一阶一般常微分多项式微分结式的矩阵公式
Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials
摘要：
给出了任意阶一阶微分不定$y$中两个一般常微分多项式$f_1$和$f_2$的微分结式的矩阵表示.也就是说，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，将$f_1, f_2, δf_1, δf_2$的代数稀疏结果作为$y, y', y"$中的多项式处理，证明了它是$f_1, f_2$的微分结果的非零倍数.虽然非常特殊，这似乎是第一个矩阵表示的一类非线性一般微分多项式。
英文摘要：
In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials $f_1$ and $f_2$ in the differential indeterminate $y$ with order one and arbitrary degree is given. That is, a non-singular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant of $f_1, f_2, δf_1, δf_2$ treated as polynomials in $y, y', y"$ is shown to be a non-zero multiple of the differential resultant of $f_1, f_2$. Although very special, this seems to be the first matrix representation for a class of nonlinear generic differential polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
