L’élément principal de ce projet réalisé chez MapleSoft, Inc., une société de développement de logiciels et de conseil en affaires, consistera à concevoir la mise en œuvre la plus performante (dans C) d’un ensemble de procédures que le stagiaire a créé au moyen du langage Maple. Ces procédures fournissent l’environnement nécessaire pour faire de l’arithmétique […]

Computer Algebra Systems (CAS), with their unique ability to analyze and solve mathematical problems, are gathering new communities of users, who challenge them with more and more complex tasks. It is necessary, therefore, that the core engines of CAS implement state-of-the-art algorithms. At the same time, CAS need to build new bridges to specialized software […]

The main component of this project with MapleSoft, Inc., a software development and business consulting firm, will be to design a high performance implementation (in C) of a set of procedures the intern has created in Maple language. These procedures provide an environment for doing polynomial arithmetic in a ‘lazy’ way. That is, they allow […]

In this internship, the team proposes to develop high performance sequential and parallel algorithms for multiplication and division of multivariate polynomials. They propose to use a recursive data structure. One of the possible advantages of a recursive data structure is that we can also see how to parallelize polynomial division. Potentially high level algorithms such […]

  The goal of this project is to design and implement new algorithms for factoring polynomials in more than one variable with coefficients which involve algebraic numbers such as the sqrt(2) and algebraic functions such as sqrt(1-c^2).  Our goal is to find new algorithms which are efficient in practice so that scientists and engineers can […]

In many industrial and engineering applications, process control plays a central role. Among the possible control strategies, model predictive control (MPC), also called receding horizon control (RHC), stands out for its excellent ability to handle constraints. While MPC has been successfully applied to many industrial applications, further developments are limited when it becomes necessary to […]

Factoring large polynomials is one of the main tools provided by mathematical software packages like Maple. It is used by scientists, engineers and mathematicians directly to simplify and study large formulas. It is also used inside Maple to do other tasks such as solving systems of polynomial equations. This project proposes to dramatically improve the […]

The goal of this project is to design computationally-efficient solvers that can be used for autonomous vehicle control developments. Because autonomous cars have complex mathematical models, it is usually hard to perform their necessary control computations on-line and when the vehicle is running. Therefore, it is required to come up with much faster solvers for […]