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gfan - tool to compute Gröbner fans and tropical varieties
gfan _tool [options]
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.
--help Display a help message describing the functionality of gfan_tool and the available
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.
Specify a file to use as input instead of reading from the standard input.
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.)
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