Related papers: Constructing minimal telescopers for rational func…
We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is…
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for…
In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of bivariate rational functions, which has been solved recently. The…
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of…
We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition and allows to decide…
Continuing a series of articles in the past few years on creative telescoping using reductions, we develop a new algorithm to construct minimal telescopers for algebraic functions. This algorithm is based on Trager's Hermite reduction and…
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain…
We give necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers. Using this…
We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…
This paper is a plea for diagonals and telescopers of rational, or algebraic, functions using creative telescoping, in a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and…
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
The ubiquity of the class of D-finite functions and P-recursive sequences in symbolic computation is widely recognized. In this thesis, the presented work consists of two parts related to this class. In the first part, we generalize the…
We show that the results we had obtained on diagonals of nine and ten parameters families of rational functions using creative telescoping, yielding modular forms expressed as pullbacked $ _2F_1$ hypergeometric functions, can be obtained,…
Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them…
Continuing a series of articles in the past few years on creative telescoping using reductions, we adapt Trager's Hermite reduction for algebraic functions to fuchsian D-finite functions and develop a reduction-based creative telescoping…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We showcase a collection of practical strategies to deal with a problem arising from an analysis of integral estimators derived via quasi-Monte Carlo methods. The problem reduces to a triple binomial sum, thereby enabling us to open up the…
This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative…