A polynomial-time algorithm to compute generalized Hermite normal forms of matrices over Z[x]
文献类型：期刊论文
| 作者 | Jing, Rui-Juan; Yuan, Chun-Ming ; Gao, Xiao-Shan
|
| 刊名 | THEORETICAL COMPUTER SCIENCE
 |
| 出版日期 | 2019-01-10 |
| 卷号 | 755页码:89-109 |
| 关键词 | Generalized Hermite normal form Grobner basis Polynomial-time algorithm Z[x] module |
| ISSN号 | 0304-3975 |
| DOI | 10.1016/j.tcs.2018.07.003 |
| 英文摘要 | 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. |
| 资助项目 | NSFC[11688101] |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000456359300008 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32137]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Gao, Xiao-Shan |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, UCAS, KLMM, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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