## table of contents

GFAN(1) | Mathematics | GFAN(1) |

# NAME¶

gfan - tool to compute Gröbner fans and tropical varieties

# SYNOPSIS¶

**gfan_ tool [options]**

**gfan _ tool [options]**

# DESCRIPTION¶

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 *tool*s 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
*tool*s. For specific options of a given *tool*, we refer to the
help message of that tool.

# OPTIONS¶

**--help**- Display a help message describing the functionality of
**gfan_***tool*and the available specific options. **--log1, --log2...**- Tell Gfan how much information to write to standard error while a computation is running. These options are very useful when you wish to know if Gfan is making any progress in its computation.
**--stdin***value*- Specify a file to use as input instead of reading from the standard input.
**--stdout***value*- Specify a file to write output to instead of writing to the standard output.
**--xml**- Let polyhedral fans be output in an XML format instead of in the text format. (The XML files are not readable by Gfan.)

# SEE ALSO¶

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 |