# action -- the group action that produced a ring of invariants

## Synopsis

• Usage:
action S
• Inputs:
• S, an instance of the type RingOfInvariants, of the group action being returned
• Outputs:
• an instance of the type GroupAction, the action that produced the ring of invariants in the input

## Description

This function is provided by the package InvariantRing.

This example shows how to recover the action of a torus that produced a certain ring of invariants. Note other action types are possible and may produce a different looking output.

 i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing i2 : T = diagonalAction(matrix {{0,1,-1,1},{1,0,-1,-1}}, R) * 2 o2 = R <- (QQ ) via | 0 1 -1 1 | | 1 0 -1 -1 | o2 : DiagonalAction i3 : S = R^T o3 = 2 QQ[x x x , x x x ] 1 2 3 1 3 4 o3 : RingOfInvariants i4 : action S * 2 o4 = R <- (QQ ) via | 0 1 -1 1 | | 1 0 -1 -1 | o4 : DiagonalAction

## Ways to use action :

• "action(RingOfInvariants)"

## For the programmer

The object action is .