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Term algebras, canonical representations and difference ring theory for symbolic summation. (English) Zbl 1484.81078

Bluemlein, Johannes (ed.) et al., Anti-differentiation and the calculation of Feynman amplitudes. Selected papers based on the presentations at the conference, Zeuthen, Germany, October 2020. Cham: Springer. Texts Monogr. Symb. Comput., 423-485 (2021).
Summary: 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.
For the entire collection see [Zbl 1475.81004].

MSC:

81T18 Feynman diagrams
81V05 Strong interaction, including quantum chromodynamics
68W30 Symbolic computation and algebraic computation
65B10 Numerical summation of series
11Y16 Number-theoretic algorithms; complexity
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