# ring(GroupAction) -- the polynomial ring being acted upon

## Synopsis

• Function: ring
• Usage:
ring G
• Inputs:
• G, an instance of the type GroupAction, a group action on a polynomial ring
• Outputs:
• a ring, the polynomial ring being acted upon

## Description

This function is provided by the package InvariantRing.

 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 : ring T === R o3 = true