On the computation of hilbert—Poincaré series

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We prove a theorem, which provides a formula for the computation of the Poincaré series of a monomial ideal ink[X1,⋯, Xn], via the computation of the Poincaré series of some monomial ideals ink[X 1,⋯, Xi,⋯, Xn]. The complexity of our algorithm is optimal for Borel-normed ideals and an implementation in CoCoA strongly confirms its efficiency. An easy extension computes the Poincaré series of graded modules over standard algebras.

The paper was partly written while the third author was visiting Queen's University, during the academic year 1989/90. It was partly supported by the Natural Sciences & Engineering Research Council of Canada, Queen's University (Kingston, Canada) and Consiglio Nazionale delle Ricerche