矩阵多元多项式的带余除法及其应用

基金项目: 国家自然科学基金资助项目(19702007);内蒙古自然科学基金资助项目(971301-1)

Pseudo-Division Algorithm for Matrix Multivariable Polynomial and Its Application

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。
- 矩阵多元多项式 /
- 无穷维Hamilton系统 /
- 吴方法 /
- 通解
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 andits 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 equationsis got, which several examples show very effective.
- matrix multivarible polynomial /
- infinite dimensional Hamiltonian system /
- Wu’smethod /
- general solution

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