SEMINAR: Groups and Combinatorics Seminar, Analysis and Implementation: the Two 'Editions' of a Matrix Group Algorithm

Brian Corr (UWA)

will speak on

Analysis and Implementation: the Two 'Editions' of a Matrix Group Algorithm

at 3pm Friday January the 10th in Blakers Lecture Theatre.

Abstract :

The quality of an algorithm in computational mathematics is represented by two separate, yet equally important measures: the theoretical analyses which measure the runtime's growth for large input, and the implementations whose runtimes we can measure in seconds. This leads to different aspects of algorithm design being prioritised in different settings, and often two very different algorithms are produced: one is described in a journal article analysing the worst-case complexity, and a very different procedure is implemented in practice.

In this talk I present the motivation, overall structure, and details of a reduction algorithm for specific irreducible modules of a classical group G, and discuss issues specific to the implementation of the algorithm in the Magma computer algebra system.

This is joint work with Cheryl Praeger and Akos Seress, with special thanks to Eamonn O'Brien.