SlackIdeals : Table of Contents

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