Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials
Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials
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DOI：
10.1007/978-3-662-43799-5_32
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
Zhi‐Yong Zhang;C. Yuan;X. Gao
中科院分区：
文献类型：
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作者：
Zhi‐Yong Zhang;C. Yuan;X. Gao
本文给出了一阶任意阶微分不定方程组中两个一般常微分多项式微分结果的矩阵表示。即，构造非奇异矩阵，使得其行列式包含微分结果作为因子。此外，被视为多项式 in 的 和 的代数稀疏结果被证明是 和 的微分结果的非零倍数。虽然很特别，但这似乎是一类非线性通用微分多项式的第一个矩阵表示。
In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomialsandin the differential indeterminatewith order one and arbitrary degree is given. That is, a nonsingular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant ofandtreated as polynomials inis shown to be a nonzero multiple of the differential resultant ofand. Although very special, this seems to be the first matrix representation for a class of nonlinear generic differential polynomials.