Section: New Results

Efficient Algorithms in Computer Algebra

This year has seen the end of the writing and the publication of a book on computer-algebra algorithms [8]. The course at Master 2 level Algorithmes efficaces en calcul formel is a course that Alin Bostan and Frédéric Chyzak have set up progressively since 2005 together with Marc Giusti (LIX), Bruno Salvy (today AriC), as well as, initially, Éric Schost (LIX at the time) and François Ollivier (LIX), and, more recently, Grégoire Lecerf (LIX). The course is very strongly focused to presenting the design of algorithms guided by complexity analysis, with the goal to lead the students to the understanding of all algorithmic aspects that are necessary to the “creative telescoping” used for symbolic computations of sums and integrals. Their lecture notes had been circulating in and used by the (French) computer-algebra community, while they long had the goal of turning them into a book. They could publish it in 2017 (686 pages), after a big finalization effort in 2016 and 2017. The first parts of the book present fast algorithms for basic objects (integers, polynomials, series, matrices, linear recurrences), insisting on general principles to design efficient algorithms. The next parts of the work build on them to address topics that have made recent progress: factorization of polynomials, algorithms for polynomial systems, definite summation and integration. The work [8] is online as a HAL collection(https://hal.archives-ouvertes.fr/AECF/). It is available for free in pdf format and is otherwise sold at a very low price (via print-on-demand). Over the first three months after publication, the book has sold roughly 60 printed copies and the pdf has been downloaded 265 times.