We prove a theorem, which provides a formula for the computation of the Poincar\'e series of a monomial ideal in \$k[X_1,\dots,X_n]\$, via the computation of the Poincare' series of some monomial ideals in \$k[X_1,\dots ,\widehat{X_i}, \dots,X_n]\$. 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 Poincare' series of graded modules over standard algebras.

### On the computation of Hilbert-Poincare` Series

#### Abstract

We prove a theorem, which provides a formula for the computation of the Poincar\'e series of a monomial ideal in \$k[X_1,\dots,X_n]\$, via the computation of the Poincare' series of some monomial ideals in \$k[X_1,\dots ,\widehat{X_i}, \dots,X_n]\$. 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 Poincare' series of graded modules over standard algebras.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11567/509119`
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