PROGRAM SUMMARY
Title of program:
GYutsis: VAN DYCK, FACK
Catalogue identifier:
ADSA
Ref. in CPC:
154(2003)219
Distribution format: tar gzip file
Operating system: Windows, Linux/Unix
Number of lines in distributed program, including test data, etc:
9400
Keywords:
Angular momentum, General recoupling coef., Yutsis graph,
Reduction rules, Cyclic structure, Heuristic, Computational Methods.
Programming language used: Java
Computer:
ANY .
Other versions of this program:
Cat. Id. Title Ref. in CPC ADRM CycleCostAlgorithm, GYutsis 151(2003)354
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 frontt end).
Method of solution:
Using the graphical techniques of Yutsis, Levinson and Vanagas (1962) a
summation formula for a general coupling 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 some new heuristic approaches for selecting an edge from
a k-cycle in order to transform it into a (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 30 s for the heaviest
problems on a Pentium II-350 Linux-system with a 256MB RAM.
Additional Comments:
Using the code
The tar.gz file for this program contains three files.
A readme file describing the system. The file gyutsis.1.1.tar.gz, which
contains the files required for a Unix installation and the file
gyutsis.1.1.zip which contains the Windows files.