research-article

A refined denominator bounding algorithm for multivariate linear difference equations

Authors:

Carsten SchneiderAuthors Info & Claims

ISSAC '11: Proceedings of the 36th international symposium on Symbolic and algebraic computation

Pages 201 - 208

https://doi.org/10.1145/1993886.1993919

Published: 08 June 2011 Publication History

Abstract

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we have introduced the distinction between periodic and aperiodic factors in the denominator, and we have given an algorithm for predicting the aperiodic ones. Now we extend this technique towards the periodic case and present a refined algorithm which also finds most of the periodic factors.

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Cited By

Blümlein JSaragnese MSchneider C(2023)Hypergeometric structures in Feynman integralsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-023-09831-891:5(591-649)Online publication date: 3-Apr-2023
https://doi.org/10.1007/s10472-023-09831-8
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Kauers MKauers M(2023)OperatorsD-Finite Functions10.1007/978-3-031-34652-1_4(287-391)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_4
Show More Cited By

Index Terms

A refined denominator bounding algorithm for multivariate linear difference equations
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Conferences

ISSAC '11: Proceedings of the 36th international symposium on Symbolic and algebraic computation

June 2011

372 pages

ISBN:9781450306751

DOI:10.1145/1993886

General Chair:
Éric Schost
The University of Western Ontario, Canada
,
Program Chair:
Ioannis Z. Emiris
University of Athens, Greece

Copyright © 2011 ACM.

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Published: 08 June 2011

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ISSAC '11: International Symposium on Symbolic and Algebraic Computation

June 8 - 11, 2011

California, San Jose, USA

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Blümlein JSaragnese MSchneider C(2023)Hypergeometric structures in Feynman integralsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-023-09831-891:5(591-649)Online publication date: 3-Apr-2023
https://doi.org/10.1007/s10472-023-09831-8
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Kauers MKauers M(2023)OperatorsD-Finite Functions10.1007/978-3-031-34652-1_4(287-391)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_4
Kauers MKauers M(2023)The Differential Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_3(185-286)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_3
Kauers MKauers M(2023)The Recurrence Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_2(81-183)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_2
Kauers MKauers M(2023)Background and Fundamental ConceptsD-Finite Functions10.1007/978-3-031-34652-1_1(1-80)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_1
Blümlein JSchneider C(2022)The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integralsJournal of Physics A: Mathematical and Theoretical10.1088/1751-8121/ac808655:44(443005)Online publication date: 30-Nov-2022
https://doi.org/10.1088/1751-8121/ac8086
Barkatou MCluzeau TEl Hajj A(2021)On Rational Solutions of Pseudo-linear SystemsComputer Algebra in Scientific Computing10.1007/978-3-030-85165-1_4(42-61)Online publication date: 16-Aug-2021
https://doi.org/10.1007/978-3-030-85165-1_4
Abramov SPetkovšek M(2012)On polynomial solutions of linear partial differential and (q-)difference equationsProceedings of the 14th international conference on Computer Algebra in Scientific Computing10.1007/978-3-642-32973-9_1(1-11)Online publication date: 3-Sep-2012
https://dl.acm.org/doi/10.1007/978-3-642-32973-9_1

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