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Bounds for Substituting Algebraic Functions into D-finite Functions

Authors:

Manuel Kauers,

Gleb PogudinAuthors Info & Claims

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

Pages 245 - 252

https://doi.org/10.1145/3087604.3087616

Published: 23 July 2017 Publication History

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Abstract

It is well known that the composition of a D-finite function with an algebraic function is again D-finite. We give the first estimates for the orders and the degrees of annihilating operators for the compositions. We find that the analysis of removable singularities leads to an order-degree curve which is much more accurate than the order-degree curve obtained from the usual linear algebra reasoning.

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Cited By

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Bostan ANeiger VYurkevich S(2023)Beating binary powering for polynomial matricesProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597118(70-79)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597118
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

Bounds for Substituting Algebraic Functions into D-finite Functions
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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Published In

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

July 2017

466 pages

ISBN:9781450350648

DOI:10.1145/3087604

Editor:
Michael Burr
Clemson University, USA
,
General Chair:
Chee K. Yap
New York University, USA
,
Program Chair:
Mohab Safey El Din
University Pierre et Marie Curie, France

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 the author(s) 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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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: 23 July 2017

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Austrian Science Fund (FWF)

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ISSAC '17

ISSAC '17: International Symposium on Symbolic and Algebraic Computation

July 23 - 28, 2017

Kaiserslautern, Germany

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

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Bostan ANeiger VYurkevich S(2023)Beating binary powering for polynomial matricesProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597118(70-79)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597118
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

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