A perturbed differential resultant based implicitization algorithm for linear DPPEs

摘要

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.