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

## Synopsis

• Usage:
molienSeries G
• Inputs:
• Outputs:
• , 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

## Ways to use molienSeries :

• "molienSeries(FiniteGroupAction)"

## For the programmer

The object molienSeries is .