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- W4296572937 abstract "A differential system $[A] : ; Y'=AY$, with $Ain mathrm{Mat}(n, bar{k})$ is said to be in reduced form if $Ain mathfrak{g}(bar{k})$ where $mathfrak{g}$ 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." @default.
- W4296572937 created "2022-09-21" @default.
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- W4296572937 date "2012-06-28" @default.
- W4296572937 modified "2023-09-29" @default.
- W4296572937 title "A Characterization of Reduced Forms of Linear Differential Systems" @default.
- W4296572937 doi "https://doi.org/10.48550/arxiv.1206.6661" @default.
- W4296572937 hasPublicationYear "2012" @default.
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