
Hilbert seriesLet M be a graded module over K[x_{1},...,x_{n}] with respect to weights w_{1},...,w_{n} . The Hilbert function H_{M} is defined (on Z) by H_{M}(k) := dim_{K}M_{k} . The HilbertPoincaré series of M is the power series where Q(t) and P(t) are polynomials with coefficients in Z.
where Q(t) is a polynomial in Z[t], the first (weighted) Hilbert series of M . 


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