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

Alexandre Sedoglavic 1, 2, 3, *
* Corresponding author
1 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
3 CALFOR - Calcul Formel
LIFL - Laboratoire d'Informatique Fondamentale de Lille
Abstract : 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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Alexandre Sedoglavic. Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries. Algebraic Biology 2007, Jul 2007, RISC, Castle of Hagenberg, Austria, Austria. pp.277-291, ⟨10.1007/978-3-540-73433-8_20⟩. ⟨inria-00120991⟩

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