Use this function to get the ring where the equivariant Hilbert series of the diagonal group action lives in.
The following example defines an action of the product of a two-dimensional torus and two cyclic group of order 3 on a polynomial ring in four variables.
i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing |
i2 : W = matrix{{0,1,-1,1},{1,0,-1,-1}} o2 = | 0 1 -1 1 | | 1 0 -1 -1 | 2 4 o2 : Matrix ZZ <--- ZZ |
i3 : W1 = matrix{{1,0,1,0},{0,1,1,0}} o3 = | 1 0 1 0 | | 0 1 1 0 | 2 4 o3 : Matrix ZZ <--- ZZ |
i4 : T = diagonalAction(W,W1,{3,3},R) * 2 o4 = R <- (QQ ) x ZZ/3 x ZZ/3 via (| 0 1 -1 1 |, | 1 0 1 0 |) | 1 0 -1 -1 | | 0 1 1 0 | o4 : DiagonalAction |
i5 : degreesRing T o5 = ZZ[z ..z ][T] 0 3 o5 : PolynomialRing |