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 …

We consider n * n-matrices whose entries are scalar ordinary differential operators of
order\leqslant d over a constructive differential field K. We show that to choose an algorithm …

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 …

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 …

We link n-jets of the affine monomial scheme defined by xp to the stable set polytope of
some perfect graph. We prove that, as p varies, the dimension of the coordinate ring of a …

We review our work on elimination theory for algebraic differential and difference equations
over the past decade, highlighting some key developments. Our journey began with the …

We present bounds for the geometric degree of the tangent bundle and the tangential variety
of a smooth affine algebraic variety $ V $ in terms of the geometric degree of $ V $. We first …

One method to determine whether or not a system of partial differential equations is
consistent is to attempt to construct a solution using merely the “algebraic data” associated …

Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic
set method, the resultant and the Chow form are three fundamental tools in the elimination …