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Paper   IPM / M / 13483
School of Mathematics
  Title:   Deterministically computing reduction numbers of polynomial ideals
  Author(s):  A. Hashemi (Joint with M. Schweinfurter and W. M. Seiler)
  Status:   Published
  Journal: LNCS
  Vol.:  8660
  Year:  2014
  Pages:   188-203
  Supported by:  IPM
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 �?? 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 dimI parameters and n variables.

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