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gfanInterface :: gfanInterface

gfanInterface -- a Macaulay2 interface to gfan

Description

gfanInterface is an interface to Anders Jenssen's gfan package, which is a C++ program to compute the Groebner fan (i.e. all the initial ideals) of an ideal.

The main function in this package is gfan, which computes all of the Groebner bases and initial ideals of a given ideal. A useful feature of this function is that it can handle symmetries in the ideal. If you want the geometric information of this list of Groebner basis, see groebnerFan.

There are other functions in the gfan package. If you wish to use one whose interface is not included here, you have two options: either write the interface yourself, and then send it to the package author, so it can be included for others, or ask the package author to write it.

Authors

Version

This documentation describes version 0.2.1 of gfanInterface.

Source code

The source code from which this documentation is derived is in the file gfanInterface.m2. The auxiliary files accompanying it are in the directory gfanInterface/.

Exports

  • Functions and commands
    • gfan -- all initial ideals of an ideal
    • groebnerCone -- the cone whose interior weight vectors give the given initial ideal
    • groebnerFan -- the fan of all groebner bases of an ideal
    • initialIdeal -- initial ideal with respect to a weight vector
    • render -- draws the Groebner fan an ideal.
    • renderStaircase -- draws staircases of an initial ideal.
    • universalGroebnerBasis -- the union of all reduced Groebner bases of an ideal.
    • weightVector -- weight vector of a marked set of polynomials
  • Symbols
    • Symmetries -- permutations leaving an ideal invariant to speed up gfan computations.