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Manuscript Title: Explicit formulae of angular momentum coupling coefficients.
Authors: F. Koike
Program title: ANALG
Catalogue identifier: ACJV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 72(1992)154
Programming language: Reduce.
Computer: HITAC M682H.
Operating system: VOS3.
Keywords: General purpose, Rotation group, Angular momentum, Coupling coefficient, Clebsch-gordan Coefficient, 3j-symbol, Racah coefficient, 6j-symbol, X-coefficient, 9j-symbol, Computer algebra, Wigner, Racah, Reduce, Reduce33.
Classification: 4.1, 5.

Nature of problem:
The program allows us algebraic reductions of Wigner's formula for Clebsch-Gordan coefficients and Racah's formula for Racah coefficients. With use of these two formulae, the program gives explicit algebraic expressions for Clebsch-Gordan coefficients, Racah coefficients, the X-coefficients, and other related coupling coefficients of angular momenta. The program contains several operators and each of them returns a coefficient accepting both values and variables of angular momentum as their arguments. The present program helps us with analytic manipulations of expressions containing those coefficients.

Restrictions:
There is no special restriction for the range of angular momentum values if enough memory is supplied. However, the reduction of the coupling coefficient that contains a high angular momentum value is sometimes time consuming and, therefore, is not practical.

Unusual features:
The program has no unusual features as a REDUCE program. The present program carries out no floating point operation. As far as the REDUCE and the LISP system are compatible, the present program is strictly machine independent.

Running time:
This varies widely from problem to problem. The three examples in the test deck took about 47 seconds in total, of which 45 percent are used by the X-coefficient. For details, see the output listings given in LONG WRITEUP.