Skip to Main content Skip to Navigation

Étude et implantation de quelques algorithmes en algèbre différentielle

Abstract : This thesis aims at making effective some theorems and at implemeting efficiently some algorithms in differential algebra in order to apply them to the nonlinear control theory. We present three original results. The first one is an algorithm, Rosenfeld-Gröbner, which describes the models of a polynomial system of equations and inequations in differential algebra (ordinary or with partial derivatives). The algorithm solves the emptyness problem hence the membership problem to radicals of finitely generated differential ideals. Our second result is a method which computes the characteristic set of a prime differential ideal given by a generating family. We last give some new proofs for Seidenberg's elimination algorithms. The algorithms that we describe are effective: they only rely on addition, multiplication, derivations and the the equality to zero test in the base field of the equations.
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download
Contributor : François Boulier <>
Submitted on : Thursday, March 22, 2007 - 12:15:07 PM
Last modification on : Thursday, February 21, 2019 - 10:52:44 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 9:54:42 PM


  • HAL Id : tel-00137866, version 1



François Boulier. Étude et implantation de quelques algorithmes en algèbre différentielle. Modélisation et simulation. Université des Sciences et Technologie de Lille - Lille I, 1994. Français. ⟨tel-00137866⟩



Record views


Files downloads