Linear Complete Differential Resultants and the Implicitization of Linear DPPEs

TL;DR

This paper introduces the concept of linear complete differential resultants and explores their use in computing implicit equations for systems of linear differential parametric equations, providing conditions for system properness.

Contribution

It defines linear complete differential resultants and applies them to implicitization of linear DPPEs, including criteria for system properness.

Findings

Defined linear complete differential resultants.

Established methods for implicitization of linear DPPEs.

Provided necessary conditions for system properness.

Abstract

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters. We give necessary conditions to ensure properness of the system of differential polynomial parametric equations.