Article

Computer proofs for polynomial identities in arbitrary many variables

Author:

Manuel KauersAuthors Info & Claims

ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation

Pages 199 - 204

https://doi.org/10.1145/1005285.1005315

Published: 04 July 2004 Publication History

Abstract

We present an algorithm for proving certain families of nomial identities in which the number of variables appears as a parameter.Typically,indefinite sums and products (possibly nested)are used for defining such polynomial ties, but in principle the definition of the problem may be given in terms of arbitrary polynomial recurrences (possibly nonlinear). An implementation of our algorithm in Mat e-matica was able to verify identities appearing in textbooks, which, to our knowledge,were previously not accessible by any symbolic method. A collection of examples is included in the paper.

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G.E.Andrews,R.Askey,and R.Roy. Special Functions, volume 71 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1999.

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F. Chyzak. An extension of Zeilberger's fast algorithm to general holonomic functions. Discrete Mathematics, 217:115--134, 2000.

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R. M. Cohn. Difference Algebra. Interscience Publishers, John Wiley & Sons,1965.

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R. L. Graham, D. E. Knuth,and O. Patashnik. Concrete Mathematics. Addison-Wesley, second edition, 1994.

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M. Kauers. An algorit m for deciding zero equivalence of nested polynomially recurrent sequences. Technical Report 2003-48,SFB F013,Johannes Kepler Universität, 2003.(submitted).

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M. Petkovsek, H. Wilf,and D. Zeilberger. A = B. AK Peters, Ltd.,1997.

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C. Scheider. Symbolic Summation in Difference Fields . PhD thesis, RISC-Linz, Johannes Kepler Universit7auml;t Linz,2001.

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D. Zeilberger. A fast algorithm for proving terminating hypergeometric identities. Discrete Mathematics, 80:207--211,1990.

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Cited By

Kauers MSchneider C(2019)Indefinite summation with unspecified summandsDiscrete Mathematics10.1016/j.disc.2006.04.005306:17(2073-2083)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.disc.2006.04.005
Kauers M(2007)An algorithm for deciding zero equivalence of nested polynomially recurrent sequencesACM Transactions on Algorithms10.1145/1240233.12402413:2(18-es)Online publication date: 1-May-2007
https://dl.acm.org/doi/10.1145/1240233.1240241
Kauers MSchneider CTrager B(2006)Application of unspecified sequences in symbolic summationProceedings of the 2006 international symposium on Symbolic and algebraic computation10.1145/1145768.1145800(177-183)Online publication date: 9-Jul-2006
https://dl.acm.org/doi/10.1145/1145768.1145800
Show More Cited By

Index Terms

Computer proofs for polynomial identities in arbitrary many variables
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Conferences

ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation

July 2004

334 pages

ISBN:158113827X

DOI:10.1145/1005285

General Chair:
Josef Schicho
RICAM, Austrian Academy of Sciences, Linz, Austria

Copyright © 2004 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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Published: 04 July 2004

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ISSAC04: International Symposium on Symbolic and Algebraic Computation

July 4 - 7, 2004

Santander, Spain

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Kauers MSchneider C(2019)Indefinite summation with unspecified summandsDiscrete Mathematics10.1016/j.disc.2006.04.005306:17(2073-2083)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.disc.2006.04.005
Kauers M(2007)An algorithm for deciding zero equivalence of nested polynomially recurrent sequencesACM Transactions on Algorithms10.1145/1240233.12402413:2(18-es)Online publication date: 1-May-2007
https://dl.acm.org/doi/10.1145/1240233.1240241
Kauers MSchneider CTrager B(2006)Application of unspecified sequences in symbolic summationProceedings of the 2006 international symposium on Symbolic and algebraic computation10.1145/1145768.1145800(177-183)Online publication date: 9-Jul-2006
https://dl.acm.org/doi/10.1145/1145768.1145800
Kauers M(2006)SumCracker: A package for manipulating symbolic sums and related objectsJournal of Symbolic Computation10.1016/j.jsc.2006.06.00541:9(1039-1057)Online publication date: Sep-2006
https://doi.org/10.1016/j.jsc.2006.06.005
Gerhold SKauers MGao XLabahn G(2005)A procedure for proving special function inequalities involving a discrete parameterProceedings of the 2005 international symposium on Symbolic and algebraic computation10.1145/1073884.1073907(156-162)Online publication date: 24-Jul-2005
https://dl.acm.org/doi/10.1145/1073884.1073907

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