The Canon package: a fast kernel for tensor manipulators

Abstract This paper describes the Canon package written in the Maple programming language. Canon's purpose is to work as a kernel for complete Maple tensor packages or any Maple package for manipulating indexed objects obeying generic permutation symmetries and possibly having dummy indices. Canon uses Computational Group Theory algorithms to efficiently simplify or manipulate generic tensor expressions. We describe the main command to access the package, give examples, and estimate typical computatio... Title of program: Canon Catalogue Id: ADSP_v1_0 Nature of problem Manipulation and simplification of tensor expressions (or any expression in terms of indexed objects) in explicit index notation, where the indices obey generic permutation symmetries and there may exist dummy (summed over) indices. Versions of this program held in the CPC repository in Mendeley Data ADSP_v1_0; Canon; 10.1016/S0010-4655(03)00494-6 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要 本文介绍了以Maple编程语言编写的Canon软件包。Canon的设计用途为完整Maple张量软件包，或任意用于操作满足通用置换对称性、可含哑指标的带指标对象的Maple软件包，提供内核级支持。Canon借助计算群论（Computational Group Theory）算法，可高效化简或处理通用张量表达式。本文将介绍调用该软件包的主命令，给出示例，并对典型计算量进行预估…… 程序标题：Canon；目录编号：ADSP_v1_0；问题本质：采用显式指标记法的张量表达式（或任意基于带指标对象的表达式）的处理与化简，其中指标需遵循通用置换对称性，且可能存在哑（求和）指标。 收录于Mendeley Data中的CPC存储库程序版本：ADSP_v1_0; Canon; 10.1016/S0010-4655(03)00494-6。本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）