gfanInterface : Index
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Conventions for calling methods with options
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gfan -- all reduced Groebner bases of a polynomial ideal
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gfan(Ideal) -- all reduced Groebner bases of a polynomial ideal
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gfan(List) -- all reduced Groebner bases of a polynomial ideal
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gfan(MarkedPolynomialList) -- all reduced Groebner bases of a polynomial ideal
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gfanBuchberger -- reduced Groebner basis with respect to some monomial order
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gfanBuchberger(Ideal) -- reduced Groebner basis with respect to some monomial order
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gfanBuchberger(List) -- reduced Groebner basis with respect to some monomial order
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gfanBuchberger(MarkedPolynomialList) -- reduced Groebner basis with respect to some monomial order
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gfanDoesIdealContain -- check ideal membership by the division algorithm
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gfanDoesIdealContain(Ideal,List) -- check ideal membership by the division algorithm
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gfanDoesIdealContain(List,List) -- check ideal membership by the division algorithm
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gfanDoesIdealContain(MarkedPolynomialList,List) -- check ideal membership by the division algorithm
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gfanFanCommonRefinement -- find the common refinement of two polyhedral fans
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gfanFanCommonRefinement(Fan,Fan) -- find the common refinement of two polyhedral fans
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gfanFanLink -- the link of a vertex in a polyhedral fan
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gfanFanLink(Fan,List) -- the link of a vertex in a polyhedral fan
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gfanFanProduct -- computes the product of polyhedral fans
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gfanFanProduct(Fan,Fan) -- computes the product of polyhedral fans
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gfanFunctions (missing documentation)
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gfanGroebnerCone -- polyhedral information about a Groebner cone
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gfanGroebnerCone(Ideal) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(Ideal,Ideal) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(Ideal,List) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(Ideal,MarkedPolynomialList) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(List) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(List,Ideal) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(List,List) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(List,MarkedPolynomialList) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(MarkedPolynomialList) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(MarkedPolynomialList,Ideal) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(MarkedPolynomialList,List) -- polyhedral information about a Groebner cone
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gfanGroebnerCone(MarkedPolynomialList,MarkedPolynomialList) -- polyhedral information about a Groebner cone
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gfanHomogeneitySpace -- homogeneity space of a list of polynomials
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gfanHomogeneitySpace(Ideal) -- homogeneity space of a list of polynomials
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gfanHomogeneitySpace(List) -- homogeneity space of a list of polynomials
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gfanHomogeneitySpace(MarkedPolynomialList) -- homogeneity space of a list of polynomials
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gfanHomogenize -- homogenize a list of polynomials with respect to a weight vector
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gfanHomogenize(Ideal,Symbol) -- homogenize a list of polynomials with respect to a weight vector
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gfanHomogenize(List,Symbol) -- homogenize a list of polynomials with respect to a weight vector
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gfanHomogenize(MarkedPolynomialList,Symbol) -- homogenize a list of polynomials with respect to a weight vector
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gfanInitialForms -- initial forms of polynomials with respect to a weight vector
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gfanInitialForms(Ideal,List) -- initial forms of polynomials with respect to a weight vector
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gfanInitialForms(List,List) -- initial forms of polynomials with respect to a weight vector
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gfanInitialForms(MarkedPolynomialList,List) -- initial forms of polynomials with respect to a weight vector
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gfanInteractive -- not implemented
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gfanInterface -- a Macaulay2 interface to gfan
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gfanIsMarkedGroebnerBasis -- checks if a list of polynomials are a Groebner basis
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gfanIsMarkedGroebnerBasis(Ideal) -- checks if a list of polynomials are a Groebner basis
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gfanIsMarkedGroebnerBasis(List) -- checks if a list of polynomials are a Groebner basis
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gfanIsMarkedGroebnerBasis(MarkedPolynomialList) -- checks if a list of polynomials are a Groebner basis
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gfanKrullDimension -- krull dimension
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gfanKrullDimension(Ideal) -- krull dimension
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gfanKrullDimension(List) -- krull dimension
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gfanKrullDimension(MarkedPolynomialList) -- krull dimension
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gfanLatticeIdeal -- computes the lattice ideal of a lattice
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gfanLatticeIdeal(List) -- computes the lattice ideal of a lattice
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gfanLeadingTerms -- leading terms of a list (or list of lists) of marked polynomials
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gfanLeadingTerms(List) -- leading terms of a list (or list of lists) of marked polynomials
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gfanLeadingTerms(MarkedPolynomialList) -- leading terms of a list (or list of lists) of marked polynomials
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gfanMarkPolynomialSet -- mark the initial terms of a list of polynomials with respect to a weight vector
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gfanMarkPolynomialSet(List,List) -- mark the initial terms of a list of polynomials with respect to a weight vector
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gfanMinkowskiSum -- the Minkowski sum of Newton polytopes
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gfanMinkowskiSum(Ideal) -- the Minkowski sum of Newton polytopes
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gfanMinkowskiSum(List) -- the Minkowski sum of Newton polytopes
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gfanMinors -- minors of a matrix of indeterminates
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gfanMinors(ZZ,ZZ,ZZ) -- minors of a matrix of indeterminates
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gfanMixedVolume -- mixed volume of a list of polynomials
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gfanMixedVolume(List) -- mixed volume of a list of polynomials
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gfanOverIntegers -- all reduced Groebner bases of a polynomial ideal with coefficients in ZZ
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gfanOverIntegers(Ideal) -- all reduced Groebner bases of a polynomial ideal with coefficients in ZZ
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gfanOverIntegers(Ideal,List) -- all reduced Groebner bases of a polynomial ideal with coefficients in ZZ
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gfanParsePolyhedralFan (missing documentation)
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gfanPolynomialSetUnion -- union of two lists of polynomials
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gfanPolynomialSetUnion(List,List) -- union of two lists of polynomials
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gfanPolynomialSetUnion(List,MarkedPolynomialList) -- union of two lists of polynomials
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gfanPolynomialSetUnion(MarkedPolynomialList,List) -- union of two lists of polynomials
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gfanPolynomialSetUnion(MarkedPolynomialList,MarkedPolynomialList) -- union of two lists of polynomials
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gfanRender -- render an image of a Groebner fan
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gfanRender(List) -- render an image of a Groebner fan
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gfanRender(String,List) -- render an image of a Groebner fan
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gfanRenderStaircase -- render the staircase of a monomial initial ideal
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gfanRenderStaircase(List) -- render the staircase of a monomial initial ideal
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gfanRenderStaircase(String,List) -- render the staircase of a monomial initial ideal
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gfanResultantFan -- Tropical variety of the sparse (toric) resultant variety.
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gfanResultantFan(List) -- Tropical variety of the sparse (toric) resultant variety.
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gfanSaturation -- saturation of an ideal
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gfanSaturation(Ideal) -- saturation of an ideal
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gfanSecondaryFan -- computes the secondary fan of a vector configuration
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gfanSecondaryFan(List) -- computes the secondary fan of a vector configuration
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gfanStableIntersection -- computes the stable intersection of two balanced fans
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gfanStats -- display certain properties of a list of polynomials
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gfanStats(List) -- display certain properties of a list of polynomials
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gfanSubstitute -- rename the variables of a list of polynomials
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gfanSubstitute(Ideal,PolynomialRing) -- rename the variables of a list of polynomials
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gfanSubstitute(List,PolynomialRing) -- rename the variables of a list of polynomials
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gfanSubstitute(MarkedPolynomialList,PolynomialRing) -- rename the variables of a list of polynomials
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gfanToLatex -- convert a list of polynomials to LaTeX
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gfanToLatex(List) -- convert a list of polynomials to LaTeX
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gfanToLatex(MarkedPolynomialList) -- convert a list of polynomials to LaTeX
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gfanToPolyhedralFan -- polyhedral data about the fan of a list of Groebner bases
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gfanToPolyhedralFan(List) -- polyhedral data about the fan of a list of Groebner bases
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gfanTropicalBasis -- tropical basis of an ideal
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gfanTropicalBasis(Ideal) -- tropical basis of an ideal
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gfanTropicalBruteForce -- computes the tropical variety of an ideal
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gfanTropicalBruteForce(List) -- computes the tropical variety of an ideal
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gfanTropicalEvaluation -- evaluates a tropical polynomial function
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gfanTropicalEvaluation(RingElement,List) -- evaluates a tropical polynomial function
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gfanTropicalFunction -- tropicalizes a polynomial
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gfanTropicalFunction(RingElement) -- tropicalizes a polynomial
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gfanTropicalHyperSurface -- the tropical hypersurface of a principal ideal
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gfanTropicalHyperSurface(RingElement) -- the tropical hypersurface of a principal ideal
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gfanTropicalHyperSurfaceReconstruction (missing documentation)
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gfanTropicalIntersection -- polyhedral data describing intersection of tropical hypersurfaces
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gfanTropicalIntersection(List) -- polyhedral data describing intersection of tropical hypersurfaces
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gfanTropicalLifting -- not implemented
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gfanTropicalLinearSpace -- equations of a tropical linear space from Plücker coordinates
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gfanTropicalLinearSpace(List,ZZ,ZZ) -- equations of a tropical linear space from Plücker coordinates
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gfanTropicalMultiplicity -- multiplicity of a tropical cone
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gfanTropicalMultiplicity(List) -- multiplicity of a tropical cone
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gfanTropicalRank -- the tropical rank of a matrix
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gfanTropicalRank(Matrix) -- the tropical rank of a matrix
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gfanTropicalStartingCone -- a pair of Groebner bases for use with gfanTropicalTraverse
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gfanTropicalStartingCone(...,stable=>...) -- a pair of Groebner bases for use with gfanTropicalTraverse
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gfanTropicalStartingCone(Ideal) -- a pair of Groebner bases for use with gfanTropicalTraverse
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gfanTropicalStartingCone(List) -- a pair of Groebner bases for use with gfanTropicalTraverse
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gfanTropicalTraverse -- polyhedral data describing a tropical variety
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gfanTropicalTraverse(...,stable=>...) -- polyhedral data describing a tropical variety
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gfanTropicalTraverse(List) -- polyhedral data describing a tropical variety
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gfanTropicalWeilDivisor -- the tropical Weil divisor of a piecewise linear function
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gfanTropicalWeilDivisor(Fan,Fan) -- the tropical Weil divisor of a piecewise linear function
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gfanVersion (missing documentation)
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Installation and Configuration of gfanInterface
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MarkedPolynomialList
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markedPolynomialList -- constructs a MarkedPolynomialList
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MPLConverter -- Converts lists or ideals into markedPolynomialLists
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MPLConverter(Ideal) -- Converts lists or ideals into markedPolynomialLists
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MPLConverter(List) -- Converts lists or ideals into markedPolynomialLists
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multiplicitiesReorder (missing documentation)
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polymakeConeToCone (missing documentation)
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polymakeFanToFan (missing documentation)
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toPolymakeFormat (missing documentation)