This function is provided by the package InvariantRing.
It implements King's algorithm to compute a minimal set of generating invariants for the action of a finite group on a polynomial ring following Algorithm 3.8.2 in:
The following example computes the invariants of the alternating group on 4 elements.
i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing |
i2 : L = apply({"2314","2143"},permutationMatrix); |
i3 : A4 = finiteAction(L,R) o3 = R <- {| 0 0 1 0 |, | 0 1 0 0 |} | 1 0 0 0 | | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 1 | | 0 0 1 0 | o3 : FiniteGroupAction |
i4 : netList invariants A4 +---------------------------------------------------------------------------------------------------------+ o4 = |x + x + x + x | | 1 2 3 4 | +---------------------------------------------------------------------------------------------------------+ | 2 2 2 2 | |x + x + x + x | | 1 2 3 4 | +---------------------------------------------------------------------------------------------------------+ | 3 3 3 3 | |x + x + x + x | | 1 2 3 4 | +---------------------------------------------------------------------------------------------------------+ | 4 4 4 4 | |x + x + x + x | | 1 2 3 4 | +---------------------------------------------------------------------------------------------------------+ | 3 2 3 2 2 3 2 3 3 2 2 3 3 2 3 2 3 2 2 3 2 3 2 3| |x x x + x x x + x x x + x x x + x x x + x x x + x x x + x x x + x x x + x x x + x x x + x x x | | 1 2 3 1 2 3 1 2 3 1 2 4 1 3 4 2 3 4 1 2 4 2 3 4 1 3 4 1 2 4 1 3 4 2 3 4| +---------------------------------------------------------------------------------------------------------+ |