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Mathematics of Computer Algebra and Analysis

Project Type: 
Past

This project focuses on the design and implementation of algorithms for these systems.

Project Leader(s): 

Dr. Michael Monagan, Simon Fraser University & Dr. George Labahn, University of Waterloo

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems. These include a new compact way to represent the core tools (polynomials) and their fundamental arithmetic operations. Additional advances also include new algorithms for computing the greatest common divisors of polynomials, which have been incorporated into Maple. The latter advance provides a huge improvement for important operations such as the simplification of large complex formulae. It is the inability of Maple and other computer algebra systems to efficiently simplify large formulae that has often been a key problem in preventing the system from solving industrial sized problems.

Project team: 
Dr. Jonathan Borwein, Dalhousie University
Dr. Peter Borwein, Simon Fraser University
Dr. Petr Lisonek, Simon Fraser University
Dr. Marni Mishna, Simon Fraser University
Dr. Mark Giesbrecht, University of Waterloo
Dr. Arne Storjohann, University of Waterloo
Dr. Rob Corless, University of Western Ontario
Dr. David Jeffrey, University of Western Ontario
Dr. Marc Moreno Maza, University of Western Ontario
Dr. Greg Reid, University of Western Ontario
Dr. Eric Schost, University of Western Ontario
Dr. Stephen Watt, University of Western Ontario
Dr. Jacques Carette, McMaster University
Dr. Howard Cheng, University of Lethbridge
Dr. Wayne Eberly, University of Calgary
Non-academic participants: 
Funding period: 
February 25, 2022 - March 31, 2021