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Séminaire Lotharingien de Combinatoire, S43b (2000), 10 pp.

# Carsten Schneider

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An Implementation of Karr's Summation Algorithm in Mathematica

**Abstract.**
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 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.

Received: February 16, 2000; Accepted: February 28, 2000.

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