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 62 articles , 1 standard article )

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  1. Ardila, Federico; Boocher, Adam: The closure of a linear space in a product of lines (2016)
  2. Jensen, Anders; Yu, Josephine: Stable intersections of tropical varieties (2016)
  3. Joswig, Michael; Kileel, Joe; Sturmfels, Bernd; Wagner, André: Rigid multiview varieties (2016)
  4. Katz, Eric; Stapledon, Alan: Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces (2016)
  5. Schönemann, Hans: Extending singular with new types and algorithms (2016)
  6. Yu, Josephine: Do most polynomials generate a prime ideal? (2016)
  7. Boocher, Adam; Robeva, Elina: Robust toric ideals (2015)
  8. Brodsky, Sarah; Joswig, Michael; Morrison, Ralph; Sturmfels, Bernd: Moduli of tropical plane curves (2015)
  9. Brouwer, Andries E.; Draisma, Jan; Frenk, Bart J.: Lossy gossip and composition of metrics (2015)
  10. Dück, Natalia; Márquez-Corbella, Irene; Martínez-Moro, Edgar: On the fan associated to a linear code (2015)
  11. Hartshorne, Robin; Lella, Paolo; Schlesinger, Enrico: Smooth curves specialize to extremal curves (2015)
  12. Rossmann, Tobias: Computing topological zeta functions of groups, algebras, and modules. II. (2015)
  13. Cueto, Maria Angelica; Häbich, Mathias; Werner, Annette: Faithful tropicalization of the Grassmannian of planes (2014)
  14. Deopurkar, Anand; Fedorchuk, Maksym; Swinarski, David: Gröbner techniques and ribbons (2014)
  15. Herrmann, Sven; Joswig, Michael; Speyer, David E: Dressians, tropical Grassmannians, and their rays (2014)
  16. Ren, Qingchun; Sam, Steven V.; Sturmfels, Bernd: Tropicalization of classical moduli spaces (2014)
  17. Adrovic, Danko; Verschelde, Jan: Polyhedral methods for space curves exploiting symmetry applied to the cyclic $n$-roots problem (2013)
  18. Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha: A Hilbert scheme in computer vision (2013)
  19. Aroca, Fuensanta; Gómez-Morales, Mirna; Shabbir, Khurram: Torical modification of Newton non-degenerate ideals (2013)
  20. Chan, Melody; Sturmfels, Bernd: Elliptic curves in honeycomb form (2013)

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