Additive Normal Forms and Integration of ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Additive Normal Forms and Integration of Differential Fractions
Author(s) :
Boulier, François [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Lallemand, Joseph [Auteur]
École normale supérieure - Cachan [ENS Cachan]
Lemaire, Francois [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Regensburger, Georg [Auteur]
Johann Radon Institute for Computational and Applied Mathematics [RICAM]
Rosenkranz, Markus [Auteur]
University of Kent [Canterbury]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Lallemand, Joseph [Auteur]
École normale supérieure - Cachan [ENS Cachan]
Lemaire, Francois [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Regensburger, Georg [Auteur]
Johann Radon Institute for Computational and Applied Mathematics [RICAM]
Rosenkranz, Markus [Auteur]
University of Kent [Canterbury]
Journal title :
Journal of Symbolic Computation
Publisher :
Elsevier
Publication date :
2016
ISSN :
0747-7171
English keyword(s) :
Differential algebra
differential fraction
integration
differential fraction
integration
HAL domain(s) :
Informatique [cs]/Calcul formel [cs.SC]
English abstract : [en]
This paper presents two new normal forms for fractions ofdifferential polynomials, as well as algorithms for computingthem. The first normal form allows to write a fraction as thederivative of a fraction plus a non ...
Show more >This paper presents two new normal forms for fractions ofdifferential polynomials, as well as algorithms for computingthem. The first normal form allows to write a fraction as thederivative of a fraction plus a non integrable part. The secondnormal form is an extension of the first one, involving iterateddifferentiations. The main difficulty in this paper consists indefining normal forms which are linear operations over the fieldof constants, a property which was missing in our previous works.Our normal forms do not require fractions to be converted intopolynomials, a key feature for further problems such asintegrating differential fractions, and more generally solvingdifferential equations.Show less >
Show more >This paper presents two new normal forms for fractions ofdifferential polynomials, as well as algorithms for computingthem. The first normal form allows to write a fraction as thederivative of a fraction plus a non integrable part. The secondnormal form is an extension of the first one, involving iterateddifferentiations. The main difficulty in this paper consists indefining normal forms which are linear operations over the fieldof constants, a property which was missing in our previous works.Our normal forms do not require fractions to be converted intopolynomials, a key feature for further problems such asintegrating differential fractions, and more generally solvingdifferential equations.Show less >
Language :
Anglais
Popular science :
Non
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