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Manuscript Title: [QPSI] a MAPLE package for the determination of quasi-polynomial symmetries and invariants of ODEs system.
Authors: T.M. Rocha Filho, A. Figueiredo, L. Brenig
Program title: QPSI
Catalogue identifier: ADJX_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 117(1999)263
Programming language: Maple.
Operating system: UNIX, WINDOWS/95.
Word size: 32
Keywords: General purpose, Differential equations, Ode's system, First-integrals, Invariants, Lie symmetries, Lotka-volterra, Maple, Symbolic computation.
Classification: 4.3.

Nature of problem:
The search of invariant tensors and invariants for dynamical systems.

Solution method:
The algorithm to calculate a quasi-polynomial invariant tensor field for a quasi-polynomial dynamical system is described in [1,2].

Restrictions:
The time consuming becomes higher when the order of the semi-invariant increases.

Unusual features:
QPSI is the first MAPLE program that calculates quasi-polynomial invariant tensor fields for ODE's systems in the quasi-polynomial form (including the scalar invariant).

Running time:
Depends strongly on the order and the complexity of the ODE's system.

References:
[1] A. Figueiredo, T.M. Rocha Filho, L. Brenig, "Algebraic structures and invariants of differential systems", accepted for publication in J. Math. Phys. (1997).
[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", submitted in Physica A (1997).