CS 652 - Algorithms and Software for
Symbolic Solvers for Polynomial Systems

University of Western Ontario
Computer Science Department

Date: September 11, 2009

Systems of equations have been studied for centuries. However, the development of symbolic (or exact) methods for solving them is quite recent. No efficient software existed 10 years ago. Many theoretical and practical questions are still open and many problems in mathematical and engineering sciences are solved today by symbolic solvers. Digital signal processing, theoretical physics, cryptography, auto-correcting codes are some of the areas where exact solutions of systems of equations are used. In this course we will describe the key ideas of some of the most popular algorithms for solving systems of equations symbolically (Grobner bases, triangular decompositions). These algorithms are quite elegant but their implementation leads to several difficult challenges. We will explain how emerging techniques (modular algorithms, distributed computations) address these difficulties. Finally, a detailed application will be presented.

Outlines.

This presents the contents of the course, its assignments, quizzes and projects. outline.html

Lectures.

The lecture notes are part of a textbook currently written by the instructor. For this reason, they are distributed directly to the students and not published yet.

Projects.

The dead-line for choosing a project has been extended to Thursday 11 of March and the dead-line for the preliminary mini-project has been extended to Sunday 21 of March. Description of projects (html pages). Description of projects (compressed postscript).

Quizzes.

Quiz 1	Thursday 12 of February
Quiz 2	Thursday 11 of March
Quiz 3	Thursday 25 of March
Quiz 4	Thursday 8 of April

Quiz 1 (html pages). Quiz 1 (compressed postscript). Quiz 2 (html pages). Quiz 2 (compressed postscript). Quiz 3 (html pages). Quiz 3 (compressed postscript). Quiz 4 (html pages). Quiz 4 (compressed postscript).

Ressources.

These are links to some books and software related to the course.

• The Ideals, Varieties, and Algorithms book
• The Using Algebraic Geometry book
• The Modern Computer Algebra book
• The CoCoA Computer Algebra System
• The Singular Computer Algebra System
• The Aldor web site
• The AXIOM Computer Algebra System at NAG ltd
• More about AXIOM