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Manuscript Title: Generation of the Clebsch-Gordan coefficients for Sn.
Authors: S. Schindler, R. Mirman
Program title: SYMCC
Catalogue identifier: ACYI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 15(1978)131
Programming language: Fortran.
Computer: IBM 370/168.
Operating system: OS/MVT/ASP.
RAM: 246K words
Word size: 8
Peripherals: magnetic tape.
Keywords: General purpose, Symmetric group, Homogeneous equation, Precision, Algebras.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
ACXV_v1_0 SYMCGM CPC 15(1978)131
ACXW_v1_0 SYMFUNC CPC 15(1978)147

Nature of problem:
The Clebsch-Gordan coefficients of SN must satisfy certain homogeneous equations. The program SYMCGM described in this paper computes these coefficients and SYMCC checks that the computed coefficients actually satisfy the equations. In addition, SYMCC provides some indication of the accuracy of the calculation and the precision of the coefficients.

Solution method:
The program SYMCC is closely related to SYMCGM, in general, following its notation and routines. Its input is the output of that program, as well as output from SYMFUNC, and a single data card. The information and setting of indices for n and a triplet is the same as for SYMCGM. The data card also contains two other numbers (NSK) and (LST). The homogeneous equations can be checked for all the neighboring transpositions or only the last one as specified by the variable (NSK). The difference between the values of the two sides of each equation (which should be zero) is computed. For each neighbouring transposition the sum of the absolute values of the differences, and the largest absolute value of all the differences are found. The output is headed by the label of the neighboring transposition and the triplet indices. Then, for each set of indices there is a line listing the indices, the values of the right- and left-hand sides and the difference. Instead of every line being printed, only every (LCT) lines can be printed. After all this information is the sum, and the largest, of the absolute values of the differences.

Any coefficient computed by SYMCGM can be checked.