degreesRing(DiagonalAction) -- of a diagonal action

Synopsis

Function: degreesRing
Usage:

degreesRing D
Inputs:
- D, an instance of the type DiagonalAction
Outputs:
- a ring, where the equivariant Hilbert series of the diagonal group action lives in

Description

This function is provided by the package InvariantRing.

Use this function to get the ring where the equivariant Hilbert series of the diagonal group action lives in.

The following example defines an action of the product of a two-dimensional torus and two cyclic group of order 3 on a polynomial ring in four variables.

i1 : R = QQ[x_1..x_4]

o1 = R

o1 : PolynomialRing

i2 : W = matrix{{0,1,-1,1},{1,0,-1,-1}}

o2 = | 0 1 -1 1  |
     | 1 0 -1 -1 |

              2       4
o2 : Matrix ZZ  <-- ZZ

i3 : W1 = matrix{{1,0,1,0},{0,1,1,0}}

o3 = | 1 0 1 0 |
     | 0 1 1 0 |

              2       4
o3 : Matrix ZZ  <-- ZZ

i4 : T = diagonalAction(W,W1,{3,3},R)

             * 2
o4 = R <- (QQ )  x ZZ/3 x ZZ/3 via 

     (| 0 1 -1 1  |, | 1 0 1 0 |)
      | 1 0 -1 -1 |  | 0 1 1 0 |

o4 : DiagonalAction

i5 : degreesRing T

o5 = ZZ[z ..z ][T]
         0   3

o5 : PolynomialRing

Ways to use this method: