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Synthetic division in the context of indefinite summation

Published: 07 June 2012 Publication History

Abstract

Let K be a field of characteristic zero, x - an independent variable, E - shift operator with respect to x, i.e. Ef(x) = f(x + 1) for an arbitrary expression f(x). The problem of indefinite summation in general is: given a closed form expression F(x) to find a closed form expression G(x), which satisfies the first order linear difference equation
[EQUATION]

References

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S. A. Abramov. The summation of rational functions. Ž. Vyčisl. Mat. i Mat. Fiz., 11:1071--1075, 1971.
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S. A. Abramov. The rational component of the solution of a first order linear recurrence relation with rational right hand side. Ž. Vyčisl. Mat. i Mat. Fiz., 15(4):1035--1039, 1090, 1975.
[3]
S. A. Abramov. Indefinite sums of rational functions. In Proceedings of the 1995 international symposium on Symbolic and algebraic computation, ISSAC '95, pages 303--308, New York, NY, USA, 1995. ACM.
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J. Gerhard, M. Giesbrecht, A. Storjohann, and E. V. Zima. Shiftless decomposition and polynomial-time rational summation. In Proc. of ISSAC'03, pages 119--126, New York, 2003. ACM.
[5]
R. Pirastu. A note on the minimality problem in indefinite summation of rational functions. In Séminaire Lotharingien de Combinatoire (Saint-Nabor, 1993), volume 1994/21 of Prépubl. Inst. Rech. Math. Av., pages 95--101. Univ. Louis Pasteur, Strasbourg, 1994.
[6]
S. P. Polyakov. Indefinite summation of rational functions with additional minimization of the summable part. Programmirovanie, (2):48--53, 2008.

Cited By

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  • (2021)Efficient rational creative telescopingJournal of Symbolic Computation10.1016/j.jsc.2021.07.005Online publication date: Jul-2021
  • (2013)Accelerating Indefinite Summation: Simple Classes of SummandsMathematics in Computer Science10.1007/s11786-013-0170-97:4(455-472)Online publication date: 29-Dec-2013

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    cover image ACM Conferences
    SNC '11: Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
    June 2012
    194 pages
    ISBN:9781450305150
    DOI:10.1145/2331684

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    New York, NY, United States

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    Published: 07 June 2012

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    1. efficient indefinite summation
    2. synthetic division

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    View all
    • (2021)Efficient rational creative telescopingJournal of Symbolic Computation10.1016/j.jsc.2021.07.005Online publication date: Jul-2021
    • (2013)Accelerating Indefinite Summation: Simple Classes of SummandsMathematics in Computer Science10.1007/s11786-013-0170-97:4(455-472)Online publication date: 29-Dec-2013

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