The Summation of Rational Functions by an Extended Gosper Algorithm

Malm, Donald E. G.; Subramaniam, T. N.

doi:10.1006/jsco.1995.1018

Cited by 4 publications

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“…Concerning rational summation we want to point out that Malm and Subramaniam (1995) came up with another Horowitz analogue. A de nite answer concerning the question of optimality of such analogues has been given by Pirastu & Strehl (1994) in the following sense: given the proper rational function r with a generic numerator they are able to solve the decomposition problem r = s + t optimally in the sense that also the degree of the reduced denominator of s is minimal.…”

Section: Resultsmentioning

confidence: 99%

Greatest Factorial Factorization and Symbolic Summation

Paule

1995

Journal of Symbolic Computation

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The greatest factorial factorization (GFF) of a polynomial provides an analogue to square-free factorization but with respect to integer shifts instead to multiplicities. We illustrate the fundamental role of that concept in the context of symbolic summation. Besides a detailed discussion of the basic GFF notions we present a new approach to the inde nite rational summation problem as well as to Gosper's algorithm for summing hypergeometric sequences.

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Section: Resultsmentioning

confidence: 99%

Greatest Factorial Factorization and Symbolic Summation

Paule

1995

Journal of Symbolic Computation

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“…Let us conclude by illustrating some of our procedures on the following example considered in both [PS95,MS95]. In order to make the computations easier for the human reader to follow, we have allowed ourselves to write down explicitly in this small example both irreducible factorizations of denominators.…”

Section: Examplementioning

confidence: 99%

Mahler Discrete Residues and Summability for Rational Functions

Arreche

Zhang

2022

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

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We construct Mahler discrete residues for rational functions and show that they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function f (x) is of the form д(x p ) − д(x) for some rational function д(x) and an integer p > 1. This extends to the Mahler case the analogous notions, properties, and applications of discrete residues (in the shift case) and q-discrete residues (in the q-difference case) developed by Chen and Singer. Along the way we define several additional notions that promise to be useful for addressing related questions involving Mahler difference fields of rational functions, including in particular telescoping problems and problems in the (differential) Galois theory of Mahler difference equations. CCS CONCEPTS• Computing methodologies → Algebraic algorithms.

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Accelerating Indefinite Summation: Simple Classes of Summands

Zima

2013

Math.Comput.Sci.

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The Summation of Rational Functions by an Extended Gosper Algorithm

Cited by 4 publications

References 0 publications

Greatest Factorial Factorization and Symbolic Summation

Greatest Factorial Factorization and Symbolic Summation

Mahler Discrete Residues and Summability for Rational Functions

Accelerating Indefinite Summation: Simple Classes of Summands

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