A New Algorithmic Scheme for Computing Characteristic Sets

TL;DR

This paper introduces a new algorithmic scheme for computing generalized characteristic sets of polynomial systems, replacing pseudo-division with other reductions, leading to improved performance and simpler outputs.

Contribution

The paper presents a novel algorithmic framework that uses alternative admissible reductions for characteristic set computation, enhancing efficiency and simplicity over traditional methods.

Findings

Outperforms Ritt-Wu's algorithm in computation time

Produces simpler and more manageable outputs

Effective on complex polynomial examples

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.