gfan: Groebner fans and tropical varieties - Packages and Features

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# 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.

## License

- 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

## Special Update/Build Instructions

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

## Type

standard

## Dependencies

- $(MP_LIBRARY)

- cddlib: Double description method for polyhedral representation conversion

## Version Information

package-version.txt:

    0.6.2.p1

## Equivalent System Packages

Arch Linux

    $ sudo pacman -S gfan

conda-forge

    $ conda install gfan

Debian/Ubuntu

    $ sudo apt-get install gfan

Fedora/Redhat/CentOS

    $ sudo dnf install gfan

FreeBSD

    $ sudo pkg install math/gfan

Gentoo Linux

    $ sudo emerge sci-mathematics/gfan

Nixpkgs

    $ nix-env --install gfan

openSUSE

    $ sudo zypper install gfan

Void Linux

    $ sudo xbps-install gfan

See https://repology.org/project/gfan/versions

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