This paper addresses systems of linear functional equations from an algebraic point of view.
We give an introduction to and an overview of recent work by a small group of people …

The purpose of this paper is to give four new applications of the Quillen-Suslin theorem to
mathematical systems theory. Using a constructive version of the Quillen-Suslin theorem …

Investigating the correspondence between systems of partial differential equations and their
analytic solutions using a formal approach, this monograph presents algorithms to …

We algorithmically construct multi-output Gaussian process priors which satisfy linear
differential equations. Our approach attempts to parametrize all solutions of the equations …

In this paper, we consider systems of algebraic and non-linear partial differential equations
and inequations. We decompose these systems into so-called simple subsystems and …

In this paper we describe an efficient involutive algorithm for constructing Groebner bases of
polynomial ideals. The algorithm is based on the concept of involutive monomial division …

An introduction to constructive algebraic analysis and its applications Page 1 Journées
Nationales de Calcul Formel Rencontre organisée par : Jean-Guillaume Dumas, Grégoire …

In this paper we consider finite difference approximations for numerical solving of systems of
partial differential equations of the form f 1=⊙⊙⊙= fp= 0, where F:={f 1,..., fp} is a set of …

A Maple package for computing Gröbner bases of linear difference ideals is described. The
underlying algorithm is based on Janet and Janet-like monomial divisions associated with …

Janet's algorithm to create normal forms for systems of linear pdes is outlined and used as a
tool to construct resolutions for finitely generated modules over polynomial rings over fields …