xPerm：张量计算机代数的快速指标规范化
xPerm: fast index canonicalization for tensor computer algebra
摘要：
我们提出了一个非常快速的实现巴特勒-葡萄牙算法的索引规范化置换对称。它被称为xPerm，并已被编写为Mathematica包和C子例程的组合。后者执行计算中最苛刻的部分，并且可以从任何其他程序或计算机代数系统链接。我们证明了测试和定时的有效多项式性能的巴特勒-葡萄牙算法的指数的数量，虽然我们也展示了一个情况下，它是指数。我们的实现在百分之一秒内处理几十个索引的通用张量表达式，或者在几秒钟内处理一百个索引，明显优于当前所有其他规范化器。该代码已经进行了几年的密集测试，并在最近的大规模张量计算机代数研究中发挥了重要作用。
英文摘要：
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.
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