GFAN(1)

📦 version 0.8~beta, in ubuntu stonking

💖 GFAN — the manual page, but make it make sense 💖

okay bestie, gather round, because this is the gfan page from the Mathematics section and it is lowkey a whole universe. yes, that's the same gfan everybody keeps whispering about. let's go. 🦋

✨ NAME ✨

gfan — the tool that computes Gröbner fans and tropical varieties. periodt. 👑

🌸 SYNOPSIS 🌸

gfan_tool [options]

gfan _tool [options]

💅 DESCRIPTION 💅

so Gfan is a whole software package for computing Gröbner fans and tropical varieties. these are polyhedral fans associated to polynomial ideals, if you were wondering. and the glow-up? the maximal cones of a Gröbner fan are in bijection with the marked reduced Gröbner bases of its defining ideal. not me getting emotional over a bijection. 😭

the software computes all marked reduced Gröbner bases of an ideal. their union is a universal Gröbner basis. iconic behavior honestly.

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, plus specialized algorithms for:

  • tropical curves
  • tropical hypersurfaces
  • tropical varieties of prime ideals

and on top of all those core functions, the package contains many tools that are useful in the study of Gröbner bases, initial ideals and tropical geometry. she does it all, no cap. 💖

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. iykyk. 🫶

🎀 OPTIONS 🎀

  • --help — this one displays a help message describing the functionality of gfan_tool and the available specific options. ask and she shall answer. ✨
  • --log1, --log2... — these tell Gfan how much information to write to standard error while a computation is running. super useful when you just want to know if Gfan is actually making any progress in its computation, bestie is she cooking or is she stuck in the group chat. 👀
  • --stdin value — specify a file to use as input instead of reading from the standard input. so you don't have to pipe it in like a peasant. 💅
  • --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.
🚨 real talk bestie: the XML files are not readable by Gfan. like, she writes them but she will not read them back. it's giving letters to an ex. 😭 so do not try it.

🌈 SEE ALSO 🌈

the complete manual of Gfan lives on the website of the project:

http://home.imf.au.dk/jensen/software/gfan/gfan.html

go read it. it's the main character's origin story. 👑

and that's the whole page bestie!! this was from gfan 0.8~beta, dated July 2026, page GFAN(1). slay, go compute some fans 💖✨🎀🦋🌸

📦 where this page comes from