Computational Algebra Seminar

John Voight
(University of Sydney)
Basic algorithms for quaternion algebras (cont)
2:30pm–3pm, Thursday 16th February, 2006
Carslaw 351
A quaternion algebra is a central simple algebra of dimension 4 over a field F; they are noncommutative analogues of quadratic field extensions, and hence arise naturally in many different areas of mathematics. In this talk, we introduce quaternion algebras and survey some basic algorithmic questions: giving a standard representation and determining if a quaternion algebra is isomorphic to a matrix ring.

Stephen Watt
(University of Western Ontario, Canada)
Interfaces for Pen-Based Mathematics
3pm–4pm, Thursday 16th February, 2006
Carslaw 351
This talk presents our work in computer interfaces for pen-based mathematics. The goal of our project is to understand how best to build pen-based computer interfaces for mathematics that can be used across a wide variety of applications from PDAs to digital white boards. A robust system for pen-based mathematical computation will comprise a number of components, many of which are sophisticated software systems in their own right. We present the components of our pen-based interface for mathematics, and describe the relationship among them. We describe in some detail:
1. our approach to recognition of characters from large sets of mathematical symbols,
2. our use of empirical sub-expression frequency data, and
3. our portable architecture for a pen-based component that may be embedded in Maple or Microsoft Office.