Summary: We discuss the problem of determining reduction numbers of a polynomial ideal \(\mathcal{I}\) in \(n\) variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of \(\mathcal{I}\) and requires computations in a polynomial ring with \((n-\dim \mathcal{I})\dim \mathcal{I}\) parameters and \(n - \dim \mathcal{I}\) variables. The second one computes via a Gröbner system the set of all reduction numbers of the ideal \(\mathcal{I}\) and thus in particular also its big reduction number. However, it requires computations in a ring with \(n \dim \mathcal{I}\) parameters and \(n\) variables.
For the entire collection see [Zbl 1295.68022].