符号张量操纵的群论方法：I。免费指数
Group-theoretic Approach for Symbolic Tensor Manipulation: I. Free Indices
摘要：
我们描述了如何计算群论提供的工具，操纵张量显式索引符号。特别地，我们提出了一个算法，把张量的自由指数服从置换对称的标准形式。该方法是基于用于确定典型陪集代表的对称群的子群的算法。该算法的复杂度是指数个数的多项式，对于在计算机代数系统上实现通用张量包是有用的。
英文摘要：
We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form. The method is based on algorithms for determining the canonical coset representative of a subgroup of the symmetric group. The complexity of our algorithm is polynomial on the number of indices and is useful for implementating general purpose tensor packages on the computer algebra systems.
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