A characterization of reduced forms of linear differential systems

Aparicio-Monforte, Ainhoa; Compoint, Elie; Weil, Jacques-Arthur

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jpaa.2012.11.007

Title :

A characterization of reduced forms of linear differential systems

Author(s) :

Aparicio-Monforte, Ainhoa [Auteur]
Calcul Formel [CALFOR]
Laboratoire d'Informatique Fondamentale de Lille [LIFL]
Compoint, Elie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Weil, Jacques-Arthur [Auteur]
DMI [XLIM-DMI]

Journal title :

Journal of Pure and Applied Algebra

Pages :

1504-1516

Publisher :

Elsevier

Publication date :

2013

ISSN :

0022-4049

HAL domain(s) :

Informatique [cs]/Calcul formel [cs.SC]

English abstract : [en]

A differential system [A] : Y' = AY, with A is an element of Mat(n, (k) over bar) is said to be in reduced form if A is an element of g((k) over bar) where g is the Lie algebra of the differential Galois group G of [A].In ...
Show more >A differential system [A] : Y' = AY, with A is an element of Mat(n, (k) over bar) is said to be in reduced form if A is an element of g((k) over bar) where g is the Lie algebra of the differential Galois group G of [A].In this article, we give a constructive criterion for a system to be in reduced form. When G is reductive and unimodular, the system [A] is in reduced form if and only if all of its invariants (rational solutions of appropriate symmetric powers) have constant coefficients (instead of rational functions). When G is non-reductive, we give a similar characterization via the semi-invariants of G. In the reductive case, we propose a decision procedure for putting the system into reduced form which, in turn, gives a constructive proof of the classical Kolchin-Kovacic reduction theorem.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1206.6661
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