An approach to the zero recognition problem by Buchberger algorithm
type: Item
instance of: scholarly article
title: An approach to the zero recognition problem by Buchberger algorithm
zbMATH Open document ID: 0763.65007
DOI: 10.1016/0747-7171(92)90039-7
author: Nobuki Takayama
published in: Journal of Symbolic Computation
publication date: 1993-01-16T00:00:00Z
review text: This paper has two purposes. The first is to present an algorithm to obtain differential equations for a definite integral with parameters, which is based on the Buchberger algorithm [cf. \textit{B. Buchberger} and \textit{R. Loos}, Computing Suppl. 4, 11-43 (1982; Zbl 0494.68045)]. The second purpose is to improve \textit{D. Zeilberger's} zero recognition method [J. Comput. Appl. Math. 32, No. 3, 321-368 (1990; Zbl 0738.33001)]\ for holonomic functions by the first algorithm. The author presents conjectures and open problems concerning the ``correctness'' of the algorithm.
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 96019
zbMATH Keywords: Buchberger algorithm
zbMATH Keywords: zero recognition method
zbMATH Keywords: holonomic functions
reviewed by: Shiro Ogawa
describes a project that uses: DEtools
MaRDI profile type: Publication
full work available at URL: 0747-7171(92)90039-7
OpenAlex ID: W2086764169
cites work: The method of differentiating under the integral sign
cites work: The analytic continuation of generalized functions with respect to a parameter
cites work: Q3964695
cites work: Algebraic simplification
cites work: Q3714165
cites work: On Canonical Forms and Simplification
cites work: Q3772359
cites work: On the holonomic systems of linear differential equations. II
cites work: Gröbner basis and the problem of contiguous relations
cites work: A holonomic systems approach to special functions identities
cites work: The method of creative telescoping
description: scientific article; zbMATH DE number 96019