| GFAN(1) | Mathematics | GFAN(1) |
gfan - tool to compute Gröbner fans and tropical varieties
gfan_tool [options]
gfan _tool [options]
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 complete list of tools is:
bases, buchberger, combinerays, doesidealcontain, fancommonrefinement, fanhomology, fanlink, fanproduct, fansubfan, genericlinearchange, groebnercone, groebnerfan, homogeneityspace, homogenize, initialforms, interactive, ismarkedgroebnerbasis, krulldimension, latticeideal, leadingterms, list, markpolynomialset, minkowskisum, minors, mixedvolume, overintegers, padic, polynomialsetunion, render, renderstaircase, saturation, secondaryfan, stats, substitute, symmetries, tolatex, topolyhedralfan, tropicalbasis, tropicalbruteforce, tropicalevaluation, tropicalfunction, tropicalhypersurface, tropicalintersection, tropicallifting, tropicallinearspace, tropicalmultiplicity, tropicalrank, tropicalstartingcone, tropicaltraverse, tropicalweildivisor, version.
Below are presented the generic options available with all tools. For specific options of a given tool, we refer to the help message of that tool.
The complete manual of Gfan is available from the website of the project: http://home.imf.au.dk/jensen/software/gfan/gfan.html
| December 2020 | gfan 0.6.2 |