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CSpace
Squarefree normal representation of zeros of zero-dimensional polynomial systems
Xu, Juan1; Wang, Dongming2,3; Lu, Dong4
2024-05-01
摘要For any zero-dimensional polynomial ideal a and any nonzero polynomial F, this paper shows that the union of the multi-set of zeros of the ideal sum a + (F) and that of the ideal quotient a : (F) is equal to the multi-set of zeros of a, where zeros are counted with multiplicities. Based on this zero relation and the computation of Grobner bases, a complete multiplicity-preserved algorithm is proposed to decompose any zero-dimensional polynomial set into finitely many squarefree normal triangular sets, resulting in a squarefree normal representation for the zeros of the polynomial set. In the representation the multiplicities of the zeros of the triangular sets can be read out directly. Examples and experiments are presented to illustrate the algorithm and its performance.(c) 2023 Elsevier Ltd. All rights reserved.
关键词Polynomial system Multiplicity Triangular decomposition Normal set Simple set
DOI10.1016/j.jsc.2023.102273
发表期刊JOURNAL OF SYMBOLIC COMPUTATION
ISSN0747-7171
卷号122页码:14
通讯作者Xu, Juan(xujuan@cigit.ac.cn)
收录类别SCI
WOS记录号WOS:001125101100001
语种英语