Theory of Multiple Polynomial Remainder Sequence

Sasaki, Tomohiro; Furukawa, Akio

doi:10.2977/prims/1195181611

Cited by 6 publications

(1 citation statement)

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“…In this paper we follow the work of Wang (2001a) to present a new algorithmic scheme for computing generalized characteristic sets efficiently. To compute characteristic sets, one can replace pseudo-division by one-step pseudo-reduction, but this does not enhance the efficiency very much because extraneous factors for the pseudo-rests may be created (see the analysis in Sasaki andFurukawa 1984 andWang 2001a). Our intention here is to design a reduction mechanism that can take advantage of the structure and properties of the polynomials under consideration and thus provide more flexibility for reduction strategies.…”

Section: Introductionmentioning

confidence: 99%

A new algorithmic scheme for computing characteristic sets

Jin

Wang

2013

Journal of Symbolic Computation

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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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