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A new algorithmic scheme for computing characteristic sets

Meng Jin 1 Xiaoliang Li 2 Dongming Wang 3 
3 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : Ritt-Wu@?s algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for computing generalized characteristic sets by introducing other admissible reductions than pseudo-division. A concrete subalgorithm is designed to triangularize polynomial sets using selected admissible reductions and several effective elimination strategies and to replace the algorithm of basic sets (used in Ritt-Wu@?s algorithm). The proposed algorithm has been implemented and experimental results show that it performs better than Ritt-Wu@?s algorithm in terms of computing time and simplicity of output for a number of non-trivial test examples
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Submitted on : Thursday, February 21, 2013 - 4:12:48 PM
Last modification on : Friday, January 21, 2022 - 3:22:10 AM

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Meng Jin, Xiaoliang Li, Dongming Wang. A new algorithmic scheme for computing characteristic sets. Journal of Symbolic Computation, Elsevier, 2013, 50, pp.431-449. ⟨10.1016/j.jsc.2012.04.004⟩. ⟨hal-00793120⟩



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