相关论文: On the length of integers in telescopers for prope…

Leveraging a general framework adapted from symbolic integration, a unified reduction-based algorithm for computing telescopers of minimal order for hypergeometric and q-hypergeometric terms has been recently developed. In this paper, we…

Based on a modified version of Abramov-Petkov\v{s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for…

Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…

Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the…

We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower…

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the…

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 consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…

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 criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed…

We address the problem, not of the determination -- which usually needs numerical methods -- but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there…

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 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…

In this paper, we bound the number of solutions to a quadratic Vinogradov system of equations in which the variables are required to satisfy digital restrictions in a given base. Certain sets of permitted digits, namely those giving rise to…

In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute…

We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the upper bound can be significantly improved on average. As a…

The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified.…

We develop a new approach to address some classical questions concerning the size and structure of integer distance sets. Our main result is that any integer distance set in the Euclidean plane is either very sparse or has all but an…

We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm…

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…