A new algorithmic scheme for computing characteristic sets

  • Authors:

  • Meng Jin;Xiaoliang Li;Dongming Wang

  • Affiliations:

  • SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100195, China;School of Computer Science, Dongguan University of Technology, Dongguan, Guangdong 523808, China;Laboratoire dInformatique de Paris 6, CNRS, Université Pierre et Marie Curie, 4 place Jussieu, BP 169, 75252 Paris Cedex 05, France

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2013

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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.