Abstract Matrices in Symbolic Computation
Volker Sorge, University of Birmingham, UK
Friday, March 9, 2007, at U. of Waterloo.
Abstract:
Computer Algebra systems commonly deal well with matrix structures and
calculations. However, their handling of matrices is still far from
every day mathematical practice, where matrices are often not given as
fully specified objects, but rather are of indefinite dimension and
In my talk I shall describe work on developing procedures to handle
general matrix expressions involving precisely these features. For
such a useful representation of a common mathematical structure, two
dimensional matrix expressions possess some surprisingly subtle
complexities that require careful analysis and correspondingly
involved algorithms to tease out their true meaning. I shall present
our approach, which involves graph analysis, constraint maintenance,
2d region finding, antiunification and surface interpolation.
Our procedures can be used as an input mechanism for diverse
mathematical software. In particular, they provide a framework for a
constraint based exploration of matrix problems in a computer algebra
system. In addition they have applications as search and storage
structure, or as a semantic validator for improving document
recognition accuracy.
This is joint work with Alan Sexton.
