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TitleA characterization of reduced forms of linear differential systems
Author(s) Ainhoa Aparicio-Monforte, Elie Compoint, Jacques-Arthur Weil
TypeArticle in Journal
AbstractA differential system [ A ] : Y ′ = A Y , with A ∈ Mat ( n , k ¯ ) is said to be in reduced form if A ∈ g ( k ¯ ) 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.
URL http://www.sciencedirect.com/science/article/pii/S0022404912003404
JournalJournal of Pure and Applied Algebra
Pages1504 - 1516
Translation No
Refereed No