ToricQuiver -- the ToricQuiver datatype

Functions and methods returning an object of class ToricQuiver :

• mergeOnArrow(Matrix,ZZ,Matrix,ZZ) -- see mergeOnArrow -- join two quivers together by identifying an arrow from each
• mergeOnArrow(Matrix,ZZ,ToricQuiver,ZZ) -- see mergeOnArrow -- join two quivers together by identifying an arrow from each
• mergeOnArrow(ToricQuiver,ZZ,Matrix,ZZ) -- see mergeOnArrow -- join two quivers together by identifying an arrow from each
• mergeOnArrow(ToricQuiver,ZZ,ToricQuiver,ZZ) -- see mergeOnArrow -- join two quivers together by identifying an arrow from each
• mergeOnVertex(Matrix,ZZ,Matrix,ZZ) -- see mergeOnVertex -- join two quivers together by identifying a vertex from each
• mergeOnVertex(Matrix,ZZ,ToricQuiver,ZZ) -- see mergeOnVertex -- join two quivers together by identifying a vertex from each
• mergeOnVertex(ToricQuiver,ZZ,Matrix,ZZ) -- see mergeOnVertex -- join two quivers together by identifying a vertex from each
• mergeOnVertex(ToricQuiver,ZZ,ToricQuiver,ZZ) -- see mergeOnVertex -- join two quivers together by identifying a vertex from each
• threeVertexQuiver(List) -- see threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
• toricQuiver(Graph) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(Graph,List) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(List) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(List,List) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(Matrix) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(Matrix,List) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(ToricQuiver) -- see toricQuiver -- the toricQuiver constructor
• toricQuiver(ToricQuiver,List) -- see toricQuiver -- the toricQuiver constructor
• ToricQuiver ^ List -- taking a subquiver by indexing
• ToricQuiver _ List -- taking a subquiver by indexing

Methods that use an object of class ToricQuiver :

• basisForFlowPolytope(List,ToricQuiver) -- see basisForFlowPolytope -- compute the necessary basis vectors for the hyperplane of a flow polytope
• basisForFlowPolytope(ToricQuiver) -- see basisForFlowPolytope -- compute the necessary basis vectors for the hyperplane of a flow polytope
• flowPolytopeVertices(List,ToricQuiver) -- see flowPolytopeVertices -- generate the polytope associated to a toric quiver
• flowPolytopeVertices(ToricQuiver) -- see flowPolytopeVertices -- generate the polytope associated to a toric quiver
• getWeights(ToricQuiver) -- see getWeights -- image of the flow on the vertices
• incInverse(List,ToricQuiver) -- see incInverse -- compute a flow in the preimage for a given weight
• isAcyclic(ToricQuiver) -- see isAcyclic -- whether a toric quiver has no cycles
• isClosedUnderArrows(List,ToricQuiver) -- see isClosedUnderArrows -- whether a subquiver closed under arrows
• isClosedUnderArrows(Matrix,ToricQuiver) -- see isClosedUnderArrows -- whether a subquiver closed under arrows
• isClosedUnderArrows(ToricQuiver,ToricQuiver) -- see isClosedUnderArrows -- whether a subquiver closed under arrows
• isSemistable(List,ToricQuiver) -- see isSemistable -- whether a subquiver is semistable with respect to a given weight
• isSemistable(ToricQuiver,ToricQuiver) -- see isSemistable -- whether a subquiver is semistable with respect to a given weight
• isStable(List,ToricQuiver) -- see isStable -- whether a subquiver is semistable with respect to a given weight
• isStable(ToricQuiver,ToricQuiver) -- see isStable -- whether a subquiver is semistable with respect to a given weight
• isTight(List,ToricQuiver) -- see isTight -- determine if toric quiver is tight
• isTight(ToricQuiver) -- see isTight -- determine if toric quiver is tight
• isTight(ToricQuiver,List) -- see isTight -- determine if toric quiver is tight
• isWellDefined(ToricQuiver) -- see isWellDefined -- determine if toric quiver is correctly constructed
• maxCodimensionUnstable(ToricQuiver) -- see maxCodimensionUnstable -- compute the maximal codimension of the unstable loci of a quiver
• potentialWalls(ToricQuiver) -- see potentialWalls -- lists the potential walls in the weight chamber decomposition for a given quiver
• quiverEdges(ToricQuiver) -- see quiverEdges -- return the graph edges associated to the toric quiver
• quiverFlow(ToricQuiver) -- see quiverFlow -- return the flow attribute associated to the toric quiver
• quiverIncidenceMatrix(ToricQuiver) -- see quiverIncidenceMatrix -- return the graph incidence matrix attribute associated to the toric quiver
• quiverVertices(ToricQuiver) -- see quiverVertices -- return the vertices of the toric quiver
• quiverWeights(ToricQuiver) -- see quiverWeights -- return the weight attribute associated to the toric quiver
• samePolytope(List,List,ToricQuiver) -- see samePolytope -- whether two weights produce the same flow polytope
• subquivers(ToricQuiver) -- see subquivers -- return all possible subquivers of a given quiver
• ToricQuiver == ToricQuiver -- whether two toric quivers are equal.
• wallType(List,ToricQuiver) -- see wallType -- get the type of a wall for a given quiver

For the programmer

The object ToricQuiver is a type, with ancestor classes HashTable < Thing.