KMS Of Academy of mathematics and systems sciences, CAS
A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x] | |
Jing, Rui-Juan; Yuan, Chun-Ming; Gao, Xiao-Shan | |
2019-01-10 | |
Source Publication | THEORETICAL COMPUTER SCIENCE |
ISSN | 0304-3975 |
Volume | 755Pages:89-109 |
Abstract | In this paper, we give the first polynomial time algorithm to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Grobner basis of the Z[x]-module generated by the column vectors of F. The algorithm has polynomial bit size computational complexities and is also shown to be practically more efficient than existing algorithms. The algorithm is based on three key ingredients. First, an F4 style algorithm to compute the Grobner basis is adopted, where a novel prolongation is designed such that the sizes of coefficient matrices under consideration are nicely controlled. Second, the complexity bound of the algorithm is achieved by a nice estimation for the degree and height bounds of the polynomials in the generalized Hermite normal form. Third, fast algorithms to compute Hermite normal forms of matrices over Z are used as the computational tool. (C) 2018 Elsevier B.V. All rights reserved. |
Keyword | Generalized Hermite normal form Grobner basis Polynomial-time algorithm Z[x] module |
DOI | 10.1016/j.tcs.2018.07.003 |
Language | 英语 |
Funding Project | NSFC[11688101] |
WOS Research Area | Computer Science |
WOS Subject | Computer Science, Theory & Methods |
WOS ID | WOS:000456359300008 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32138 |
Collection | 系统科学研究所 |
Corresponding Author | Gao, Xiao-Shan |
Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, UCAS, KLMM, Beijing 100190, Peoples R China |
Recommended Citation GB/T 7714 | Jing, Rui-Juan,Yuan, Chun-Ming,Gao, Xiao-Shan. A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x][J]. THEORETICAL COMPUTER SCIENCE,2019,755:89-109. |
APA | Jing, Rui-Juan,Yuan, Chun-Ming,&Gao, Xiao-Shan.(2019).A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x].THEORETICAL COMPUTER SCIENCE,755,89-109. |
MLA | Jing, Rui-Juan,et al."A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x]".THEORETICAL COMPUTER SCIENCE 755(2019):89-109. |
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