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gfanInterface :: gfanInterface

gfanInterface -- a Macaulay2 interface to gfan

Description

gfanInterface is an interface to Anders Jensen’s Gfan software (available at http://home.imf.au.dk/jensen/software/gfan/gfan.html), 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 gfanGroebnerCone.

Most of the functions in gfanInterface require MarkedPolynomialList marked polynomial lists as input. In a marked polynomial list, the leading term of each polynomial is distinguished. New users should read the the guide Conventions for calling methods with options. Since gfan is distributed with Macaulay2, one rarely needs to consult the guide for Installation and Configuration of gfanInterface.

Most of functions in the gfan package are accessible through this interface. If you wish to use one whose interface is not included here send a message to the package author. Also, please feel free to suggest changes to the parameter types and return types of each method.

Authors

Version

This documentation describes version 0.4 of gfanInterface.

Source code

The source code from which this documentation is derived is in the file gfanInterface.m2.

Exports

  • Functions and commands
  • Methods
    • expression(MarkedPolynomialList) (missing documentation)
    • gfan(MarkedPolynomialList), see gfan -- all reduced Groebner bases of a polynomial ideal
    • gfanBuchberger(MarkedPolynomialList), see gfanBuchberger -- reduced Groebner basis with respect to some monomial order
    • gfanDoesIdealContain(MarkedPolynomialList,List), see gfanDoesIdealContain -- check ideal membership by the division algorithm
    • gfanGroebnerCone(Ideal,MarkedPolynomialList), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanGroebnerCone(List,MarkedPolynomialList), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanGroebnerCone(MarkedPolynomialList), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanGroebnerCone(MarkedPolynomialList,Ideal), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanGroebnerCone(MarkedPolynomialList,List), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanGroebnerCone(MarkedPolynomialList,MarkedPolynomialList), see gfanGroebnerCone -- polyhedral information about a Groebner cone
    • gfanHomogeneitySpace(MarkedPolynomialList), see gfanHomogeneitySpace -- homogeneity space of a list of polynomials
    • gfanHomogenize(MarkedPolynomialList,Symbol), see gfanHomogenize -- homogenize a list of polynomials with respect to a weight vector
    • gfanInitialForms(MarkedPolynomialList,List), see gfanInitialForms -- initial forms of polynomials with respect to a weight vector
    • gfanIsMarkedGroebnerBasis(MarkedPolynomialList), see gfanIsMarkedGroebnerBasis -- checks if a list of polynomials are a Groebner basis
    • gfanKrullDimension(MarkedPolynomialList), see gfanKrullDimension -- krull dimension
    • gfanLeadingTerms(MarkedPolynomialList), see gfanLeadingTerms -- leading terms of a list (or list of lists) of marked polynomials
    • gfanPolynomialSetUnion(List,MarkedPolynomialList), see gfanPolynomialSetUnion -- union of two lists of polynomials
    • gfanPolynomialSetUnion(MarkedPolynomialList,List), see gfanPolynomialSetUnion -- union of two lists of polynomials
    • gfanPolynomialSetUnion(MarkedPolynomialList,MarkedPolynomialList), see gfanPolynomialSetUnion -- union of two lists of polynomials
    • gfanSubstitute(MarkedPolynomialList,PolynomialRing), see gfanSubstitute -- rename the variables of a list of polynomials
    • gfanToLatex(MarkedPolynomialList), see gfanToLatex -- convert a list of polynomials to LaTeX
    • net(MarkedPolynomialList) (missing documentation)
    • RingMap MarkedPolynomialList (missing documentation)
  • Symbols
    • polymakeConeToCone (missing documentation)
    • polymakeFanToFan (missing documentation)
  • Other things
    • gfanFunctions (missing documentation)