A perturbed differential resultant based implicitization algorithm for linear DPPEs

Let \bbK be an ordinary differential field with derivation $\partial$. Let \cP be a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters with implicit ideal \id. Given a nonzero linear differential polynomial $A$ in \id we give necessary and sufficient conditions on $A$ for \cP to be $n-1$ dimensional. We prove the existence of a linear perturbation \cP_{\phi} of \cP so that the linear complete differential resultant \dcres_{\phi} associated to \cP_{\phi} is nonzero. A nonzero linear differential polynomial in \id is obtained from the lowest degree term of \dcres_{\phi} and used to provide an implicitization algorithm for \cP

Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P