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 -- get a list of d-spanning elements for each facet
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getFacetBases(...,Object=>...) -- specify combinatorial object
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getFacetBases(List) -- get a list of d-spanning elements for each facet
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getFacetBases(Matrix) -- get a list of d-spanning elements for each facet
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getFacetBases(Matroid) -- get a list of d-spanning elements for each facet
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getFacetBases(Polyhedron) -- get a 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 -- compute the Grassmannian section ideal corresponding to a slack matrix
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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) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(List) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(List,List) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(Matrix) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(Matrix,List) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(Matroid) -- compute the Grassmannian section ideal corresponding to a slack matrix
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grassmannSectionIdeal(Polyhedron) -- compute the Grassmannian section ideal corresponding to a slack matrix
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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 -- fill the slack matrix with Plücker coordinates of the Gale transform
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slackFromGalePlucker(List,List) -- fill the slack matrix with Plücker coordinates of the Gale transform
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slackFromGalePlucker(List,Matrix) -- fill the slack matrix with Plücker coordinates of the Gale transform
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slackFromPlucker -- fill the slack matrix of a given polytope, cone or matroid with Plücker coordinates
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slackFromPlucker(...,Object=>...) -- specify combinatorial object
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slackFromPlucker(List) -- fill the slack matrix of a given polytope, cone or matroid with Plücker coordinates
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slackFromPlucker(List,List) -- fill the slack matrix of a given polytope, cone or matroid with Plücker coordinates
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slackFromPlucker(Matroid) -- fill the slack matrix of a given polytope, cone or matroid with Plücker coordinates
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slackFromPlucker(Polyhedron) -- fill the slack matrix of a given polytope, cone or matroid with Plücker 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 -- fill the slack matrix with Plücker 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) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(List,List) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(Matrix) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(Matrix,List) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(Matroid) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(Polyhedron) -- fill the slack matrix with Plücker variables
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symbolicSlackOfPlucker(ZZ,List) -- fill the slack matrix with Plücker 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