# momentGraph -- creates a moment graph

## Synopsis

• Usage:
G = momentGraph(L,E,H)
• Inputs:
• L, a list, of vertices
• E, , whose keys are lists of two vertices representing edges and values are characters of corresponding 1-dimensional orbits
• H, a ring, a polynomial ring representing the equivariant cohomology ring of a point
• Outputs:
• G, ,

## Description

This method creates a MomentGraph from the data of vertices, edges and their associated characters, and a ring representing the equivariant cohomology ring of a point (with trivial torus-action). The following example is the moment graph of the projective 2-space $\mathbb P^2$.

 i1 : V = {set{0}, set{1}, set{2}}; i2 : E = hashTable {({set{0},set{1}},{-1,1,0}), ({set{0},set{2}},{-1,0,1}), ({set{1},set{2}},{0,-1,1})} o2 = HashTable{{set {0}, set {1}} => {-1, 1, 0}} {set {0}, set {2}} => {-1, 0, 1} {set {1}, set {2}} => {0, -1, 1} o2 : HashTable i3 : t = symbol t; H = QQ[t_0..t_2] o4 = H o4 : PolynomialRing i5 : G = momentGraph(V,E,H) o5 = a "moment graph" on 3 vertices with 3 edges o5 : MomentGraph i6 : peek G o6 = MomentGraph{cache => CacheTable{} } edges => HashTable{{set {0}, set {1}} => {-1, 1, 0}} {set {0}, set {2}} => {-1, 0, 1} {set {1}, set {2}} => {0, -1, 1} HTpt => H vertices => {set {0}, set {1}, set {2}} i7 : underlyingGraph G o7 = Graph{set {0} => {set {1}, set {2}}} set {1} => {set {0}, set {2}} set {2} => {set {0}, set {1}} o7 : Graph