Bruno Salvy

Non-commutative Elimination in Ore Algebras Proves Multivariate Identities

Many computations involving special functions, combinatorial sequences or theirq-analogues can be performed using linear operators and simple arguments on the dimension of related vector spaces. In this article, we develop a theory of ?-finite sequences and functions which provides a unified framework to express algorithms for computing sums and integrals and for the proof or discovery of multivariate identities. This approach is vindicated by an implementation.

Examples of automatic asymptotic expansions

We describe the current state of a Maple library, gdev, designed to perform asymptotic expansions for a large class of expressions. Many examples are provided, along with a short sketch of the underlying principles. At the time when this report is written, a striking feature of these examples is that none of them can be computed directly with any of todays most widespread symbolic computation systems (Macsyma, Mathematica, Maple or Scratchpad II).

Lambda - Upsilon - Omega: An Assistant Algorithms Analyzer

Lambda-Upsilon-Omega, ΛΥΩ, is a system designed to perform automatic analysis of well-defined classes of algorithms operating over “decomposable” data structures.

Efficient programming in Maple: a case study

Studying the computation of orbits of some given group acting on a set, we show how successive refinements of a simple program provide a speedup factor of up to 200. The initial program cannot solve the problem at all, it is first converted into a program which needs one c.p.u. week and after all the optimizations have been performed, the computation takes only four hours. Although the problem is specific, we shall show that many of the optimizations we use are of interest for other problems as well.