ambient(RingOfInvariants) -- the ambient polynomial ring where the group acted upon

Synopsis

• Function: ambient

• Usage:

  ambient S

• Inputs:
  • S, an instance of the type RingOfInvariants, of the group action being returned
• Outputs:
  • a polynomial ring, where the group acted upon

Description

This example shows how to recover the polynomial ring when a torus acted upon.

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 : ambient S

o4 = R

o4 : PolynomialRing