 Finally let "B" be a Gröbner basis of "I" for a monomial ordering refining the total degree partial ordering and "G" the (homogeneous) ideal generated by the leading monomials of the elements of "B".The computation of the Hilbert series is based on the fact that "the filtered algebra R/I and the graded algebras R/H and R/G have the same Hilbert series".Thus the computation of the Hilbert series is reduced, through the computation of a Gröbner basis, to the same problem for an ideal generated by monomials, which is usually much easier than the computation of the Gröbner basis.