proc displayHilbPoly(ideal G)
"USAGE:  displayHilbPoly(G), G of type ideal
ASSUME:  G must be a homogeneous Groebner basis for an ideal of the 
         active ring in the SINGULAR session; say, G generates the 
         homogeneous ideal I of R.
RETURN:  None.
NOTE:    Displays the Hilbert polynomial of R/I.
"
{
  int d = dim(G)-1;       // degree of Hibert polynomial
  intvec co = hilb(G,2);  // representation II of Hilbert series
  int s = size(co)-1;     // s = deg(Q_M) +1
  ring Qt = 0, t, dp;     // change active ring to Q[t]
  poly QM = 0;
  for (int i=1; i<=s; i=i+1)
  {
    QM = QM+co[i]*t^(i-1);
  }
  poly QMi = QM;          // the polynomial Q_M(t)
  int ifac = 1; 
  list a; 
  for (i=1; i<=d+1; i=i+1)
  {
    a = insert(a, subst(QMi,t,1)/ifac, i-1);
    QMi = diff((QMi),t);
    ifac = ifac*i;
  }
  poly PM = (-1)^(d)*a[d+1]; 
  poly bin = 1;
  for (i=1; i<=d; i=i+1)
  {
    bin = bin*(t+i)/i;    // compute binomial coeff. by recursion 
    PM = PM+(-1)^(d-i)*a[d+1-i]*bin;
  }
  print(PM);
}