Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators

Carsten Schneider

doi:10.1145/3597066.3597073

Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators

Carsten Schneider

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.

Original language	English
Title of host publication	ISSAC'23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation
Editors	Gabriela Jeronimo
Publisher	ACM
Pages	498-507
Number of pages	10
ISBN (Print)	9788400700392
DOIs	https://doi.org/10.1145/3597066.3597073
Publication status	Published - 2023

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1145/3597066.3597073

Cite this

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title = "Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators",

abstract = "We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.",

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N2 - We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.

AB - We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.

U2 - 10.1145/3597066.3597073

DO - 10.1145/3597066.3597073

M3 - Conference proceedings

SN - 9788400700392

SP - 498

EP - 507

BT - ISSAC'23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation

A2 - Gabriela Jeronimo, null

PB - ACM

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