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A method for the integration of solutions of Ore equations

Authors:

Sergei A. Abramov,

Mark van HoeijAuthors Info & Claims

ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation

Pages 172 - 175

https://doi.org/10.1145/258726.258774

Published: 01 July 1997 Publication History

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References

[1]

S. A. Abramov (1989): Rational solutions of linear difference and differential equations with polynomial coefficients, USSR Comput. Maths. Math. Phys. 29, 7- 12. Transl. from Zl. Vych~slit. matem, mat. fiz. 29, 1611 - 1620.

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S. A. Abramov, K. Yu. Kvashenko (1991): Fast algorithm to search for the rational solutions of linear differential equations, Proc. ISSAC'91,267- 270.

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S. A. Abramov (1995): Rational solutions of linear difference and q-difference equations with polynomial coefficients, Programmin9 and Comput. Software 21, No 6, 273 -- 278. Transl. from Programmirovanie, No 6, 3 -ll.

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F. Chyzak, B. Salvy (1996): Non-commutative elimination in Ore algebra proves multivariate holonomic identities, INRIA Research Report, No 2799.

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M. van Hoeij (1996): Rational Solutions of the Mixed Differential Equation and its Application to Factorization of Differential Operators, Proc. ISSAC'96, 219- 225.

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O. Ore (1933): The theory of non-commutative polynomials, Ann. Maths. 34, 480- 508.

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Cited By

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Du HRaab C(2025)Reduction systems and degree bounds for integrationJournal of Symbolic Computation10.1016/j.jsc.2025.102432(102432)Online publication date: Feb-2025
https://doi.org/10.1016/j.jsc.2025.102432
Chen SFeng RKauers MLi X(2024)Parallel Summation in P-Recursive ExtensionsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669678(82-90)Online publication date: 16-Jul-2024
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Chen SFeng RGuo ZLu W(2023)Stability Problems on D-finite FunctionsProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597085(164-172)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597085
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A method for the integration of solutions of Ore equations
1. Mathematics of computing

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Published In

ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computation

July 1997

414 pages

ISBN:0897918754

DOI:10.1145/258726

Chairmen:
Bruce Char
Drexel Univ., Philadelphia, PA
,
Paul S. Wang
Kent State Univ., Kent, OH
,
Editor:
Wolfgang W. Küchlin
Univ. of Tu¨bingen, Tu¨bingen, Germany

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1997

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ISSAC97: International Symposium on Symbolic and Algebraic Computation

July 21 - 23, 1997

Hawaii, Kihei, Maui, USA

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

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Du HRaab C(2025)Reduction systems and degree bounds for integrationJournal of Symbolic Computation10.1016/j.jsc.2025.102432(102432)Online publication date: Feb-2025
https://doi.org/10.1016/j.jsc.2025.102432
Chen SFeng RKauers MLi X(2024)Parallel Summation in P-Recursive ExtensionsProceedings of the 2024 International Symposium on Symbolic and Algebraic Computation10.1145/3666000.3669678(82-90)Online publication date: 16-Jul-2024
https://dl.acm.org/doi/10.1145/3666000.3669678
Chen SFeng RGuo ZLu W(2023)Stability Problems on D-finite FunctionsProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597085(164-172)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597085
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 HLi ZKauers MOvchinnikov ASchost É(2018)Additive Decompositions in Primitive ExtensionsProceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3208976.3208987(135-142)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3208976.3208987
Chen S(2018)Bivariate Extensions of Abramov’s Algorithm for Rational SummationAdvances in Computer Algebra10.1007/978-3-319-73232-9_4(93-104)Online publication date: 26-Feb-2018
https://doi.org/10.1007/978-3-319-73232-9_4
Chen SHou QLabahn GWang RAbramov SZima EGao X(2016)Existence Problem of TelescopersProceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930895(167-174)Online publication date: 20-Jul-2016
https://dl.acm.org/doi/10.1145/2930889.2930895
Abramov SRyabenko A(2013)Linear q-difference equations depending on a parameterJournal of Symbolic Computation10.1016/j.jsc.2011.12.01749(65-77)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1016/j.jsc.2011.12.017
Gheffar AAbramov S(2011)Valuations of rational solutions of linear difference equations at irreducible polynomialsAdvances in Applied Mathematics10.1016/j.aam.2010.07.00247:2(352-364)Online publication date: 1-Aug-2011
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Abramov SGheffar AKhmelnov D(2010)Factorization of polynomials and GCD computations for finding universal denominatorsProceedings of the 12th international conference on Computer algebra in scientific computing10.5555/1893832.1893834(4-18)Online publication date: 6-Sep-2010
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