  A differential system $[A] : \; Y'=AY$, with $A\in \mathrm{Mat}(n, \bar{k})$
is said to be in reduced form if $A\in \mathfrak{g}(\bar{k})$ 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.
