ThinSincereQuivers : Table of Contents

• ThinSincereQuivers -- creating and manipulating Toric Quivers

  • ToricQuiver -- the ToricQuiver datatype
  • Creating toric quivers
  • Creating subquiver representations
  • toricQuiver -- the toricQuiver constructor
  • ToricQuiver _ List -- taking a subquiver by indexing
  • ToricQuiver ^ List -- taking a subquiver by indexing
  • ToricQuiver == ToricQuiver -- whether two toric quivers are equal.
  • bipartiteQuiver -- make a toric quiver on underlying bipartite graph
  • chainQuiver -- make a toric quiver on underlying graph in the form of a chain
  • threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
  • allSpanningTrees -- find the spanning trees of the underlying graph
  • basisForFlowPolytope -- compute the necessary basis vectors for the hyperplane of a flow polytope
  • coneSystem -- compute the chamber decomposition of weights
  • flowPolytopeVertices -- generate the polytope associated to a toric quiver
  • incInverse -- compute a flow in the preimage for a given weight
  • isAcyclic -- whether a toric quiver has no cycles
  • isClosedUnderArrows -- whether a subquiver closed under arrows
  • isSemistable -- whether a subquiver is semistable with respect to a given weight
  • isStable -- whether a subquiver is semistable with respect to a given weight
  • isTight -- determine if toric quiver is tight
  • isWellDefined -- determine if toric quiver is correctly constructed
  • makeTight -- return a tight quiver with the same flow polytope
  • maxCodimensionUnstable -- compute the maximal codimension of the unstable loci of a quiver
  • maximalNonstableSubquivers -- return the maximal subquivers that are semistable
  • maximalUnstableSubquivers -- return the maximal subquivers that are unstable
  • mergeOnArrow -- join two quivers together by identifying an arrow from each
  • mergeOnVertex -- join two quivers together by identifying a vertex from each
  • potentialWalls -- lists the potential walls in the weight chamber decomposition for a given quiver
  • primitiveArrows -- list the primitive arrows in a quiver
  • quiverIncidenceMatrix -- return the graph incidence matrix attribute associated to the toric quiver
  • quiverEdges -- return the graph edges associated to the toric quiver
  • quiverFlow -- return the flow attribute associated to the toric quiver
  • quiverVertices -- return the vertices of the toric quiver
  • quiverWeights -- return the weight attribute associated to the toric quiver
  • referenceThetas -- return a weight for all polytopes associated to a toric quiver
  • samePolytope -- whether two weights produce the same flow polytope
  • stableTrees -- return the spanning trees that are stable
  • subquivers -- return all possible subquivers of a given quiver
  • wallType -- get the type of a wall for a given quiver
  • getWeights -- image of the flow on the vertices
  • AsSubquiver
  • Flow
  • ReturnSingletons