符号张量操作的群论方法：II。虚拟指数
Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices
摘要：
计算群论应用于具有虚拟索引的索引对象（张量、旋量等）。有两组需要考虑：一组描述对象的内在对称性，另一组描述虚拟索引名称的交换。寻找具有伪索引的索引对象的标准型的问题归结为寻找双陪集标准表示。众所周知的计算群算法应用于索引操作，这允许解决具有数百个索引的表达式的简化，进一步满足实际应用中的需要。
英文摘要：
Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of names of dummy indices. The problem of finding canonical forms for indexed objects with dummy indices reduces to finding double coset canonical representatives. Well known computational group algorithms are applied to index manipulation, which allow to address the simplification of expressions with hundreds of indices going further to what is needed in practical applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
