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Manuscript Title: GLie; a MAPLE program for Lie supersymmetries of Grassmann-valued differential equations.
Authors: M.A. Ayari, V. Hussin
Program title: GLie
Catalogue identifier: ADEP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 100(1997)157
Programming language: Maple.
Operating system: UNIX.
Word size: 32
Keywords: General purpose, Symmetry and Supersymmetry groups, Lie algebra and Superalgebra, Grassmann-valued Differential equations, Partial differential Equations, Maple, Symbolic computation, Computer algebra.
Classification: 4.2, 4.3, 5.

Nature of problem:
The construction of the Lie symmetry superalgebra of a system of Grassmann-valued differential equations (SGVDE) is a first step in the resolution of such a system. The next step would be the use of symmetry reduction method to get a simpler system which could be solved easily.

Solution method:
The algorithm to calculate the Lie supersymmetries for Grassmann-valued differential equations is a direct extension of the one described in [1]. All the steps of these calculation techniques are now modelled into a MAPLE program.

The time consuming becomes higher when the order, as well as the number of odd dependent and independent variables of the SGVDE is increasing.

Unusual features:
GLie is the first MAPLE program that calculates the determining equations for both usual and Grassmann-valued systems of partial differential equations. The resolution of such equations leads to the construction of Lie superalgebras of symmetries.

Running time:
It depends strongly on the SGVDE to be solved. Typical running time is given in section 5.

[1] P.J. Olver, Applications of Lie Groups to Differential Equations (Springer, Berlin, 1986).