Description
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:
-
Derksen, H. & Kemper, G. (2015).Computational Invariant Theory. Heidelberg: Springer.
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|
+---------------------------------------------------------------------------------------------------------+
|