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 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
