We show that the generic zeros of a differential ideal [A]:H∞A defined by a differential chain A are birationally equivalent to the general zos of a single regular differential polynomial.Expand

Abstract Within a constructive homological algebra approach, we study the factorization and decomposition problems for a class of linear functional (determined, over-determined, under-determined)… Expand

We present a new algorithm for computing exponential solutions of differential operators with rational function coefficients that uses a combination of local and modular computations.Expand

We consider the problem of computing regular formal solutions of systems of linear differential equations with analytic coefficients. The classical approach consists in reducing the system to an… Expand

In this paper, we show how to conjointly use module theory and constructive homological algebra to obtain general conditions for a matrix R of functional operators (e.g.,… Expand

We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections by adapting existing algorithms handling ordinary linear differential systems.Expand

We investigate polynomial solutions of homogeneous linear differential equations with coefficients that are polynomials with integer coefficients.Expand

Les methodes modulaires conduisent a des algorithmes tres efficaces dans de nombreux domaines en calcul formel et notamment dans celui des equations algebriques. Le but de cette these est de montrer… Expand