KMS Of Academy of mathematics and systems sciences, CAS
| Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method | |
| Xiao Fanghui1; Lu Dong2,3; Wang Dingkang4,5 | |
| 2021-02-04 | |
| Source Publication | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| ISSN | 1009-6124 |
| Pages | 14 |
| Abstract | Different from previous viewpoints, multivariate polynomial matrix Diophantine equations are studied from the perspective of modules in this paper, that is, regarding the columns of matrices as elements in modules. A necessary and sufficient condition of the existence for the solution of equations is derived. Using powerful features and theoretical foundation of Grobner bases for modules, the problem for determining and computing the solution of matrix Diophantine equations can be solved. Meanwhile, the authors make use of the extension on modules for the GVW algorithm that is a signature-based Grobner basis algorithm as a powerful tool for the computation of Grobner basis for module and the representation coefficients problem directly related to the particular solution of equations. As a consequence, a complete algorithm for solving multivariate polynomial matrix Diophantine equations by the Grobner basis method is presented and has been implemented on the computer algebra system Maple. |
| Keyword | Grö bner basis matrix Diophantine equation module multivariate polynomial |
| DOI | 10.1007/s11424-021-0072-x |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[12001030] ; CAS Key Project[QYZDJ-SSW-SYS022] ; National Key Research and Development Project[2020YFA0712300] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000614789100008 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58120 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Lu Dong |
| Affiliation | 1.Hunan Normal Univ, Coll Math & Stat, Changsha 410006, Peoples R China 2.Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China 3.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Xiao Fanghui,Lu Dong,Wang Dingkang. Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2021:14. |
| APA | Xiao Fanghui,Lu Dong,&Wang Dingkang.(2021).Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,14. |
| MLA | Xiao Fanghui,et al."Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2021):14. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment