A MAPLE program for calculations with Schur functions. M.J. Carvalho, S. D'Agostino.

PROGRAM SUMMARY
Title of program: SCHUROPERA
Catalogue identifier: ADPF
Ref. in CPC: 141(2001)282
Distribution format: tar gzip file
Operating system: Windows 95/98
Number of lines in distributed program, including test data, etc: 1175
Keywords: Schur functions, Outer product, Internal product, Plethysm, Unitary group, Symmetric group, Character table, General purpose, Algebras, Computer algebra.
Programming language used: Maple
Computer: Pentium 933 MHz , Compaq Presario 1260 , Pentium 300 MHz .

Nature of physical problem:
Most common operations involving Schur functions, which are widely applied, in particular to many-body physics.

Method of solution:
The outer product, skew division, and other plethysm of Schur functions rely on an algorithm for the multiplication and division of monomial symmetric functions [1]. For the internal product of Schur functions, extensive use is made of the MAPLE library program "combinat" [2].

Restrictions:
Main limitation is running time.

Typical running time:
Running time depends both on the operation performed and on the computer processor type. Elapsed times for specific operations are reported in the test runs.

References:

 [1] M.J. Carvalho, S. D'Agostino, Plethysms of Schur functions and the  
     Shell model, J. Phys. A: Math. Gen. 34 (2001) 1375-1392.            
 [2] MAPLE 6, copyright 2000, Waterloo Maple Inc.