Linear differential implicitization and differential resultants

Abstract

Given a system P of n linear ordinary differential polynomial parametric equations (linear DPPEs) in n−1 differential parameters, we proved in [2] that if nonzero a differential resultant gives the implicit equation of P. Differential resultants often vanish under specialization, which prevented us from giving an implicitization algorithm in [2]. Motivated by Canny's method and its generalizations we consider now a linear perturbation of P and use it to give an algorithm to decide if the dimension of the implicit ideal of P is n − 1 and in the affirmative case obtain the implicit equation of P. This poster presentation will contain this development together with examples illustrating the results. An extended version of this work can be found in [1].