Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries
<|reference_start|>Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries: 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.<|reference_end|>
@article{sedoglavic2006reduction,
    title={Reduction of Algebraic Parametric Systems by Rectification of their
  Affine Expanded Lie Symmetries},
    author={Alexandre Sedoglavic (INRIA Futurs, LIFL)},
    journal={Dans Algebraic Biology 2007 4545 (2007) 277--291},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0612094},
    primaryClass={cs.SC}
}