Applicable Algebra in Engineering, Communication and Computing

, Volume 2, Issue 1, pp 21–33

On the computation of hilbert—Poincaré series

  • Anna Maria Bigatti
  • Massimo Caboara
  • Lorenzo Robbiano
Article

DOI: 10.1007/BF01810852

Cite this article as:
Bigatti, A.M., Caboara, M. & Robbiano, L. AAECC (1991) 2: 21. doi:10.1007/BF01810852

Abstract

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[X1,⋯, 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.

Keywords

Hilbert functionsPoincaré seriesBorel-normed ideals

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Anna Maria Bigatti
    • 1
  • Massimo Caboara
    • 1
  • Lorenzo Robbiano
    • 1
  1. 1.Departimento di Matematica dell'Universitá di GenovaGenovaItaly