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, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  2. Chen, Tianran: Unmixing the mixed volume computation (2019)
  3. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  4. Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
  5. Ren, Yue; Martini, Johannes W. R.; Torres, Jacinta: Decoupled molecules with binding polynomials of bidegree ((n,2)) (2019)
  6. Abbott, John; Bigatti, Anna Maria: Gröbner bases for everyone with CoCoA-5 and CoCoALib (2018)
  7. Bliss, Nathan; Verschelde, Jan: The method of Gauss-Newton to compute power series solutions of polynomial homotopies (2018)
  8. Chen, Tianran: libtropicon: a scalable library for computing intersection points of generic tropical hyper-surfaces (2018)
  9. Gross, Elizabeth; Obatake, Nida; Youngs, Nora: Neural ideals and stimulus space visualization (2018)
  10. Guilloux, Antonin: Volume of representations and birationality of peripheral holonomy (2018)
  11. Hashemi, Amir; Dehghani Darmian, Mahdi; Barkhordar, Marzieh: Universal Gröbner basis for parametric polynomial ideals (2018)
  12. Hofmann, Tommy; Ren, Yue: Computing tropical points and tropical links (2018)
  13. Jordan, Charles; Joswig, Michael; Kastner, Lars: Parallel enumeration of triangulations (2018)
  14. Joswig, Michael; Schröter, Benjamin: The degree of a tropical basis (2018)
  15. Keicher, Simon: A software package to compute automorphisms of graded algebras (2018)
  16. Kileel, Joe; Kukelova, Zuzana; Pajdla, Tomas; Sturmfels, Bernd: Distortion varieties (2018)
  17. Vaccon, Tristan: Matrix-F5 algorithms and tropical Gröbner bases computation (2018)
  18. Anders Jensen, Jeff Sommars, Jan Verschelde: Computing Tropical Prevarieties in Parallel (2017) arXiv
  19. Bigatti, Anna M.; De Negri, Emanuela: Koszul algebras and computations (2017)
  20. Bigatti, Anna M. (ed.); Gimenez, Philippe (ed.); Sáenz-de-Cabezón, Eduardo (ed.): Computations and combinatorics in commutative algebra. EACA school, Valladolid, Spain, 2013 (2017)

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