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Manuscript Title: Two programs to perform certain symbolic calculations in the enveloping algebra of a Lie algebra.
Authors: H. De Meyer, G. Vanden Berghe, P. De Wilde
Program title: POLRANGE
Catalogue identifier: AATO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 44(1987)197
Programming language: Fortran.
Computer: SIEMENS 7000 SERIES.
Operating system: BS2000.
RAM: 11K words
Word size: 32
Keywords: General purpose, Lie algebras, Enveloping algebra, Standard ordering of Generators, Reduction of generator Polynomials.
Classification: 4.2.

Nature of problem:
The purpose is to transform a polynomial in the generators of a Lie algebra and with numerical coefficients into an equivalent form which exhibits a freely chosen but prescribed order of the generators.

Solution method:
Monomials in the generators are transformed into polynomials having terms which are arranged into the prescribed order, on account of the commutators which define the linear Lie algebra. The ordered terms are catalogued in such a way that their retrieval and the searching in the catalogue is very fast. Generators are internally represented by a single character. Hence monomials are represented by character strings which allow to exploit the string operations offered in FORTRAN 77.

Restrictions:
Useful for polynomials of any degree. Practical restrictions only follow from time and storage limitations and from the integer arithmetic capacity. Also the dimension of the Lie algebras that can be handled is restricted to the number of different non-control characters that can be coded.

Running time:
For monomial of degree 8: 1 s.