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An Implementation of Karr's Summation Algorithm in Mathematica

Carsten Schneider
Journal / Anthology

Séminaire Lotharingien de Combinatoire
Year: 1999
Volume: 43
Page range: 1-10

Implementations of the celebrated Gosper algorithm (1978) 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 couterpart 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 extension in which a closed form for the summation problem exists. These new aspects are illustrated by a variety of examples.

*Mathematics > Discrete Mathematics > Combinatorics