منابع مشابه
Algebraic Extensions for Symbolic Summation
The main result of this thesis is an effective method to extend Karr’s symbolic summation framework to algebraic extensions. These arise, for example, when working with expressions involving (−1)n. An implementation of this method, including a modernised version of Karr’s algorithm is also presented. Karr’s algorithm is the summation analogue of the Risch algorithm for indefinite integration. I...
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We present symbolic summation tools in the context of difference fields that help scientists in practical problem solving. Throughout this article we present multi-sum examples which are related to combinatorial problems.
متن کاملA difference ring theory for symbolic summation☆
A summation framework is developed that enhances Karr's difference field approach. It covers not only indefinite nested sums and products in terms of transcendental extensions, but it can treat, e.g., nested products defined over roots of unity. The theory of the so-called [Formula: see text]-extensions is supplemented by algorithms that support the construction of such difference rings automat...
متن کاملA Short Bibliography for Symbolic Summation
A foundation for computer science. [10] Peter Paule and Axel Riese. A Mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telescoping. [11] Peter Paule and Carsten Schneider. Computer proofs of a new family of harmonic number identities.
متن کاملSymbolic Summation | Some Recent Developments
In recent years, the problem of symbolic summation has received much attention due to the exciting applications of Zeilberger’s method for definite hypergeometric summation. This lead to renewed interest in the central part of the algorithmic machinery, Gosper’s “classical” method for indefinite hypergeometric summation. We review some of the recent (partly unpublished as yet) work done in this...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2009
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s00200-009-0115-3