A Streamlined Difference Ring Theory: Indefinite Nested Sums, the Alternating Sign, and the Parameterized Telescoping Problem

We present an algebraic framework to represent indefinite nested sums over hyper geometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extended to a ring theory in which also the alternating sign can be expressed. The unde...

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Bibliographic Details
Published in:2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 26 - 33
Main Author: Schneider, Carsten
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2014
Subjects:
creative telescoping
d'Alembertian expressions
Educational institutions
Machinery
Poles and towers
Polynomials
Reduced instruction set computing
roots of unity
Scientific computing
symbolic summation
telescoping
ISBN:9781479984473, 1479984477
Online Access:Get full text
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Summary:We present an algebraic framework to represent indefinite nested sums over hyper geometric expressions in difference rings. In order to accomplish this task, parts of Karr's difference field theory have been extended to a ring theory in which also the alternating sign can be expressed. The underlying machinery relies on algorithms that compute all solutions of a given parameterized telescoping equation. As a consequence, we can solve the telescoping and creative telescoping problem in such difference rings.
ISBN:9781479984473
1479984477
DOI:10.1109/SYNASC.2014.12