Macaulay2 » Documentation
Packages » GKMVarieties :: Table of Contents
next | previous | forward | backward | up | index | toc

# 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