Abstract
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in the framework of (differential) creative telescoping introduced in [1]. Our approach bases on complexity analysis, by obtaining tight degree bounds on the various differential operators and polynomials involved in the method and its variants. To make the problem more tractable, we restrict in this work to the integration of rational functions. Indeed, by considering a more constrained class of inputs, we are able to blend the general method of creative telescoping with the well-known Hermite reduction [3]. The rational class already has many applications, for instance in combinatorics, where many non-trivial problems are encoded as diagonals of rational formal power series, themselves expressible as integrals.
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