  We discuss the problem of determining reduction number of a polynomial ideal
I in n variables. We present two algorithms based on parametric computations.
The first one determines the absolute reduction number of I and requires
computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I)
variables. The second one computes via a Grobner system the set of all
reduction numbers of the ideal I and thus in particular also its big reduction
number. However,it requires computations in a ring with n.dim(I) parameters and
n variables.
