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

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 affine derivations that induces expanded Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we reduce the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is quasi-polynomial in input's size.

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