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

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

2006-12-19

arxiv.org/abs/cs/0612094v1

Dans Algebraic Biology 2007 4545 (2007) 277--291

Computer Science

Symbolic Computation

Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the sys

Scientific paper

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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