This method presents the ring of invariants as a polynomial ring modulo the defining ideal. The default variable name in the polynomial ring is u_i. You can pass the variable name you want as optional input.
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 = 4 2 3 5 3 2 6 3 3 2 QQ[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 3 4 1 3 4 1 2 3 o4 : RingOfInvariants |
i5 : definingIdeal S 2 2 3 o5 = ideal (u - u u , u - u u , u - u ) 1 4 5 2 4 5 3 4 o5 : Ideal of QQ[u ..u ] 1 5 |
The object definingIdeal is a method function with options.