Macaulay2
»
Documentation
Packages
»
ThinSincereQuivers
::
Index
next | previous | forward | backward | up |
index
|
toc
ThinSincereQuivers : Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
allSpanningTrees
-- find the spanning trees of the underlying graph
AsSubquiver
basisForFlowPolytope
-- compute the necessary basis vectors for the hyperplane of a flow polytope
basisForFlowPolytope(List,ToricQuiver)
-- compute the necessary basis vectors for the hyperplane of a flow polytope
basisForFlowPolytope(ToricQuiver)
-- compute the necessary basis vectors for the hyperplane of a flow polytope
bipartiteQuiver
-- make a toric quiver on underlying bipartite graph
bipartiteQuiver(...,Flow=>...)
-- make a toric quiver on underlying bipartite graph
chainQuiver
-- make a toric quiver on underlying graph in the form of a chain
chainQuiver(...,Flow=>...)
-- make a toric quiver on underlying graph in the form of a chain
coneSystem
-- compute the chamber decomposition of weights
Creating subquiver representations
Creating toric quivers
Flow
flowPolytopeVertices
-- generate the polytope associated to a toric quiver
flowPolytopeVertices(...,Format=>...)
-- generate the polytope associated to a toric quiver
flowPolytopeVertices(List,ToricQuiver)
-- generate the polytope associated to a toric quiver
flowPolytopeVertices(ToricQuiver)
-- generate the polytope associated to a toric quiver
getWeights
-- image of the flow on the vertices
getWeights(Matrix)
-- image of the flow on the vertices
getWeights(ToricQuiver)
-- image of the flow on the vertices
incInverse
-- compute a flow in the preimage for a given weight
incInverse(List,ToricQuiver)
-- compute a flow in the preimage for a given weight
isAcyclic
-- whether a toric quiver has no cycles
isAcyclic(Matrix)
-- whether a toric quiver has no cycles
isAcyclic(ToricQuiver)
-- whether a toric quiver has no cycles
isClosedUnderArrows
-- whether a subquiver closed under arrows
isClosedUnderArrows(List,Matrix)
-- whether a subquiver closed under arrows
isClosedUnderArrows(List,ToricQuiver)
-- whether a subquiver closed under arrows
isClosedUnderArrows(Matrix,List)
-- whether a subquiver closed under arrows
isClosedUnderArrows(Matrix,ToricQuiver)
-- whether a subquiver closed under arrows
isClosedUnderArrows(ToricQuiver,ToricQuiver)
-- whether a subquiver closed under arrows
isSemistable
-- whether a subquiver is semistable with respect to a given weight
isSemistable(List,ToricQuiver)
-- whether a subquiver is semistable with respect to a given weight
isSemistable(ToricQuiver,ToricQuiver)
-- whether a subquiver is semistable with respect to a given weight
isStable
-- whether a subquiver is semistable with respect to a given weight
isStable(List,ToricQuiver)
-- whether a subquiver is semistable with respect to a given weight
isStable(ToricQuiver,ToricQuiver)
-- whether a subquiver is semistable with respect to a given weight
isTight
-- determine if toric quiver is tight
isTight(...,Format=>...)
-- determine if toric quiver is tight
isTight(List,ToricQuiver)
-- determine if toric quiver is tight
isTight(ToricQuiver)
-- determine if toric quiver is tight
isTight(ToricQuiver,List)
-- determine if toric quiver is tight
isWellDefined
-- determine if toric quiver is correctly constructed
isWellDefined(ToricQuiver)
-- 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
maxCodimensionUnstable(ToricQuiver)
-- compute the maximal codimension of the unstable loci of a quiver
maximalNonstableSubquivers
-- return the maximal subquivers that are semistable
maximalNonstableSubquivers(...,Format=>...)
-- return the maximal subquivers that are semistable
maximalNonstableSubquivers(...,ReturnSingletons=>...)
-- return the maximal subquivers that are semistable
maximalUnstableSubquivers
-- return the maximal subquivers that are unstable
maximalUnstableSubquivers(...,Format=>...)
-- return the maximal subquivers that are unstable
maximalUnstableSubquivers(...,ReturnSingletons=>...)
-- return the maximal subquivers that are unstable
mergeOnArrow
-- join two quivers together by identifying an arrow from each
mergeOnArrow(Matrix,ZZ,Matrix,ZZ)
-- join two quivers together by identifying an arrow from each
mergeOnArrow(Matrix,ZZ,ToricQuiver,ZZ)
-- join two quivers together by identifying an arrow from each
mergeOnArrow(ToricQuiver,ZZ,Matrix,ZZ)
-- join two quivers together by identifying an arrow from each
mergeOnArrow(ToricQuiver,ZZ,ToricQuiver,ZZ)
-- join two quivers together by identifying an arrow from each
mergeOnVertex
-- join two quivers together by identifying a vertex from each
mergeOnVertex(Matrix,ZZ,Matrix,ZZ)
-- join two quivers together by identifying a vertex from each
mergeOnVertex(Matrix,ZZ,ToricQuiver,ZZ)
-- join two quivers together by identifying a vertex from each
mergeOnVertex(ToricQuiver,ZZ,Matrix,ZZ)
-- join two quivers together by identifying a vertex from each
mergeOnVertex(ToricQuiver,ZZ,ToricQuiver,ZZ)
-- join two quivers together by identifying a vertex from each
potentialWalls
-- lists the potential walls in the weight chamber decomposition for a given quiver
potentialWalls(Matrix)
-- lists the potential walls in the weight chamber decomposition for a given quiver
potentialWalls(ToricQuiver)
-- lists the potential walls in the weight chamber decomposition for a given quiver
primitiveArrows
-- list the primitive arrows in a quiver
quiverEdges
-- return the graph edges associated to the toric quiver
quiverEdges(ToricQuiver)
-- return the graph edges associated to the toric quiver
quiverFlow
-- return the flow attribute associated to the toric quiver
quiverFlow(ToricQuiver)
-- return the flow attribute associated to the toric quiver
quiverIncidenceMatrix
-- return the graph incidence matrix attribute associated to the toric quiver
quiverIncidenceMatrix(ToricQuiver)
-- return the graph incidence matrix attribute associated to the toric quiver
quiverVertices
-- return the vertices of the toric quiver
quiverVertices(ToricQuiver)
-- return the vertices of the toric quiver
quiverWeights
-- return the weight attribute associated to the toric quiver
quiverWeights(ToricQuiver)
-- return the weight attribute associated to the toric quiver
referenceThetas
-- return a weight for all polytopes associated to a toric quiver
referenceThetas(List)
-- return a weight for all polytopes associated to a toric quiver
ReturnSingletons
samePolytope
-- whether two weights produce the same flow polytope
samePolytope(List,List,ToricQuiver)
-- 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
subquivers(...,AsSubquiver=>...)
-- return all possible subquivers of a given quiver
subquivers(...,Format=>...)
-- return all possible subquivers of a given quiver
subquivers(Matrix)
-- return all possible subquivers of a given quiver
subquivers(ToricQuiver)
-- return all possible subquivers of a given quiver
ThinSincereQuivers
-- creating and manipulating Toric Quivers
threeVertexQuiver
-- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
threeVertexQuiver(...,Flow=>...)
-- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
threeVertexQuiver(List)
-- make a toric quiver on underlying graph with three vertices and a specified number of edges between each
ToricQuiver
-- the ToricQuiver datatype
toricQuiver
-- the toricQuiver constructor
ToricQuiver == ToricQuiver
-- whether two toric quivers are equal.
ToricQuiver ^ List
-- taking a subquiver by indexing
ToricQuiver _ List
-- taking a subquiver by indexing
toricQuiver(...,Flow=>...)
-- the toricQuiver constructor
toricQuiver(Graph)
-- the toricQuiver constructor
toricQuiver(Graph,List)
-- the toricQuiver constructor
toricQuiver(List)
-- the toricQuiver constructor
toricQuiver(List,List)
-- the toricQuiver constructor
toricQuiver(Matrix)
-- the toricQuiver constructor
toricQuiver(Matrix,List)
-- the toricQuiver constructor
toricQuiver(ToricQuiver)
-- the toricQuiver constructor
toricQuiver(ToricQuiver,List)
-- the toricQuiver constructor
wallType
-- get the type of a wall for a given quiver
wallType(List,Matrix)
-- get the type of a wall for a given quiver
wallType(List,ToricQuiver)
-- get the type of a wall for a given quiver