| Abstract | Gfan is a software package for computing Gr ̈bner fans and tropical varieties. These are polyhedral fans associated to polynomial ideals. The
maximal cones of a Gr ̈bner fan are in bijection with the marked reduced
Grobner bases of its defining ideal. The software computes all marked
reduced Grobner bases of an ideal. Their union is a universal Grobner
basis. The tropical variety of a polynomial ideal is a certain subcomplex
of the Grobner 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 Gr ̈bner bases, initial ideals and tropical geometry. The full
list of commands can be found in Appendix B. For ordinary Grobner basis
computations Gfan is not competitive in speed compared to programs such
as CoCoA, Singular and Macaulay2. |
