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We discuss the problem of determining reduction numbers 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 computations in a polynomial ring with (n ï¿½?? dim I) dim I parameters and n ï¿½?? 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 dimI parameters and n variables.
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