A perturbed differential resultant based implicitization algorithm for linear DPPEs

Let K be an ordinary differential field with derivation ∂. Let P 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 P to be n−1 dimensional. We prove the existence of a linear perturbation Pϕ of P, so that the linear complete differential resultant ∂CResϕ associated to Pϕ is nonzero. A nonzero linear differential polynomial in ID is obtained, from the lowest degree term of ∂CResϕ, and used to provide an implicitization for P.