MITACS Projects at Simon Fraser University
Michael Monagan, Centre for Experimental and Constructive Mathematics,
Simon Fraser University
Thursday, March 9, 2006, at U. of Waterloo.
Abstract:
In this talk I will present three projects, two detailing some of the work
undertaken by the computer algebra group at SFU for our MITACS project with
MapleSoft. The first project is to develop a new graph theory package for
Maple. Included amongst its many features is a good graph drawing algorithm
for 2 and 3 dimensions which I will demonstrate during the talk.
The second project involves implementations of algorithms for linear algebra
operations, like Gaussian elimination, that work over an arbitrary field or
integral domain. For this we need to define what a field is in Maple. Our
solution is simple and easy to use. I will demonstrate this for doing
linear algebra over quotient rings.
The third project is to develop an efficient modular algorithm for solving a
sequence of large (400 by 400) linear systems involving roots of unity (up
to e^276=1) that come from a group theory application. In the course of
getting an efficient solution, I have found a simple trick that essentially
eliminates the cost of rational number reconstruction.
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