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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References
Murray, J.D.: Mathematical Biology. Interdisciplinary Applied Mathematics, vol. 17. Springer, Heidelberg (2002)
Khanin, R.: Dimensional Analysis in Computer Algebra. In: Mourrain, B. (ed.) Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, London, Ontario, Canada, ACM, pp. 201–208. ACM press, New York (2001)
Bluman, G., Anco, S.: Symmetry and Integration Methods for Differential Equations. Applied Mathematical Sciences, vol. 154. Springer, Heidelberg (2002)
Olver, P.J.: Applications of Lie groups to differential equations, 2nd edn. Graduate Texts in Mathematics, vol. 107. Springer, Heidelberg (1993)
Gatermann, K.: Computer algebra methods for equivariant dynamical systems. Lecture Notes in Mathematics, vol. 1728. Springer, New York (2000)
Hubert, É., Kogan, I.: Rational invariants of an algebraic group action. Construction and rewriting. Journal of Symbolic Computation 42(1-2), 203–217 (2007)
Burde, G.I.: Expanded Lie group transformations and similarity reductions of differential equations. In: Nikitin, A.G., Boyko, V.M., Popovych, R.O. (eds.) Symmetry in nonlinear mathematical physics Part I. In: Proceedings of Institute of Mathematics of NAS of Ukraine, Kiev, Ukraine, vol 43, pp. 93–101 (2002)
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Sedoglavic, A. (2007). Reduction of Algebraic Parametric Systems by Rectification of Their Affine Expanded Lie Symmetries. In: Anai, H., Horimoto, K., Kutsia, T. (eds) Algebraic Biology. AB 2007. Lecture Notes in Computer Science, vol 4545. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73433-8_20
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DOI: https://doi.org/10.1007/978-3-540-73433-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73432-1
Online ISBN: 978-3-540-73433-8
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