Rational Summation and Gosper-Petkovšek Representation

Pirastu, Roberto; Strehl, Volker

doi:10.1006/jsco.1995.1068

Cited by 33 publications

(21 citation statements)

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“…This formulation agrees with the minimal additive decomposition problem for rational functions (Abramov, 1975(Abramov, , 1995Pirastu and Strehl, 1995) because if T 2 ∈ K(x), then r = s = 1 and v is the denominator of T 2 .…”

Section: Introductionmentioning

confidence: 58%

“…The following well-known form is used in algorithms for hypergeometric summation (Gosper, 1978), finding hypergeometric solutions of difference equations (Petkovšek, 1992), and rational summation (Pirastu and Strehl, 1995).…”

Section: Rational Normal Formsmentioning

confidence: 99%

“…(For definitions, see the last paragraph of this section.) First, recall the well-known decomposition problems for indefinite integrals (Hermite, 1872;Ostrogradsky, 1845) and indefinite sums (Abramov, 1975(Abramov, , 1995Paule, 1995;Pirastu and Strehl, 1995) of rational functions. Suppose for simplicity that a rational function R has no poles at non-negative arguments.…”

Section: Introductionmentioning

confidence: 99%

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Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms

Абрамов

Petkovšek

2002

Journal of Symbolic Computation

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We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. On the basis of this form we propose an algorithm which, given a rational function R, extracts a rational part F from the product of consecutive values of R: R(k).We also present an algorithm which, given a hypergeometric term T (n), constructs hypergeometric terms T 1 (n) and T 2 (n) such that T (n) = ∆ T 1 (n) + T 2 (n) and T 2 (n) is minimal in some sense. This solves the additive decomposition problem for indefinite sums of hypergeometric terms: ∆ T 1 (n) is the "summable part", and T 2 (n) the "nonsummable part" of T (n). In other words, we get a minimal additive decomposition of the hypergeometric term T (n).

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Section: Introductionmentioning

confidence: 58%

Section: Rational Normal Formsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms

Абрамов

Petkovšek

2002

Journal of Symbolic Computation

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“…Ehrhart's theorem is the prime example of this phenomenon. To set the stage, we introduce some terminology and refer to [46,57] for concepts from polyhedral geometry not defined here.…”

Section: Ehrhart Theorymentioning

confidence: 99%

Computer Algebra and Polynomials

2015

Lecture Notes in Computer Science

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“…Later, several other algorithms for problem 2 were invented (see [3][4][5]). In [6], a survey of these algorithms is given, and the efficiencies of their Maple implementations are compared.…”

Section: Introductionmentioning

confidence: 99%