| 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; |
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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 无穷维Hamilton系统 吴方法 通解 |
| 收稿时间： | 1999-01-21 |
| 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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| Affiliation: | 1.Inner Mongolia University, Hohhot 010021, P R China;2.Dalian University of Technology, Dalian 116023, P R China |
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| Abstract: | Pseudo-divisionalgorithm for matrix multivariable polynomial are given, thereby with the view ofdifferential algebra, the sufficient and necessary conditions for transforming a class ofpartial differential equations into infinite dimensional Hamiltonian system and itsconcrete form are obtained. Then by combining this method with Wu's method, a new methodof constructing general solution of a class of mechanical equations is got, which severalexamples show very effective. |
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| Keywords: | matrix multivarible polynomial infinite dimensional Hamiltonian system Wu's method general solution |
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