generators S, gens S
This method gets the algebra generators for a ring of invariants.
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 : T = diagonalAction(W, R) * 2 o3 = R <- (QQ ) via | 0 1 -1 1 | | 1 0 -1 -1 | o3 : DiagonalAction
i4 : S = R^T o4 = 2 QQ[x x x , x x x ] 1 2 3 1 3 4 o4 : RingOfInvariants
i5 : gens S 2 o5 = {x x x , x x x } 1 2 3 1 3 4 o5 : List