Authors: Jose M. Martin-Garcia
Date: 6 Mar 2008
Abstract: We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine. The latter performs the most demanding parts of the computations and can be linked from any other program or computer algebra system. We demonstrate with tests and timings the effectively polynomial performance of the Butler-Portugal algorithm with respect to the number of indices, though we also show a case in which it is exponential. Our implementation handles generic tensorial expressions with several dozen indices in hundredths of a second, or one hundred indices in a few seconds, clearly outperforming all other current canonicalizers. The code has been already under intensive testing for several years and has been essential in recent investigations in large-scale tensor computer algebra.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis