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={A^0,A,A^2,B,A*B,A^2*B} o4 = {| 1 0 |, | a 0 |, | -a-1 0 |, | 0 1 |, | 0 a |, | 0 -a-1 |} | 0 1 | | 0 -a-1 | | 0 a | | 1 0 | | -a-1 0 | | a 0 | o4 : List |
i5 : molienSeries D6 1 o5 = --------------------------- 2 2 (1 - T) (1 + T)(1 + T + T ) o5 : Expression of class Divide |
This function is provided by the package InvariantRing.