Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] abvn_v1_0.gz(24 Kbytes)
Manuscript Title: Root-rational-fraction package for exact calculation of vector- coupling coefficients.
Authors: A.J. Stone, C.P. Wood
Program title: ROOT
Catalogue identifier: ABVN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 21(1980)195
Programming language: Fortran.
Computer: IBM 370/165.
Operating system: HASP II/PHOENIX.
Program overlaid: yes
RAM: 7K words
Word size: 32
Keywords: General purpose, Rotation group, Vector coupling Coefficients, Wigner 3j, Wigner 6j, Wigner 9j, Power-of-prime Arithmetic.
Classification: 4.1.

Nature of problem:
A subroutine package is provided for the exact evaluation of vector coupling coefficients (Wigner 3j, 6j and 9j symbols) and for exact arithmetic involving these and related quantities. The main program supplied with the package can be used interactively like a calculator working in Reverse Polish Notation, to evaluate vector-coupling coefficients and to perform simple arithmetic on them.

Solution method:
The program uses power-of-prime arithmetic, with a list processing technique which avoids arbitrary limits on the size of prime which can arise.

The program works in terms of numbers whose squares are rational fractions, and the only restriction is that all numbers which arise should be expressible in this form. In no problem investigated so far has this restriction caused any difficulty.

Unusual features:
The program is written in Ryder's Portable FORTRAN subset of USANSI FORTRAN, so that it should run without modification on most computers.

Running time:
Calculation of a coupling coefficient takes a small fraction of a second. Extensive calculations involving sums and products of coupling coefficients, factorials etc. have been completed in a few seconds of IBM 360/165 cpu time.