Indefinite summation of rational functions with factorization of denominators

Polyakov, S. P.

doi:10.1134/s0361768811060077

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…This suggests a solution to the above issue. Namely, find an initial decomposition (1.3) with the smallest possible g 0 using the method proposed in (Polyakov, 2011;Zima, 2011) to initiate the iterative process of the reduction-based approach. However this process requires a full irreducible factorization of polynomials.…”

Section: Introductionmentioning

confidence: 99%

Efficient Rational Creative Telescoping

Giesbrecht¹,

Huang²,

Labahn³

et al. 2019

Preprint

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We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approach, our algorithm has the nice feature that the computation of a telescoper is independent of its certificate. Moreover, our algorithm uses a sparse representation of the certificate, which allows it to be easily manipulated and analyzed without knowing the precise expanded form. This representation hides potential expression swell until the final (and optional) expansion, which can be accomplished in time polynomial in the size of the expanded certificate. A complexity analysis, along with a Maple implementation, suggests that our algorithm has better theoretical and practical performance than the reductionbased approach in the rational case.

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Section: Introductionmentioning

confidence: 99%

Efficient Rational Creative Telescoping

Giesbrecht¹,

Huang²,

Labahn³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, there has been a surge of interest in problems of summation thanks to the development of symbolic algorithms of summation of rational functions in papes by S. A. Abramov [3] and S. P. Polyakov [4], who call these problems "the indefinite summation". In some cases, however, it is more appropriate to use a more general difference equation than (1).…”

Section: Introductionmentioning

confidence: 99%