典型文献
Solving Multivariate Polynomial Matrix Diophantine Equations with Gr(o)bner Basis Method
文献摘要：
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 Gr(o)bner 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 Gr(o)bner basis algorithm as a powerful tool for the computation of Gr(o)bner 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 Gr(o)bner basis method is presented and has been implemented on the computer algebra system Maple.
文献关键词：
中图分类号：
作者姓名：
XIAO Fanghui;LU Dong;WANG Dingkang
作者机构：
College of Mathematics and Statistics,Hunan Normal University,Changsha 410006,China;Beijing Advanced Innovation Center for Big Data and Brain Computing,Beihang University,Beijing 100191,China;School of Mathematical Sciences,Beihang University,Beijing 100191,China;KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China
文献出处：
引用格式：
[1]XIAO Fanghui;LU Dong;WANG Dingkang-.Solving Multivariate Polynomial Matrix Diophantine Equations with Gr(o)bner Basis Method)[J].系统科学与复杂性学报（英文版）,2022(01):413-426
A类：
GVW
B类：
Solving,Multivariate,Polynomial,Matrix,Diophantine,Equations,Gr,bner,Basis,Method,Different,from,previous,viewpoints,multivariate,polynomial,matrix,equations,are,studied,perspective,modules,this,paper,that,regarding,columns,matrices,elements,necessary,sufficient,condition,existence,solution,derived,Using,powerful,features,theoretical,foundation,bases,problem,determining,computing,can,solved,Meanwhile,authors,make,use,extension,algorithm,signature,basis,tool,computation,representation,coefficients,directly,related,particular,consequence,complete,solving,by,method,presented,has,been,implemented,computer,algebra,system,Maple
AB值：
0.540945
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