PROGRAM SUMMARY
Title of program:
CycleCostAlgorithm, GYutsis
Catalogue identifier:
ADRM
Ref. in CPC:
151(2003)354
Distribution format: tar gzip file
Operating system: Linux
Number of lines in distributed program, including test data, etc:
7823
Keywords:
Angular momentum, General recoupling coefficient, Racah coefficient,
Wigner n-j symbols, Rules graphical, Yutsis graph,
Computational methods, Rotation group.
Programming language used: Java 1.2
Computer:
Pentium II-350 .
Nature of physical problem:
A general recoupling coefficient for an arbitrary number of (integer or
half-integer) angular momenta can be expressed as a formula consisting
of products of 6-j coefficients summed over a certain number of
variables. Such a formula can be generated using the program GYutsis
(with a graphical user front end) or CycleCostAlgorithm (with a
text-mode user front end).
Method of solution:
Using the graphical techniques of Yutsis, Levinson and Vanagas [1] a
summation formula for a general recoupling coefficient is obtained by
representing the coefficient as a Yutsis graph and by performing a
selection of reduction rules valid for such graphs. Each reduction rule
contributes to the final summation formula by a numerical factor or by
an additional summation variable. Whereas an optimal summation formula
(i.e. with a minimum number of summation variables) is hard to obtain,
we present here a new heuristic approach for selecting an edge from a
k-cycle in order to transform it into an (k-1)-cycle (k>3) in such a way
that a 'good' summation formula is obtained.
Typical running time:
From instantaneously for the typical problems to a few seconds for the
heaviest problems on a Pentium II-350 Linux-system with 256 MB RAM.
References:
[1] A.P. Yutsis, I.B. Levinson and V.V. Vanagas, Mathematical Apparatus
of the Theory of Angular Momentum (Israel Program for Scientific
Translation, Jerusalem, 1962).