| 矩阵多元多项式的带余除法及其应用 |
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| 引用本文： | 阿拉坦仓,张鸿庆,钟万勰.矩阵多元多项式的带余除法及其应用[J].应用数学和力学,2000,21(7):661-668. |
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| 作者姓名： | 阿拉坦仓 张鸿庆 钟万勰 |
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| 作者单位： | 1. 内蒙古大学,呼和浩特,010021
2. 大连理工大学,大连,116023 |
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| 基金项目： | 国家自然科学基金!资助项目 (1970 2 0 0 7)，内蒙古自然科学基金!资助项目 (97130 1_1) |
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| 摘 要： | 给出矩阵多元多项式的带余除法，从而用微分代数的观点，得到把一类微分方程（组）化为无穷维Ｈａｍｉｌｔｏｎ系统的充要条件及其具体无穷维Ｈａｍｉｌｔｏｎ系统形式，再把此方法和吴方法相结合获得构造一类微分方程（组）的通解的新方法，几个例子表明这些方法都很有效的。
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| 关 键 词： | 矩阵多元多项式 带余除法 微分方程 哈米顿系统 |
| 修稿时间： | 1999-01-21 |
Pseudo-Division Algorithm for Matrix Multivariable Polynomial and Its Application |
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| Alatancang,Zhang Hongqing,Zhong Wanxie.Pseudo-Division Algorithm for Matrix Multivariable Polynomial and Its Application[J].Applied Mathematics and Mechanics,2000,21(7):661-668. |
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| Authors: | Alatancang Zhang Hongqing Zhong Wanxie |
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| Abstract: | Pseudo-division
algorithm for matrix multivariable polynomial are given, thereby with the view of
differential algebra, the sufficient and necessary conditions for transforming a class of
partial differential equations into infinite dimensional Hamiltonian system and its
concrete form are obtained. Then by combining this method with Wu's method, a new method
of constructing general solution of a class of mechanical equations is got, which several
examples show very effective. |
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| Keywords: | matrix multivarible polynomial infinite dimensional Hamiltonian system Wu's method general solution |
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