Masterclass: Programming in Maple: an extended example using Bohemians

CATW03 - Computational complex analysis

A Bohemian is a BOunded HEight Matrix of Integers (BOHEMI, close enough). Recently I have become very interested in such things; see bohemianmatrices.com for some reasons why. In this hour we will look at a collection of Maple procedures designed (this month!) to answer questions about complex symmetric, tridiagonal, irreducible, zero-diagonal Bohemians (a new class, chosen just for this workshop). This means that there will be (#P)^(m-1) m-dimensional such matrices for a given population of elements P, which for this class cannot contain zero. We will look at fast ways to generate these matrices, how to generate fast(ish) code to compute the characteristic polynomials (and why), and generally use this topic as an excuse to learn some Maple programming.

The hour will assume some familiarity with programming; for instance, if you know Matlab, then you very nearly know Maple already (in some ways they are similar enough that it causes confusion, unfortunately). But it will not be necessary; I hope to encourage a friendly atmosphere and we'll generate some interesting (I hope) images, and perhaps some interesting mathematical conjectures. But even if you know Maple well, you might learn something interesting. All the scripts/worksheets/workbooks have been made available at http://publish.uwo.ca/~rcorless/Maple2019/ so you may download them and run and modify the examples yourself, and generate your own Bohemian images.

Indeed I believe that it is entirely likely that you will be able to formulate your own Bohemian conjectures during this activity; and it has been known for participants to prove theorems about them, during the lecture. Who knows, perhaps your next paper will get its main result during this activity.

Licences for Maple valid for one month have been generously provided for participants by Maplesoft. There will be a representative from Maplesoft here to answer any questions.

This talk is part of the Isaac Newton Institute Seminar Series series.