molienSeries -- computes the Molien (Hilbert) series of the invariant ring of a finite group

Synopsis

• Usage:

  molienSeries G

• Inputs:
  • G, an instance of the type FiniteGroupAction
• Outputs:
  • a divide expression, the Molien series of the invariant ring of G as a rational function

Description

This function is provided by the package InvariantRing.

The example below computes the Molien series for the dihedral group with 6 elements. K is the field obtained by adjoining a primitive third root of unity to QQ.

i1 : K=toField(QQ[a]/(a^2+a+1));

i2 : A=matrix{{a,0},{0,a^2}};

             2      2
o2 : Matrix K  <-- K

i3 : B=sub(matrix{{0,1},{1,0}},K);

             2      2
o3 : Matrix K  <-- K

i4 : D6=finiteAction({A,B},K[x,y])

o4 = K[x..y] <- {| a 0    |, | 0 1 |}
                 | 0 -a-1 |  | 1 0 |

o4 : FiniteGroupAction

i5 : molienSeries D6

             1
o5 = ----------------
           2       3
     (1 - T )(1 - T )

o5 : Expression of class Divide