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.

翻译：特别强调的是用户界面:在代数和正式的代数设置中翻译和回译相应的表述,特别是,利用现有的 " 代数 " 理论,探讨 " 典型 " 的表达方式及其在采用 " 代数 " 术语中的完善之处,并在此基础上,提供 " Sigma " 组合组合现有工具的精确输入-输出规格。