The research project will bring together the latest advances in computational real algebraic geometry and high-performance computing techniques.
Postdoctoral fellow: Dr. Rong Xiao, Computer Science, University of Western Ontario
Lead faculty member: Dr. Marc Moreno Maza, Computer Science, University of Western Ontario
The theoretical and practical aspects of manipulating mathematical expressions on computers are usually referred to as computer algebra or symbolic computation. In this field, calculations are designed to yield exact and complete results, by opposition to numerical analysis which is meant to handle approximate values, potentially producing incomplete results. Exactness and completeness have some significant computational overhead. Computer algebra software is highly demanding in CPU time and memory. These challenges are even more dramatic for calculations involving real numbers that are not necessarily rational. However, many real world applications today require exact computation with such real numbers. The proposed research will bring together the latest advances in computational real algebraic geometry and high-performance computing techniques. Our goal is to generate application driven packages for MAPLE, the flagship product of our industrial partner. Our targeted areas, where we have already acquired experience, are algebraic simplification, dynamical system analysis and program verification.