An implementation of Karr's summation algorithm in Mathematica
type: Item
instance of: scholarly article
title: An implementation of Karr's summation algorithm in Mathematica
zbMATH Open document ID: 0941.68162
author: Carsten Schneider
published in: Séminaire Lotharingien de Combinatoire
publication date: 2000-04-17T00:00:00Z
full work available at URL: https://eudml.org/doc/120438
full work available at URL: s43schneider.html
review text: Implementations of the celebrated Gosper algorithm for indefinite summation are available on almost any computer algebra platform. We report here about an implementation of an algorithm by Karr, the most general indefinite summation algorithm known. Karr's algorithm is, in a sense, the summation counterpart of Risch's algorithm for indefinite integration. This is the first implementation of this algorithm in a major computer algebra system. Our version contains new extensions to handle also definite summation problems. In addition, we provide a feature to find automatically appropriate difference field extensions in which a closed form for the summation problem exists. These new aspects are illustrated by a variety of examples.
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 33F10
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 12H10
zbMATH DE Number: 1432860
zbMATH Keywords: Karr algorithm
describes a project that uses: qZeil
describes a project that uses: Mathematica
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1432860