GKMVarieties : Table of Contents

• GKMVarieties -- computations with GKM varieties and moment graphs
• affineToricRing -- computes the toric ring associated to a monomial map
• ampleKClass -- the class of an ample line bundle
• bases(FlagMatroid) -- compute the bases of a flag matroid
• bruhatOrder -- computes the Bruhat order on a generalized flag variety
• cellOrder -- the poset of a stratification of a GKM variety
• cellOrder(MomentGraph,Poset) -- define a cell order on a moment graph
• charts -- outputs the torus-invariant affine charts of a GKM variety
• compose(EquivariantMap,EquivariantMap) -- computes the composition of two equivariant morphisms
• diagonalMap -- constructs the diagonal morphism
• EquivariantMap -- the class of all equivariant morphisms between GKM varieties
• EquivariantMap ** EquivariantMap -- computes the product of two equivariant morphisms
• euler(KClass) -- computes the equivariant Euler characteristic of an equivariant K-class
• Example: generalized flag varieties
• Example: smooth toric varieties
• flagGeomTuttePolynomial -- computes the flag-geometric Tutte polynomial of flag matroids
• flagMap -- creates equivariant maps between generalized flag varieties
• FlagMatroid -- the class of all flag matroids
• flagMatroid -- construct a flag matroid
• generalizedFlagVariety -- makes a generalized flag variety as a GKM variety
• generalizedSchubertVariety -- create a generalized Schubert variety
• GKMVariety -- the class of all GKM varieties
• GKMVariety ** GKMVariety -- product of GKM varieties
• isWellDefined(FlagMatroid) -- check if a flag matroid is well-defined
• isWellDefined(KClass) -- whether the input is a well-defined equivariant K-class
• KClass -- the class of all equivariant K-classes
• KClass * KClass -- computes the product of two equivariant K-classes
• KClass + KClass -- computes the sum of two equivariant K-classes
• KClass ^ ZZ -- computes powers of an equivariant K-classes
• latticePoints(FlagMatroid) -- lattice points of a base polytope of a flag matroid
• lieType -- outputs the Lie type of a generalized flag variety
• makeCharacterRing -- constructs the character ring of a torus
• makeGKMVariety -- constructs a GKM variety
• makeKClass -- constructs an equivariant K-class
• makeKClass(GKMVariety,FlagMatroid) -- the equivariant K-class of a flag matroid
• makeKClass(GKMVariety,ToricDivisor) -- create the KClass from a ToricDivisor
• map(GKMVariety,GKMVariety,List) -- creates a EquivariantMap
• MomentGraph -- the class of all moment graphs
• momentGraph -- creates a moment graph
• MomentGraph ** MomentGraph -- the product of two moment graphs
• momentGraph(GKMVariety) -- view the moment graph of a GKM variety
• momentGraph(GKMVariety,MomentGraph) -- define a moment graph for a GKM variety
• normalToricVariety(GKMVariety) -- converts a GKM variety back into a toric variety
• orbitClosure -- computes the equivariant K-class of a torus orbit closure of a point in a generalized flag variety
• projectiveSpace -- constructs projective space as a GKM variety
• pullback(EquivariantMap) -- computes the pullback map of equivariant K-classes of an equivariant map
• pushforward -- computes the pushforward map of equivariant K-classes of an equivariant map
• setIndicator -- computes the signed indicator vector of an admissible set
• trivialKClass -- the equivariant K-class of the structure sheaf
• underlyingGraph(MomentGraph) -- the underlying (undirected) graph of a moment graph