gfanInterface : Table of Contents

• gfanInterface -- a Macaulay2 interface to gfan
• Conventions for calling methods with options
• 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 polyhedral fans
• gfanFanLink -- the link of a vertex in a polyhedral fan
• gfanFanProduct -- computes the product of polyhedral fans
• gfanFunctions (missing documentation)
• 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 -- all reduced Groebner bases of a polynomial ideal with coefficients in ZZ
• gfanParsePolyhedralFan (missing documentation)
• gfanPolynomialSetUnion -- union of two lists of polynomials
• gfanRender -- render an image of a Groebner 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 -- computes the stable intersection of two balanced fans
• 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 Plücker 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)
• Installation and Configuration of gfanInterface
• MarkedPolynomialList
• markedPolynomialList -- constructs a MarkedPolynomialList
• MPLConverter -- Converts lists or ideals into markedPolynomialLists
• multiplicitiesReorder (missing documentation)
• polymakeConeToCone (missing documentation)
• polymakeFanToFan (missing documentation)
• toPolymakeFormat (missing documentation)