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 algorithm for P.