Abstract

Computer algebra is increasingly used in research and applied computations. An example is tensor computations or, in a wide sense, simplification of expressions containing indices. In this paper, the method of colored graphs designed for simplifying abstract expressions containing indices is developed for the case when the indices are of different types. An example of such indices are upper and lower indices in tensor expressions. The proposed approach significantly reduces the number of combinations to be considered when the canonical form of the expression is sought; as a result, the computations are drastically accelerated.

中文翻译：

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带索引的表达式简化彩色图的方法

摘要

计算机代数越来越多地用于研究和应用计算中。一个例子是张量计算，或者广义上讲简化包含索引的表达式。在本文中，针对索引类型不同的情况，开发了用于简化包含索引的抽象表达式的彩色图方法。这样的索引的一个例子是张量表达式中的上下索引。当寻找表达式的规范形式时，所提出的方法大大减少了要考虑的组合数量；结果，大大加快了计算速度。