research-article

Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System

Authors:

Moulay Barkatou,

Thomas Cluzeau,

Jacques-Arthur Weil,

Lucia Di VizioAuthors Info & Claims

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

Pages 63 - 70

https://doi.org/10.1145/2930889.2930932

Published: 20 July 2016 Publication History

Abstract

We consider a linear differential system [A] : y'=A, y}, where A has with coefficients in C(x). The differential Galois group G of [A] is a linear algebraic group which measures the algebraic relations among solutions. Although there exist general algorithms to compute $G$, none of them is either practical or implemented. This paper proposes an algorithm to compute the Lie algebra g of G when [A] is absolutely irreducible. The algorithm is implemented in Maple.

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Cited By

Fischler SRivoal T(2023)Effective algebraic independence of values of E-functionsMathematische Zeitschrift10.1007/s00209-023-03373-9305:3Online publication date: 23-Oct-2023
https://doi.org/10.1007/s00209-023-03373-9
Di Vizio LHardouin CGranier A(2022)Intrinsic Approach to Galois Theory of 𝑞-Difference EquationsMemoirs of the American Mathematical Society10.1090/memo/1376279:1376Online publication date: Sep-2022
https://doi.org/10.1090/memo/1376
Pagès RChyzak FLabahn G(2021)Computing Characteristic Polynomials of p-Curvatures in Average Polynomial TimeProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465524(329-336)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465524
Show More Cited By

Index Terms

Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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cover image ACM Conferences

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

July 2016

434 pages

ISBN:9781450343800

DOI:10.1145/2930889

General Chairs:
Sergei Abramov
Russian Academy of Sciences, Russia
,
Eugene Zima
Wilfrid Laurier University, Canada
,
Program Chair:
Xiao-Shan Gao
Chinese Academy of Sciences, China

Copyright © 2016 ACM.

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Publication History

Published: 20 July 2016

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ISSAC '16: International Symposium on Symbolic and Algebraic Computation

July 20 - 22, 2016

ON, Waterloo, Canada

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Cited By

Fischler SRivoal T(2023)Effective algebraic independence of values of E-functionsMathematische Zeitschrift10.1007/s00209-023-03373-9305:3Online publication date: 23-Oct-2023
https://doi.org/10.1007/s00209-023-03373-9
Di Vizio LHardouin CGranier A(2022)Intrinsic Approach to Galois Theory of 𝑞-Difference EquationsMemoirs of the American Mathematical Society10.1090/memo/1376279:1376Online publication date: Sep-2022
https://doi.org/10.1090/memo/1376
Pagès RChyzak FLabahn G(2021)Computing Characteristic Polynomials of p-Curvatures in Average Polynomial TimeProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465524(329-336)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465524
Amzallag EMinchenko APogudin G(2021)Degree bound for toric envelope of a linear algebraic groupMathematics of Computation10.1090/mcom/3695Online publication date: 28-Oct-2021
https://doi.org/10.1090/mcom/3695
Dreyfus TWeil J(2021)Differential Galois Theory and IntegrationAnti-Differentiation and the Calculation of Feynman Amplitudes10.1007/978-3-030-80219-6_7(145-171)Online publication date: 10-Jul-2021
https://doi.org/10.1007/978-3-030-80219-6_7

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