Rob Corless, Editor-in-Chief Maple Transactions

This page provides links to my papers & other expositions; connective tissue for an internet world

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Maple Transactions

I am the Editor-in-Chief for Maple Transactions , a new open-access scholarly journal. The purpose of Maple Transactions is to disseminate excellent expositions on topics of interest to the Maple community. There are no page charges, and you need not use Maple to be published in this journal.

A draft paper on special functions in symbolic computation systems, for comment.

A draft paper on a Chebfun-like environment in Maple using blends, for comment.

A draft paper applying that environment and collocation to solve the Mathieu equation, for comment.

My talk for ANODE 2023

My current obsession: Bohemian Matrices

The Wikipedia entry on Bohemian Matrices

My new book, with Neil Calkin and Eunice Chan! Open access, and in beta: comments welcome!

Computational Discovery on Jupyter Chapter 4 (or is it Unit 4? With a Jupyter Book the old words for divisions of a book are a bit obsolete) covers Bohemian matrices at an entry level.

Possible cover images from Doubly Companion Matrices:

density plot of complex eigenvalues brighter colours mean more eigenvalues

Zoomed in near the left edge:

cropped density plot of complex eigenvalues brighter colours mean more eigenvalues

The cover shows a density plot in the complex plane of the eigenvalues of all 3¹⁶ = 43,046,721 "doubly companion" matrices of dimension $m=8$ with population {-1,0,1}. Because we were unsure of rounding error effects on the delicate structures at the left and right edges, we first computed all 2,184,139 distinct degree 8 characteristic polynomials and solved those accurately in Maple. In fact we need not have worried, and eigenvalue computation, which is faster, resolves the delicate structures quite well. We do not understand those structures. Plotted on the square -2.2 < x < 2.2, -2.2 < y < 2.2. See Butcher JC, Chartier P. The effective order of singly-implicit Runge-Kutta methods. Numerical Algorithms. 1999 Aug;20:269-84 for properties of doubly companion matrices.

A version using the Maple kernel for Jupyter notebooks is under construction. Here is one such notebook, which validates a hand computation of approximate zeros of the Fibonacci function.

An example Jupyter notebook linking to a Maple kernel. The Bohemian Calendar 2023 is out! (Many images produced by the code from the book above) Licensed under CC-by-SA 4.0. See for more information about Bohemian matrices.

Research Interests

I have three major overlapping research areas: computational dynamical systems, computational algebra, and computational special functions, each of which is used in scientific and engineering applications. My main overall concern is for the fidelity and reliability of these algorithms in actual applications. The main approach that I use is Computer-Mediated Thinking or Computational Discovery, or Computational Epistemology. That link goes to a paper describing that idea in a teaching context, but it is a much broader idea, namely that the combination of human plus computer, especially equipped with thin slices of Artificial Intelligence, can be better than the human alone.