Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

2021/02/02 by Carsten Schneider, Schneider, Carsten · 2 citations
Computer Science · #FOS: Computer and information sciences #Formal Methods in Verification #Logic, programming, and type systems #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2102.01471

openalex publication_date 2021/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Complete Reduction for Derivatives in a Primitive Tower
• Telescoping Algorithms for Σ^*-Extensions via Complete Reductions

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