期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 60, 期 11, 页码 2983-2997出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.09.059
关键词
Simple set; Finite field; Regular set; Squarefree decomposition; pth root extraction
资金
- Chinese National Key Basic Research (973) Project [2005CB321901/2]
- SKLSDE [BUAA-SKLSDE-09KF-01]
- ANR-NSFC [ANR-09-BLAN-0371-01]
- Agence Nationale de la Recherche (ANR) [ANR-09-BLAN-0371] Funding Source: Agence Nationale de la Recherche (ANR)
This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product determined by a simple set. As a subprocedure of the generalized squarefree decomposition approach, a method is proposed to extract the pth root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms. (C) 2010 Elsevier Ltd. All rights reserved.
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