research-article

Parallel telescoping and parameterized Picard-Vessiot theory

Authors:

Michael F. SingerAuthors Info & Claims

ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

Pages 99 - 106

https://doi.org/10.1145/2608628.2608638

Published: 23 July 2014 Publication History

Abstract

Parallel telescoping is a natural generalization of differential creative-telescoping for single integrals to line integrals. It computes a linear ordinary differential operator L, called a parallel telescoper, for several multivariate functions, such that the application of L to the functions yields partial derivatives of a single function. We present a necessary and sufficient condition guaranteeing the existence of parallel telescopers for differentially finite functions, and develop an algorithm to compute minimal ones for compatible hyperexponential functions. Besides computing annihilators of parametric line integrals, we use the parallel telescoping for determining Galois groups of parameterized partial differential systems of first order.

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Cited By

Chen SFeng RLi ZSinger MWatt S(2024)Telescopers for differential forms with one parameterSelecta Mathematica10.1007/s00029-024-00926-630:3Online publication date: 9-Mar-2024
https://doi.org/10.1007/s00029-024-00926-6
Chen SFeng RMa PSinger MChyzak FLabahn G(2021)Separability Problems in Creative TelescopingProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465514(83-90)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465514
Chen SDu LWang RZhu C(2020)On the existence of telescopers for rational functions in three variablesJournal of Symbolic Computation10.1016/j.jsc.2020.08.006Online publication date: Aug-2020
https://doi.org/10.1016/j.jsc.2020.08.006
Show More Cited By

Index Terms

Parallel telescoping and parameterized Picard-Vessiot theory
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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cover image ACM Other conferences

ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

July 2014

444 pages

ISBN:9781450325011

DOI:10.1145/2608628

Editor:
Katsusuke Nabeshima
The University of Tokushima, Japan
,
General Chairs:
Kosaku Nagasaka
Kobe University, Japan
,
Franz Winkler
RISC, University Linz, Austria
,
Program Chair:
Agnes Szanto
North Carolina State University

Copyright © 2014 ACM.

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Publication History

Published: 23 July 2014

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ISSAC '14

ISSAC '14: International Symposium on Symbolic and Algebraic Computation

July 23 - 25, 2014

Kobe, Japan

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ISSAC '14 Paper Acceptance Rate 51 of 96 submissions, 53%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Chen SFeng RLi ZSinger MWatt S(2024)Telescopers for differential forms with one parameterSelecta Mathematica10.1007/s00029-024-00926-630:3Online publication date: 9-Mar-2024
https://doi.org/10.1007/s00029-024-00926-6
Chen SFeng RMa PSinger MChyzak FLabahn G(2021)Separability Problems in Creative TelescopingProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465514(83-90)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465514
Chen SDu LWang RZhu C(2020)On the existence of telescopers for rational functions in three variablesJournal of Symbolic Computation10.1016/j.jsc.2020.08.006Online publication date: Aug-2020
https://doi.org/10.1016/j.jsc.2020.08.006
Chen SDu LZhu CDavenport JWang DKauers MBradford R(2019)Existence Problem of Telescopers for Rational Functions in Three VariablesProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326231(82-89)Online publication date: 8-Jul-2019
https://dl.acm.org/doi/10.1145/3326229.3326231
Arreche C(2016)On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parametersJournal of Symbolic Computation10.1016/j.jsc.2015.11.00675:C(25-55)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1016/j.jsc.2015.11.006

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