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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Reduction of Algebraic Parametric Systems by Rectification of Their Affine Expanded Lie Symmetries
verfasst von : Alexandre Sedoglavic
Erschienen in: Algebraic Biology
Verlag: Springer Berlin Heidelberg
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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.