SlackIdeals : Index
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containsFlag -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid
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containsFlag(..., Object => ...) -- specify combinatorial object
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containsFlag(List,List) -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid
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containsFlag(List,Matrix) -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid
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containsFlag(List,Matroid) -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid
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containsFlag(List,Polyhedron) -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid
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cycleIdeal -- constructs the cycle ideal of a realization
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cycleIdeal(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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cycleIdeal(..., Object => ...) -- specify combinatorial object
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cycleIdeal(..., Saturate => ...) -- specifies saturation strategy to be used
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cycleIdeal(..., Strategy => ...) -- specifies saturation strategy to be used
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cycleIdeal(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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cycleIdeal(List) -- constructs the cycle ideal of a realization
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cycleIdeal(Matrix) -- constructs the cycle ideal of a realization
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cycleIdeal(Matroid) -- constructs the cycle ideal of a realization
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cycleIdeal(Polyhedron) -- constructs the cycle ideal of a realization
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findFlag -- computes a list of facet labels that make up a flag in a polytope
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findFlag(..., FlagElement => ...) -- a facet label that will be contained in a flag of facets of given polytope or matroid
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findFlag(..., Object => ...) -- specify combinatorial object
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findFlag(List) -- computes a list of facet labels that make up a flag in a polytope
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findFlag(Matrix) -- computes a list of facet labels that make up a flag in a polytope
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findFlag(Matroid) -- computes a list of facet labels that make up a flag in a polytope
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findFlag(Polyhedron) -- computes a list of facet labels that make up a flag in a polytope
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FlagElement -- a facet label that will be contained in a flag of facets of given polytope or matroid
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FlagIndices -- a list of facet labels that form a flag of facets of given polytope or matroid
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getFacetBases -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet
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getFacetBases(..., Object => ...) -- specify combinatorial object
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getFacetBases(List) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet
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getFacetBases(Matrix) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet
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getFacetBases(Matroid) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet
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getFacetBases(Polyhedron) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet
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graphFromSlackMatrix -- creates the vertex-edge incidence matrix for the bipartite non-incidence graph with adjacency matrix the given slack matrix
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graphFromSlackMatrix(Matrix) -- creates the vertex-edge incidence matrix for the bipartite non-incidence graph with adjacency matrix the given slack matrix
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graphicIdeal -- creates the toric ideal of the non-incidence graph of a polytope
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graphicIdeal(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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graphicIdeal(..., Object => ...) -- specify combinatorial object
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graphicIdeal(..., Saturate => ...) -- specifies saturation strategy to be used
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graphicIdeal(..., Strategy => ...) -- specifies saturation strategy to be used
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graphicIdeal(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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graphicIdeal(List) -- creates the toric ideal of the non-incidence graph of a polytope
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graphicIdeal(Matrix) -- creates the toric ideal of the non-incidence graph of a polytope
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graphicIdeal(Matroid) -- creates the toric ideal of the non-incidence graph of a polytope
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graphicIdeal(Polyhedron) -- creates the toric ideal of the non-incidence graph of a polytope
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grassmannSectionIdeal -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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grassmannSectionIdeal(..., Object => ...) -- specify combinatorial object
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grassmannSectionIdeal(..., Saturate => ...) -- specifies saturation strategy to be used
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grassmannSectionIdeal(..., Strategy => ...) -- specifies saturation strategy to be used
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grassmannSectionIdeal(Cone) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(List) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(List,List) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(Matrix) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(Matrix,List) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(Matroid) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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grassmannSectionIdeal(Polyhedron) -- given a slack matrix of a polytope, a cone or a matroid, or a set of polytope vertices, cone generators, or matroid vectors, and a set of set of hyperplane spanning set indices, it computes the Grassmannian section ideal corresponding to choice B of the object with slack matrix S
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Object -- select the combinatorial object which the input should be interpreted as
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reconstructSlackMatrix -- a list of facet labels that make up a flag in a polytope
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reconstructSlackMatrix(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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reconstructSlackMatrix(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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reconstructSlackMatrix(Matrix,List) -- a list of facet labels that make up a flag in a polytope
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reconstructSlackMatrix(Matrix,List,List) -- a list of facet labels that make up a flag in a polytope
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reducedSlackMatrix -- a reduced slack matrix of a polytope
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reducedSlackMatrix(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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reducedSlackMatrix(..., FlagIndices => ...) -- a list of facet labels that form a flag of facets of given polytope or matroid
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reducedSlackMatrix(..., Object => ...) -- specify combinatorial object
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reducedSlackMatrix(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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reducedSlackMatrix(List) -- a reduced slack matrix of a polytope
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reducedSlackMatrix(Matrix) -- a reduced slack matrix of a polytope
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reducedSlackMatrix(ZZ,Matrix) -- a reduced slack matrix of a polytope
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rehomogenizeIdeal -- rehomogenization of a the dehomogenized slack ideal
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rehomogenizeIdeal(..., Saturate => ...) -- specifies saturation strategy to be used
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rehomogenizeIdeal(..., Strategy => ...) -- specifies saturation strategy to be used
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rehomogenizeIdeal(ZZ,Matrix) -- rehomogenization of a the dehomogenized slack ideal
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rehomogenizeIdeal(ZZ,Matrix,Graph) -- rehomogenization of a the dehomogenized slack ideal
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rehomogenizePolynomial -- rehomogenization of a polynomial reversing the dehomogenization of the slack matrix
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rehomogenizePolynomial(Matrix) -- rehomogenization of a polynomial reversing the dehomogenization of the slack matrix
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rehomogenizePolynomial(Matrix,Matrix,Graph,RingElement) -- rehomogenization of a polynomial reversing the dehomogenization of the slack matrix
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Saturate -- choose whether to saturate with respect to the product of all variables at the same time or variable by variable.
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setOnesForest -- sets to 1 variables in a symbolic slack matrix which corresponding to edges of a spanning forest
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setOnesForest(Matrix) -- sets to 1 variables in a symbolic slack matrix which corresponding to edges of a spanning forest
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slackFromGaleCircuits -- computes the slack matrix of a polytope from a Gale transform of the polytope
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slackFromGaleCircuits(..., Tolerance => ...) -- specifies the tolerance to compute the slack matrix of a polytope from a Gale transform of a polytope
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slackFromGaleCircuits(Matrix) -- computes the slack matrix of a polytope from a Gale transform of the polytope
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slackFromGalePlucker -- given a set of vectors of a Gale transform or a matrix whose columns form a Gale transform of a polytope, it fills the slack matrix of the polytope with Plucker coordinates of the Gale transform
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slackFromGalePlucker(List,List) -- given a set of vectors of a Gale transform or a matrix whose columns form a Gale transform of a polytope, it fills the slack matrix of the polytope with Plucker coordinates of the Gale transform
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slackFromGalePlucker(List,Matrix) -- given a set of vectors of a Gale transform or a matrix whose columns form a Gale transform of a polytope, it fills the slack matrix of the polytope with Plucker coordinates of the Gale transform
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slackFromPlucker -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates
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slackFromPlucker(..., Object => ...) -- specify combinatorial object
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slackFromPlucker(List) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates
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slackFromPlucker(List,List) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates
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slackFromPlucker(Matroid) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates
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slackFromPlucker(Polyhedron) -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates
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slackIdeal -- computes the slack ideal
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slackIdeal(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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slackIdeal(..., Object => ...) -- specify combinatorial object
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slackIdeal(..., Saturate => ...) -- specifies saturation strategy to be used
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slackIdeal(..., Strategy => ...) -- specifies saturation strategy to be used
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slackIdeal(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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slackIdeal(Cone) -- computes the slack ideal
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slackIdeal(List) -- computes the slack ideal
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slackIdeal(Matrix) -- computes the slack ideal
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slackIdeal(Matroid) -- computes the slack ideal
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slackIdeal(Polyhedron) -- computes the slack ideal
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slackIdeal(ZZ,List) -- computes the slack ideal
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slackIdeal(ZZ,Matrix) -- computes the slack ideal
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SlackIdeals -- a package for slack ideals of polytopes and matroids
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slackMatrix -- computes the slack matrix of a given realization
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slackMatrix(..., Object => ...) -- specify combinatorial object
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slackMatrix(Cone) -- computes the slack matrix of a given realization
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slackMatrix(List) -- computes the slack matrix of a given realization
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slackMatrix(Matroid) -- computes the slack matrix of a given realization
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slackMatrix(Polyhedron) -- computes the slack matrix of a given realization
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specificSlackMatrix -- creates built-in slack matrices of some polytopes and matroids
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specificSlackMatrix(String) -- creates built-in slack matrices of some polytopes and matroids
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symbolicSlackMatrix -- computes the symbolic slack matrix
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symbolicSlackMatrix(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the matrix
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symbolicSlackMatrix(..., Object => ...) -- specify combinatorial object
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symbolicSlackMatrix(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the matrix
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symbolicSlackMatrix(Cone) -- computes the symbolic slack matrix
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symbolicSlackMatrix(List) -- computes the symbolic slack matrix
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symbolicSlackMatrix(Matrix) -- computes the symbolic slack matrix
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symbolicSlackMatrix(Matroid) -- computes the symbolic slack matrix
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symbolicSlackMatrix(Polyhedron) -- computes the symbolic slack matrix
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symbolicSlackOfPlucker -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the matrix
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symbolicSlackOfPlucker(..., Object => ...) -- specify combinatorial object
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symbolicSlackOfPlucker(List) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(List,List) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(Matrix) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(Matrix,List) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(Matroid) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(Polyhedron) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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symbolicSlackOfPlucker(ZZ,List) -- given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables
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Tolerance -- choose the tolerance to approximate computations over the field RR
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toricPolytope -- computes the polytope whose toric ideal is the given ideal
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toricPolytope(Ideal) -- computes the polytope whose toric ideal is the given ideal
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universalIdeal -- computes the universal realization ideal of a matroid
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universalIdeal(..., CoefficientRing => ...) -- specifies the coefficient ring of the underlying ring of the ideal
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universalIdeal(..., Vars => ...) -- specifies the variables to use to create the underlying ring of the ideal
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universalIdeal(List) -- computes the universal realization ideal of a matroid
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universalIdeal(Matroid) -- computes the universal realization ideal of a matroid
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Vars -- give a set of variables for the polynomial ring where the object created will live