New Bounds for Hypergeometric Creative Telescoping

Hui Huang

New Bounds for Hypergeometric Creative Telescoping

Hui Huang

Institut für Algebra

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

Abstract

Based on a modified version of Abramov-Petkov{\v s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination of this algorithm, which provides an independent proof of the existence of telescopers and even enables us to derive lower as well as upper bounds for the order of telescopers for hypergeometric terms. Compared to the known bounds in the literature, our bounds are sometimes better, and never worse than the known ones.

Originalsprache	Englisch
Titel	ISSAC '15 Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation
Herausgeber*innen	Markus Rosenkranz
Seitenumfang	8
Publikationsstatus	Veröffentlicht - Juni 2016

Wissenschaftszweige

101 Mathematik
101001 Algebra
101005 Computeralgebra
101013 Mathematische Logik
102031 Theoretische Informatik

JKU-Schwerpunkte

Computation in Informatics and Mathematics
TNF Allgemein

Dieses zitieren

@inproceedings{e4e4f9fe1e2e415fbad478cfcb6a04b7,

title = "New Bounds for Hypergeometric Creative Telescoping",

abstract = "Based on a modified version of Abramov-Petkov\{\textbackslash{}v s\}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination of this algorithm, which provides an independent proof of the existence of telescopers and even enables us to derive lower as well as upper bounds for the order of telescopers for hypergeometric terms. Compared to the known bounds in the literature, our bounds are sometimes better, and never worse than the known ones.",

author = "Hui Huang",

year = "2016",

month = jun,

language = "English",

editor = "\{Markus Rosenkranz\}",

booktitle = "ISSAC '15 Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation",

}

TY - GEN

T1 - New Bounds for Hypergeometric Creative Telescoping

AU - Huang, Hui

PY - 2016/6

Y1 - 2016/6

N2 - Based on a modified version of Abramov-Petkov{\v s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination of this algorithm, which provides an independent proof of the existence of telescopers and even enables us to derive lower as well as upper bounds for the order of telescopers for hypergeometric terms. Compared to the known bounds in the literature, our bounds are sometimes better, and never worse than the known ones.

AB - Based on a modified version of Abramov-Petkov{\v s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination of this algorithm, which provides an independent proof of the existence of telescopers and even enables us to derive lower as well as upper bounds for the order of telescopers for hypergeometric terms. Compared to the known bounds in the literature, our bounds are sometimes better, and never worse than the known ones.

M3 - Conference proceedings

BT - ISSAC '15 Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation

A2 - Markus Rosenkranz, null

ER -