*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.

- Types
- Functions and commands
- gfan -- all reduced Groebner bases of a polynomial ideal
- gfanBuchberger -- reduced Groebner basis with respect to some monomial order
- gfanDoesIdealContain -- check ideal membership by the division algorithm
- gfanFanCommonRefinement -- find the common refinement of two polyheadral fans
- gfanFanLink -- the link of a vertex in a polyhedral fan
- gfanFanProduct -- computes the product of polyhedral fans
- gfanGroebnerCone -- polyhedral information about a Groebner cone
- gfanHomogeneitySpace -- homogeneity space of a list of polynomials
- gfanHomogenize -- homogenize a list of polynomials with respect to a weight vector
- gfanInitialForms -- initial forms of polynomials with respect to a weight vector
- gfanInteractive -- not implemented
- gfanIsMarkedGroebnerBasis -- checks if a list of polynomials are a Groebner basis
- gfanKrullDimension -- krull dimension
- gfanLatticeIdeal -- computes the lattice ideal of a lattice
- gfanLeadingTerms -- leading terms of a list (or list of lists) of marked polynomials
- gfanMarkPolynomialSet -- mark the initial terms of a list of polynomials with respect to a weight vector
- gfanMinkowskiSum -- the Minkowski sum of Newton polytopes
- gfanMinors -- minors of a matrix of indeterminates
- gfanMixedVolume -- mixed volume of a list of polynomials
`gfanOverIntegers`(missing documentation)`gfanParsePolyhedralFan`(missing documentation)- gfanPolynomialSetUnion -- union of two lists of polynomials
- gfanRender -- render an image of a Grobener fan
- gfanRenderStaircase -- render the staircase of a monomial initial ideal
- gfanResultantFan -- Tropical variety of the sparse (toric) resultant variety.
- gfanSaturation -- saturation of an ideal
- gfanSecondaryFan -- computes the secondary fan of a vector configuration
`gfanStableIntersection`(missing documentation)- gfanStats -- display certain properties of a list of polynomials
- gfanSubstitute -- rename the variables of a list of polynomials
- gfanToLatex -- convert a list of polynomials to LaTeX
- gfanToPolyhedralFan -- polyhedral data about the fan of a list of Groebner bases
- gfanTropicalBasis -- tropical basis of an ideal
- gfanTropicalBruteForce -- computes the tropical variety of an ideal
- gfanTropicalEvaluation -- evaluates a tropical polynomial function
- gfanTropicalFunction -- tropicalizes a polynomial
- gfanTropicalHyperSurface -- the tropical hypersurface of a principal ideal
`gfanTropicalHyperSurfaceReconstruction`(missing documentation)- gfanTropicalIntersection -- polyhedral data describing intersection of tropical hypersurfaces
- gfanTropicalLifting -- not implemented
- gfanTropicalLinearSpace -- equations of a tropical linear space from Pluecker coordinates
- gfanTropicalMultiplicity -- multiplicity of a tropical cone
- gfanTropicalRank -- the tropical rank of a matrix
- gfanTropicalStartingCone -- a pair of Groebner bases for use with gfanTropicalTraverse
- gfanTropicalTraverse -- polyhedral data describing a tropical variety
- gfanTropicalWeilDivisor -- the tropical Weil divisor of a piecewise linear function
`gfanVersion`(missing documentation)- markedPolynomialList -- constructs a MarkedPolynomialList
- MPLConverter -- Converts lists or ideals into markedPolynomialLists
`multiplicitiesReorder`(missing documentation)`toPolymakeFormat`(missing documentation)

- 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)