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 equation...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 Hamiltonianian 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.展开更多
The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate main...The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.展开更多
文摘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 Hamiltonianian 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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11971161 and 11871207。
文摘The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.
