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Manuscript Title: ODEPAINLEVE: a MACSYMA package for Painleve analysis of ordinary differential equations.
Authors: D.W. Rand, P. Winternitz
Program title: ODEPAINLEVE
Catalogue identifier: AALT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 42(1986)359
Programming language: REX MACSYMA.
Computer: VAX 11/780.
Operating system: VMS.
RAM: 500K words
Word size: 32
Keywords: Ordinary, Differential equations, Painleve, General purpose, Singularity, Macsyma, Symbolic manipulation, Computer algebra.
Classification: 4.3, 5.

Nature of problem:
Given a nonlinear ordinary differential equation, the program determines whether it fulfills certain necessary conditions for having the Painleve property, i.e. being free of moving critical points. This information is useful in attempts to integrate the ODE.

Solution method:
A truncated power series in t= x-xO' where x is the independent variable y in the ODE. First only the leading term of the series is used in order to determine the negative rational value(s) of its exponent. Then for each such value the leading term and a generic term are used to locate possible resonances, i.e. indices of coefficients in the series which may be free parameters. Finally the full truncated series is used to verify these resonances.

The form of the ODE must be polynomial in both the independent and dependent variables and in all derivatives. All exponents must be explicit integers, but coefficients may be indeterminate symbols.

Unusual features:
The equation need not be linear in its highest derivative and may be of arbitrary order and degree.

Running time:
Varies widely according to the order and degree of the ODE, and depends on whether verification of resonances is performed. For the Test Runs the amount of CPU time required was of the order of a few minutes each.