A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and the formal difference ring setting. In particular, canonical (unique) representations and their refinements in the introduced term algebra are explored by utilizing the available difference ring theory. Based on that, precise input-output specifications of the available tools of the summation package Sigma are provided.

中文翻译：

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术语代数，规范表示和符号求和的差分环理论

给出了用于符号求和的现有差分环理论的一般概述。特别强调用户界面：术语代数和形式差异环设置中相应表示的翻译和反向翻译。特别是，通过利用可用的差分环理论，探索了引入的术语代数中的规范（唯一）表示形式及其改进。基于此，提供了求和包Sigma可用工具的精确输入输出规格。