[GAP Forum] Hilbert series

[Park Won-Kyu]

Hello,

I want to get hilbert series of permutation group G

gap> G;
Group([ (2,3)(4,5)(7,8)(11,12)(16,17),
(1,3,2)(4,5,6)(7,8,9)(11,12,13)(16,17,18),
(4,7)(5,8)(6,9)(14,15)(19,20),
  (4,7,11)(5,8,12)(6,9,13)(10,15,14)(19,20,21) ])
gap> IsPermGroup(G);
true
gap> IG:=Irr(G);;
gap> List([1..Size(IG)],i->MolienSeries(IG[i]));
[ ( 1 ) / ( (1-z) ), ( 1 ) / ( (1-z^2) ), ( 1 ) / ( (1-z^2) ), ( 1 ) /
( (1-z^2) ), ( 1 ) / ( (1-z^3)*(1-z^2) ),
  ( 1 ) / ( (1-z^6)*(1-z^2) ), ( 1 ) / ( (1-z^6)*(1-z^2) ), ( 1 ) / (
(1-z^3)*(1-z^2) ),
  ( 1-z+z^4-z^7+z^8 ) / ( (1-z^6)*(1-z^3)*(1-z^2)*(1-z) ) ]

from http://www.math.colostate.edu/manuals/magma/htmlhelp/text419.html
"If G is a permutation group, the Molien series always exists and
equals the Hilbert series of the invariant ring of G for any field."

how can i get the hilbert series from the output of GAP ?

Regards,

Won. K. Park