research-article

Telescopers for rational and algebraic functions via residues

Authors:

Michael F. SingerAuthors Info & Claims

ISSAC '12: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Pages 130 - 137

https://doi.org/10.1145/2442829.2442851

Published: 22 July 2012 Publication History

Abstract

We show that the problem of constructing telescopers for rational functions of m + 1 variables is equivalent to the problem of constructing telescopers for algebraic functions of m variables and we present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers.

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Cited By

Hassani SMaillard JZenine N(2024)Plea for Diagonals and Telescopers of Rational FunctionsUniverse10.3390/universe1002007110:2(71)Online publication date: 2-Feb-2024
https://doi.org/10.3390/universe10020071
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
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Index Terms

Telescopers for rational and algebraic functions via residues
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Other conferences

ISSAC '12: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

July 2012

390 pages

ISBN:9781450312691

DOI:10.1145/2442829

General Chair:
Joris van der Hoeven
École Polytechnique, France
,
Program Chair:
Mark van Hoeij
Florida State U.

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Grenoble University: Grenoble University
INRIA: Institut Natl de Recherche en Info et en Automatique

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 July 2012

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ISSAC'12

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Grenoble University
INRIA

ISSAC'12: International Symposium on Symbolic and Algebraic Computation

July 22 - 25, 2012

Grenoble, France

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ISSAC '12 Paper Acceptance Rate 46 of 86 submissions, 53%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Hassani SMaillard JZenine N(2024)Plea for Diagonals and Telescopers of Rational FunctionsUniverse10.3390/universe1002007110:2(71)Online publication date: 2-Feb-2024
https://doi.org/10.3390/universe10020071
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
Abdelaziz YBoukraa SKoutschan CMaillard J(2022)Diagonals of Rational Functions: From Differential Algebra to Effective Algebraic GeometrySymmetry10.3390/sym1407129714:7(1297)Online publication date: 22-Jun-2022
https://doi.org/10.3390/sym14071297
Trager B(2022)Comments on Integration of Algebraic FunctionsIntegration in Finite Terms: Fundamental Sources10.1007/978-3-030-98767-1_8(287-295)Online publication date: 7-Jun-2022
https://doi.org/10.1007/978-3-030-98767-1_8
Raab C(2022)Comments on Risch’s On the Integration of Elementary Functions which are Built Up Using Algebraic OperationsIntegration in Finite Terms: Fundamental Sources10.1007/978-3-030-98767-1_6(217-229)Online publication date: 7-Jun-2022
https://doi.org/10.1007/978-3-030-98767-1_6
Chen SDu LKauers MChyzak FLabahn G(2021)Lazy Hermite Reduction and Creative Telescoping for Algebraic FunctionsProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465528(75-82)Online publication date: 18-Jul-2021
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