A refined difference field theory for symbolic summation
نویسندگان
چکیده
منابع مشابه
A Refined Difference Field Theory for Symbolic Summation
In this article we present a refined summation theory based on Karr’s difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the algorithms have been applied successively to evaluate Feynman integrals from Perturbative Quantum Field Theory.
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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...
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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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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2008
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2008.01.001