Petrović, Sonja: Universal Gröbner bases of colored partition identities (2012)
  12. Cartwright, Dustin; Payne, Sam: Connectivity of tropicalizations (2012)
  13. Rincón, Felipe: Isotropical linear spaces and valuated Delta-matroids (2012)
  14. Tillmann, Stephan: Degenerations of ideal hyperbolic triangulations (2012)
  15. Vinzant, Cynthia: Real radical initial ideals (2012)
  16. Adrovic, Danko; Verschelde, Jan: Tropical algebraic geometry in Maple: a preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients (2011)
  17. Brodsky, Sarah B.; Sturmfels, Bernd: Tropical quadrics through three points (2011)
  18. Chan, Melody; Jensen, Anders; Rubei, Elena: The (4\times4) minors of a (5\timesn) matrix are a tropical basis (2011)
  19. Cueto, María Angélica; Matsen, Frederick A.: Polyhedral geometry of phylogenetic rogue taxa (2011)
  20. Hampton, Marshall; Jensen, Anders: Finiteness of spatial central configurations in the five-body problem (2011)