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arXiv · 1108.1486

A New Algorithmic Scheme for Computing Characteristic Sets

Meng Jin·Xiaoliang Li·Dongming Wang
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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.

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Meng Jin, Xiaoliang Li, Dongming Wang. 2011-08-06. A New Algorithmic Scheme for Computing Characteristic Sets. https://arxiv.org/abs/1108.1486

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