Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries
Résumé
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.
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