.
This method computes the Hilbert series of the ring of invariants.
i1 : R = QQ[x_1..x_4]
o1 = R
o1 : PolynomialRing
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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
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i3 : T = diagonalAction(W, R)
* 2
o3 = R <- (QQ ) via
| 0 1 -1 1 |
| 1 0 -1 -1 |
o3 : DiagonalAction
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i4 : S = R^T
o4 = 5 3 2 5 3 4 4 2 3 6 3 3 2
QQ[x x x x , x x x x , x x x x , x x x , x x x , x x x ]
1 2 3 4 1 2 3 4 1 2 3 4 1 3 4 1 3 4 1 2 3
o4 : RingOfInvariants
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i5 : hilbertSeries S
10 11 12 13 21 22 23 24 25 33 34 35 36 46
1 - T - T - T - T + T + T + 2T + T + T - T - T - T - T + T
o5 = --------------------------------------------------------------------------------------
13 12 11 10 4 3
(1 - T )(1 - T )(1 - T )(1 - T )(1 - T )(1 - T )
o5 : Expression of class Divide
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