As you know, I'm a MATLAB person.

What made MATLAB so great was the realization that many computations come down to vectors

and matrices.

But we had the idea, after we heard about object-oriented programming, we had the idea

of overloading discrete objects to continuous ones.

So MATLAB has a vector and you can operate on the vector.

Why not overload that to do analogous operations on functions?

Or a matrix you might put the load to become an operator.

So that was the vision of CHEBFUN 20 years ago and the idea is to implement everything

with CHEBISHEF polynomials, which I won't say very much about.

I'll say a little bit maybe.

So most of this hour I'm going to spend showing you CHEBFUN, talking about CHEBFUN.

Let's spend a moment at the website here.

I'm not sure if that's perfectly focused, but I guess it's okay.

We had a wonderful five or six years with a big team working on this and it's now a

very tidy project.

With a nice website, you Google CHEBFUN and you'll find CHEBFUN.org.

And if you go to the website, let me draw your attention to DOCS, which stands for documents,

of course.

And if you go to the CHEBFUN guide, you'll see that there are 20 chapters about what

to do.

But the first chapter is the introduction.

So just read that and you'll get the idea.

Another thing to point out at the website is the, I'll go to about and the history.

No, I'll go to people.

So if you're curious about who has been involved, they're not all here, but most of the people

involved are described here.

It's been a collection of students and post-docs mostly, some faculty members.

I could talk about all of these people at length, but I won't do that.

It's an open source project written in a commercial language because it's written in MATLAB.

So that's weird.

This is, I think, the world's biggest open source project in MATLAB or the world's most

impactful one.

But of course, a lot of people don't like MATLAB in principle because it's commercial.

And I wish there were a Python version of CHEBFUN.

There isn't right now.

There are Python versions of little parts of CHEBFUN, but nothing like the full thing.

Also in Julia, there are Julia things that do a little bit of CHEBFUN, but nothing like

all of CHEBFUN.

If I go to examples, that's the other thing I wanted to show you.

We have about 300 examples online of calculations using CHEBFUN.

So these are the chapter headings, if you like, and in each chapter, you have a bunch

of different things.

And quite a few of these are non-trivial.

So as we've learned interesting mathematics over the years, we've often written an example

about that.

And it's a lot of fun.

Pick a subject you like and take a look.

Can you open, for instance, this one, distance between the cores?

Of course.