Use R ::= QQ[w,x,y,z];
  PS := HP.PSeries(1 + 2w + 3w^2 + 4w^3 + 5w^4 + 6w^5 + 5w^6 +
        4w^7 + 3w^8 + 2w^9 + w^10,2);
  PS;
(1 + 2w + 3w^2 + 4w^3 + 5w^4 + 6w^5 + 5w^6 + 4w^7 + 3w^8 + 2w^9 + w^10) / (1-w)^2
-------------------------------
  I := Ideal((xy-zw)^3,(xz-yw)^3);
  I.PSeries := PS; -- this is how to let CoCoA know about the Poincare series
  G := GBasis(I);