Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

2011/01/19 by Jin-San Cheng, Xiao-Shan Gao, Cheng, Jin-San +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Coding theory and cryptography #FOS: Computer and information sciences #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC

paper · pdf · doi:10.48550/arxiv.1101.3603

18 pages

arxiv created 2011/01/19 · openalex publication_date 2011/01/19 · arxiv updated 2011/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.

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