We show new upper and lower bounds for the effective differential Nullstellensatz for
differential fields of characteristic zero with several commuting derivations. Seidenberg was …

Using the functional interpretation from proof theory, we analyze nonconstructive proofs of
several central theorems about polynomial and differential polynomial rings. We extract …

Motivated by the effective bounds found in [12] for ordinary differential equations, we prove
an effective version of uniform bounding for fields with several commuting derivations. More …

Motivated by the problem of the existence of bounds on degrees and orders in checking
primality of radical (partial) differential ideals, the nonstandard methods of van den Dries …

The aim of this thesis is a quantitative analysis of the set of solutions of a system of
differential equations. For this aim, this thesis generalizes the differential dimension …

We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of
differential algebraic equations over any field of constants K of characteristic 0. Let x be a set …

Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a
problem of general interest. The problem of finding an a priori upper bound for the number of …

In this paper, we first introduce the concept of Laurent differentially essential systems and
give a criterion for a Laurent differential polynomial system to be Laurent differentially …

Understanding bounds for the effective differential Nullstellensatz is a central problem in
differential algebraic geometry. Recently, several bounds have been obtained using …

We compute an upper bound for the orders of derivatives in the Rosenfeld-Grobner
algorithm. This algorithm computes a regular decomposition of a radical differential ideal in …