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

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 $y,y^{\prime },y"$ 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.

References in corpus (1)

• Intersection Theory in Differential Algebraic Geometry: Generic Intersections and the Differential Chow Form