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arXiv · 1204.3773

Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials

Zhi-Yong Zhang·Chun-Ming Yuan·Xiao-Shan Gao
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Abstract

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 $f_1, f_2, \delta f_1, \delta f_2$ 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.

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Zhi-Yong Zhang, Chun-Ming Yuan, Xiao-Shan Gao. 2012-04-17. Matrix Formula of Differential Resultant for First Order Generic Ordinary Differential Polynomials. https://arxiv.org/abs/1204.3773

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