  Lie group theory states that knowledge of a $m$-parameters solvable group of
symmetries of a system of ordinary differential equations allows to reduce by
$m$ the number of equations. We apply this principle by finding some
\emph{affine derivations} that induces \emph{expanded} Lie point symmetries of
considered system. By rewriting original problem in an invariant coordinates
set for these symmetries, we \emph{reduce} the number of involved parameters.
We present an algorithm based on this standpoint whose arithmetic complexity is
\emph{quasi-polynomial} in input's size.

Symbolic Computation