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 )

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  1. Chan, Melody: Lectures on tropical curves and their moduli spaces (2017)
  2. Hampe, Simon; Joswig, Michael: Tropical computations in \textttpolymake (2017)
  3. Hausen, Jürgen; Keicher, Simon; Wolf, Rüdiger: Computing automorphisms of Mori dream spaces (2017)
  4. Kastner, Lars: Toric Ext and Tor in \textttpolymakeand \textbfSingular: the two-dimensional case and beyond (2017)
  5. Markwig, Thomas; Ren, Yue: Gröbner fans of (x)-homogeneous ideals in (R [![ t ]!][x]) (2017)
  6. Stapledon, Alan: Formulas for monodromy (2017)
  7. Sturmfels, Bernd: Fitness, apprenticeship, and polynomials (2017)
  8. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  9. Tran, Ngoc Mai: Enumerating polytropes (2017)
  10. Ardila, Federico; Boocher, Adam: The closure of a linear space in a product of lines (2016)
  11. Bliss, Nathan; Verschelde, Jan: Computing all space curve solutions of polynomial systems by polyhedral methods (2016)
  12. Jensen, Anders; Leykin, Anton; Yu, Josephine: Computing tropical curves via homotopy continuation (2016)
  13. Jensen, Anders Nedergaard: An implementation of exact mixed volume computation (2016)
  14. Jensen, Anders; Yu, Josephine: Stable intersections of tropical varieties (2016)
  15. Joswig, Michael: Book review of: D. Maclagan and B. Sturmfels, Introduction to tropical geometry (2016)
  16. Joswig, Michael; Kileel, Joe; Sturmfels, Bernd; Wagner, André: Rigid multiview varieties (2016)
  17. Katz, Eric; Stapledon, Alan: Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces (2016)
  18. Morrison, Ralph; Tran, Ngoc M.: The tropical commuting variety (2016)
  19. Ren, Qingchun; Shaw, Kristin; Sturmfels, Bernd: Tropicalization of del Pezzo surfaces (2016)
  20. Schönemann, Hans: Extending Singular with new types and algorithms (2016)