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

Alexandre Sedoglavic 1, 2, 3, *
* Auteur correspondant
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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Communication dans un congrès
H. Anai and K. Horimoto and T. Kutsia. Algebraic Biology 2007, Jul 2007, RISC, Castle of Hagenberg, Austria, Austria. Springer, 4545, pp.277-291, 2007, Lecture Notes in Computer Science,. 〈10.1007/978-3-540-73433-8_20〉
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Alexandre Sedoglavic. Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries. H. Anai and K. Horimoto and T. Kutsia. Algebraic Biology 2007, Jul 2007, RISC, Castle of Hagenberg, Austria, Austria. Springer, 4545, pp.277-291, 2007, Lecture Notes in Computer Science,. 〈10.1007/978-3-540-73433-8_20〉. 〈inria-00120991〉

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