Mathematics of Information Technology and Complex Systems

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Mathematics of Computer Algebra and Analysis (MOCAA)

Project Leaders: Dr. George Labahn (University of Waterloo) and Dr. Michael Monagan (Simon Fraser University)

Our 2006 MITACS project proposal (.pdf)

Our 2008 MITACS project proposal (.pdf)

Our 2010 MITACS short project proposal (.pdf)

The Computer Algebra community in Canada is strong, coherent and cohesive, and clearly lends itself to functioning as a consortium. It has three substantial nodes at the University of Waterloo, the University of Western Ontario and Simon Fraser University. Each has a core of engaged scientists and students. As well, there is significant ancillary expertise, notably at the University of Calgary, McMaster University, and UQAM. It is not possible to promote, unify and fund this group as a single MITACS project, hence the existence of the Consortium.

The features that drive the success of the consortium are:

  • the size, intellectual strength and breadth of the consortium
  • the focus and cohesiveness of the consortium community
  • the importance to the mathematical sciences of the problems
  • the scientific track record
  • the management track record
  • the track record in training of Highly Qualified Personnel
  • the track record of interaction with industry

The project addresses central problems in algebraic computation. This means developing and implementing algorithms for finding the exact solution(s) to mathematical problems. For example, we may prefer the output to the output 1.727379092. We may prefer the output to the "unknown" sequence of numbers 1, 3, 11/2, 25/3, 137/12, 147/10,.... Or we may be interested in the asymptotics of a solution, e.g.

Because exact formulae tend to grow in size rapidly, algorithmic efficiency and the ability to simplify formulae, that is, to find a compact representation for a formula, is one problem we address. Another problem is that some algorithms require tools from analysis. Our goal here is to be able to deal with analytic concepts in a computational setting (specifically in Maple) as easily as one can already do with algebraic concepts. The scope of the research program includes problems like exact definite integration and summation, finding analytical solutions of ordinary differential equations, solving systems of algebraic and/or differential equations (both ODEs and PDEs), identity and inequality verification, and simplification of algebraic formulae involving symbols representing vectors and matrices as well as integers and reals.

As well as this fundamental research, our program aims to make the results accessible and visible to a wider community by incorporating procedures into Maple and through the production of interactive mathematical tools accessible from the internet.