We prove effective Nullstellensatz and elimination theorems for difference equations in
sequence rings. More precisely, we compute an explicit function of geometric quantities …

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 …

In this paper we introduce holonomic tree automata: a common extension of weighted tree
automata and holonomic recurrences. We show that the generating function of the tree …

In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain
type of systems of autonomous ordinary differential equations. More precisely, we deal with …

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 …

An important and challenging computational problem is to identify and include the missing
compatibility (integrability) conditions for general systems of partial differential equations …

Triangular decomposition is one of the standard ways to represent the radical of a
polynomial ideal. A general algorithm for computing such a decomposition was proposed by …

We present a method for rejecting competing models from noisy time‐course data that does
not rely on parameter inference. First we characterize ordinary differential equation models …

When can a primitive of a given algebraic function be con-structed by iteratively solving
algebraic equations and composing withthe primitives of some other given algebraic …

In this paper, we study unirational differential curves and the corresponding differential
rational parametrizations. We first investigate basic properties of proper differential rational …