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.