Programs in Physics & Physical Chemistry
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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.
The algorithm to calculate the Lie supersymmetries for Grassmann-valued differential equations is a direct extension of the one described in . 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.
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.
It depends strongly on the SGVDE to be solved. Typical running time is given in section 5.
|||P.J. Olver, Applications of Lie Groups to Differential Equations (Springer, Berlin, 1986).|
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