# equivariantHilbert -- stores equivariant Hilbert series expansions

## Description

This key is created in the cache table of a DiagonalAction upon calling equivariantHilbertSeries with the Order option. It stores partial expansions of the equivariant Hilbert series to avoid computing them again.

 i1 : R = QQ[x_1..x_3] o1 = R o1 : PolynomialRing i2 : W = matrix{{-1,0,1},{0,-1,1}} o2 = | -1 0 1 | | 0 -1 1 | 2 3 o2 : Matrix ZZ <--- ZZ i3 : T = diagonalAction(W, R) * 2 o3 = R <- (QQ ) via | -1 0 1 | | 0 -1 1 | o3 : DiagonalAction i4 : T.cache.?equivariantHilbert o4 = false i5 : elapsedTime equivariantHilbertSeries(T, Order => 5) -- 0.00529492 seconds elapsed -1 -1 2 2 -2 -1 -1 -2 2 o5 = 1 + (z z + z + z )T + (z z + z + z + z + z z + z )T + 0 1 1 0 0 1 0 1 1 0 1 0 ------------------------------------------------------------------------ 3 3 2 2 -1 -3 -1 -1 -2 -2 -1 -3 3 (z z + z z + z z + z z + 1 + z + z z + z z + z z + z )T 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 ------------------------------------------------------------------------ 4 4 3 2 2 3 2 -2 2 -1 -4 -1 + (z z + z z + z z + z + z z + z z + z + z + z + z + 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 ------------------------------------------------------------------------ -1 -3 -2 -2 -2 -3 -1 -4 4 z z + z z + z z + z z + z )T 0 1 0 1 0 1 0 1 0 o5 : ZZ[z ..z ][T] 0 1 i6 : T.cache.?equivariantHilbert o6 = true i7 : elapsedTime equivariantHilbertSeries(T, Order => 5); -- 0.000950203 seconds elapsed

## For the programmer

The object equivariantHilbert is .