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Based on Gosper's algorithm for indeenite hypergeometric summation, Zeilberger's algorithm for proving binomial coeecient identities constitutes a recent breakthrough in symbolic computation. Mathematica implementations of these algorithms are described. Nontrivial examples are given in order to illustrate the usage of these packages which are available by(More)
The problem of computing a closed form for sums of special functions arises in many parts of mathematics and computer science, especially in combinatorics and complexity analysis. Here we discuss two algorithms for indeenite summation of rational functions, due to Abramov and Paule. We describe some improvements and a parallel implementation on a(More)
Indeenite summation essentially deals with the problem of inverting the diierence operator : f(X) ! f(X + 1) ? f(X). In the case of rational functions over a eld k we consider the following version of the problem given 2 k(X), determine ; 2 k(X) such that = +, where is as \small" as possible (in a suitable sense). In particular, we address the question what(More)
Division of integers is called exact if the remainder is zero. We show that the high-order part and the low-order part of the exact quotient can be computed independently from each other. A sequential implementation of this algorithm is up to twice as fast as ordinary exact division and four times as fast as the general classical division algorithm if the(More)
Shows the benefits of applying modern modeling concepts for the simulation and task verification within a robotics/NC machining cell. The authors have developed a software module that is intended to be integrated into graphic robot simulation systems and focuses on the workpiece that is to be produced. The aim is to decide whether the machining process(More)
So far there is no connection between mobile nursing documents, documentation of nursing homes and care documentation of hospitals. Inadequate communication processes affect the quality of nursing care due to time delay and risk of errors due to repeated data entries, and therefore the quality of life for elderly people. In order to enable standardized(More)
This paper is intended as an introduction to the theory of symbolic integration. First a review of integral calculus is given. Then diierential elds are presented as an algebraic framework for representing elementary functions and an algorithm for computing indeenite integrals of such functions is discussed in detail. Finally, a partial implementation of(More)