Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method

doi:10.1007/s11424-021-0072-x

	Solving Multivariate Polynomial Matrix Diophantine Equations with Grobner Basis Method
	Xiao Fanghui 1; Lu Dong 4,5; Wang Dingkang 2,3
刊名	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
	2021-02-04
页码	14
关键词	Grö bner basis matrix Diophantine equation module multivariate polynomial
ISSN号	1009-6124
DOI	10.1007/s11424-021-0072-x
英文摘要	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.
资助项目	National Natural Science Foundation of China[12001030] ; CAS Key Project[QYZDJ-SSW-SYS022] ; National Key Research and Development Project[2020YFA0712300]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000614789100008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58119]
专题	中国科学院数学与系统科学研究院
通讯作者	Lu Dong
作者单位	1.Hunan Normal Univ, Coll Math & Stat, Changsha 410006, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 5.Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China
推荐引用方式 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.