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degreesRing(DiagonalAction) -- of a diagonal action

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

See also

Ways to use this method:

The source of this document is in InvariantRing/AbelianGroupsDoc.m2:389:0.