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Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method
Xiao Fanghui1; Lu Dong2,3; Wang Dingkang4,5
2021-02-04
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Pages14
AbstractDifferent 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.
KeywordGrö bner basis matrix Diophantine equation module multivariate polynomial
DOI10.1007/s11424-021-0072-x
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[12001030] ; CAS Key Project[QYZDJ-SSW-SYS022] ; National Key Research and Development Project[2020YFA0712300]
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000614789100008
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58120
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLu Dong
Affiliation1.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.
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