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xPerm: fast index canonicalization for tensor computer algebra

机译：xPerm：张量计算机代数的快速索引规范化

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摘要

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.
机译：对于排列对称性，我们提出了用于索引规范化的Butler-Portugal算法的非常快速的实现。它称为xPerm，并且被编写为Mathematica软件包和C子例程的组合。后者执行计算中最苛刻的部分，并且可以与任何其他程序或计算机代数系统链接。我们通过测试和时序证明了Butler-Portugal算法相对于索引数的有效多项式性能，尽管我们也展示了指数式的情况。我们的实现以百分之一秒的几十个索引或几秒钟的一百个索引处理通用张量表达式，明显胜过当前所有其他规范化器。该代码已经过严格的测试数年，并且在大规模张量计算机代数的最新研究中至关重要。

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