The effective differential Nullstellensatz is a fundamental result in the computational theory of algebraic differential equations. It allows one to reduce problems about differential equations to problems about polynomial equations. In particular, it provides an algorithm for checking consistency of a system of algebraic differential equations and an algorithm for testing membership in radical differential ideals. This problem and related questions received much attention during the last decade. An upper bound for the effective differential Nullstellensatz was improved several times. For the case of one derivation, we present a new bound, which is asymptotically significantly better than the previously known bounds. Moreover, our bound is the first bound that has feasible numerical values from the computational point of view.
Forschungs-