Group-Theoretic Approach for Symbolic Tensor Manipulation
Group-Theoretic Approach for Symbolic Tensor Manipulation
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DOI：
10.1142/s0129183102004571
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发表时间：
2001-07
影响因子：
1.9
通讯作者：
L. Manssur;R. Portugal;B. Svaiter
中科院分区：
文献类型：
--
作者：
L. Manssur;R. Portugal;B. Svaiter
我们描述了计算群论如何以显式索引表示法提供用于操作索引对象(张量、旋量等)的工具。特别地，我们给出了将具有服从置换对称的自由指数和虚拟指数的张量放入标准形的算法。该方法基于确定对称群的子群的典型双陪集表示的算法。该算法的复杂性与实际应用中的索引数呈多项式关系，可以解决具有数百个索引数的张量表达式的简化问题，超出了实际应用的需要。
We describe how Computational Group Theory provides tools for manipulating indexed objects (tensors, spinors, and so on) in explicit index notation. In particular, we present algorithms that put tensors with free and dummy indices obeying permutation symmetries into the canonical form. The method is based on algorithms for determining canonical double coset representatives of subgroups of the symmetric group. The complexity of the algorithms is polynomial on the number of indices in practical applications and allows one to address the simplification of tensor expressions with hundreds of indices, going beyond what is needed in practical applications.