A characterization of reduced forms of ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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 >
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
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