[QPSI] - a MAPLE package for the determination of quasi-polynomial symmetries and invariants

Computer Physics Communications

Volumn 117, Issue 3, 1999, Pages 263-272

  Rocha Filho, Tarcísio M ^a   Figueiredo, Annibal ^a   Brenig, Léon ^b  

^a UNIVERSITY OF BRASILIA   (Brazil)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FUNCTIONS; INTEGRATION; POLYNOMIALS; TENSORS;

QUASI-POLYNOMIAL SYMMETRIES AND INVARIANTS (QPSI); SOFTWARE PACKAGE MAPLE;

PHYSICS;

EID: 0033545505     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(98)00186-6     Document Type: Article

References (13)

1. A. Figueiredo, T.M. Rocha Filho, L. Brenig, Algebraic structures and invariant manifolds of differential systems, J. Math. Phys. 39 (1998) 2929.
2. A. Figueiredo, T.M. Rocha Filho, L. Brenig, Necessary conditions for the existence of quasi-polynomial invariants: The quasi-polynomial and Lotka-Volterra systems, Physica A 262 (1999) 158.
3. L.V. Ovsjannikov, Group Analysis of Differential Equations (Academic Press, New York, 1982).
4. V.I. Arnold, Geometrical Methods in the Theory of Differential Equations (Springer, New York, Berlin, 1988).
5. F. Schwarz, An algorithm for determining polynomial first-integrals of autonomous system of ordinary differential equations, J. Symb. Comput. 1 (1985) 229-233.
6. M.J. Prelle, M.F. Singer, Elementary first integrals of differential equations, Trans. Amer. Math. Soc. 279 (1983) 215-229.
7. Y.K. Man, M.A.H. MacCallum, A rational approach to the Prelle-Singer algorithm, J. Symb. Comput., to appear.
8. R. Shtokhamer, Solving First Order Differential Equations Using the Prelle-Singer Algorithm, Technical Report (Center of Mathematical Computation, University of Delaware, Newark, May 1988).
9. Y.K. Man, First integrals of autonomous systems of differential equations and Prelle-Singer procedure, J. Math. A 27 (1994) L327-332.
10. L. Brenig, A. Goriely, Universal canonical forms for the time-continuous dynamical systems, Phys. Rev. A 40 (1989) 4119-4122.
11. B. Schutz, Geometrical Method of Mathematical Physics (Cambridge Univ. Press, Cambridge, 1988).
12. A. Figueiredo, T.M. Rocha Filho, L. Brenig, Invariant Tensors of Dynamical Systems, to be published.
13. 3: The Lotka-Volterra system, Physica A 163 (1990) 683-722.