项代数、标准表示与符号和的差环理论
Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation
摘要：
对已有的符号求和的差环理论作了一个全面的综述。特别强调的是放在用户界面：翻译和回翻译的术语代数和正式差环设置内的相应表示。特别是，典型的（唯一的）表示和它们的改进，在引进的术语代数探索利用现有的差环理论。在此基础上，提供了求和包Sigma的可用工具的精确输入输出规格。
英文摘要：
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.
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。
