How to compute the Hilbert depth of a graded ideal

Abstract

We give two algorithms for computing the Hilbert depth of a \emph{graded ideal} in the polynomial ring. These algorithms work efficiently for (squarefree) lex ideals. As a consequence, we construct counterexamples to some conjectures made by Shen in \cite{B:Sh2}.Comment: In this new version, we have added some materials about comparing Algorithm 2.16 to Popescu's algorithm and Bruns et al's algorith