GFAN
Section: Mathematics (1)
Updated: September 2022
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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 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.
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
Index
- NAME
-
- SYNOPSIS
-
- DESCRIPTION
-
- OPTIONS
-
- SEE ALSO
-
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Time: 15:20:51 GMT, May 23, 2024