| Solving Multivariate Polynomial Matrix Diophantine Equations with Gr?bner Basis Method |
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| 作者姓名： | XIAO Fanghui LU Dong WANG Dingkang |
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| 作者单位： | 1. College of Mathematics and Statistics, Hunan Normal University;2. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University;3. School of Mathematical Sciences, Beihang University;4. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences;5. School of Mathematical Sciences, University of Chinese Academy of Sciences |
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| 基金项目： | supported by the National Natural Science Foundation of China under Grant No.12001030；;the National Key Research and Development Project2020YFA0712300； |
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| 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?bner bases for modules, the problem for determining and computing the solution of matrix Diophantine equations can be solved. Meanwh...
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