# gfan: Groebner fans and tropical varieties¶

## Description¶

Gfan is a software package for computing Groebner fans and tropical varieties.

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

• GPL version 2 or version 3 (according to the gfan website)

## Upstream Contact¶

Anders Nedergaard Jensen

https://users-math.au.dk/jensen/software/gfan/gfan.html

• GMP/MPIR

• CDDLIB

## Special Update/Build Instructions¶

Remove the doc, homepage, and examples subdirectories, which take up most of the space.

standard

## Version Information¶

package-version.txt:

0.6.2.p1


## Equivalent System Packages¶

arch:

$sudo pacman -S gfan  conda: $ conda install gfan


Debian/Ubuntu:

$sudo apt-get install gfan  Fedora/Redhat/CentOS: $ sudo yum install  gfan


freebsd:

$sudo pkg install gfan  gentoo: $ sudo emerge gfan


nix:

$nix-env --install gfan  opensuse: $ sudo zypper install gfan


If the system package is installed, ./configure will check whether it can be used.