I’ll admit it. There are times when I don't fully understand every mathematical advancement each release of Maple brings. Given the breadth of what Maple does, I guess that isn't surprising.

In development meetings, I make the pretence of keeping up by looking serious, nodding knowingly and occasionally asking to go back to the previous slide “for a minute”. I’ve been doing this since 2008 and no one’s caught on yet.

But I do understand

- the joy on a user’s (Zoom) face when they finally solve a complex problem with a new version of Maple
- the smiley emojis that students send us when they understand a tricky math concept with the help of an improved Maple tutor
- and the wry smile on a developer’s face when they get to work on a project they
*really* want to work on, and the bigger smile when that project gets positive feedback

These are all moments that give me that magic dopamine hit.

The job that Karishma and I have is to make users happy. We don’t have to be top-flight mathematicians, engineers or computer scientists to do that. We just have to know what itch to scratch.

Here’s some things I think might give you that dopamine hit when you get your hands on Maple 2021. You can also explore the new release yourself at What’s New in Maple 2021.

### Document Mode

Worksheet mode has been my go-to interface for when I just want to get stuff done. This is mostly because worksheet mode always felt like a more *structured* environment for developing math when I didn’t have all the steps planned out in advance, and I found that structure helpful. I’d use Document mode when I needed to use the Context Panel for math operations and didn’t want to see the commands, or I needed to create a nice looking document without input carets. And this was fine – each mode has its own strengths and uses – but I what I really wanted was the best of both worlds in a single environment.

This year, we’ve made one change that has let me transition far more of my work into Document mode.

In Document Mode, pressing Enter in a document block (math input) now *always* moves the cursor to the next math input (in previous releases, the cursor may have moved to the start of the next line of text).

This means you can now quickly update parameters and see the downstream effects with just the Enter key – previously, a key benefit of worksheet mode only.

There’s another small change we’ve made - inserting new math inputs. In previous releases of Maple, you could only insert new document blocks above the in-focus block using a menu item or a three-key shortcut.

In Maple 2021, if you move the insertion point to the left of a document block (Home position), the cursor is now bold, as illustrated here:

Now, if you press Enter, the in-focus prompt is moved down and a new empty math input is created.

Once you get used to this change, Ctrl+Shift+K seems like a distance memory!

### Numerically Solve Vectorised Differential Equations

@Scot Gould logged a request that Maple numerically solve a group of differential equations collected together in a vector. And now you can!

### New Simplifications Involving the LambertW Function

Before Maple 2021, this expression was unchanged after evaluation. Now, it is satisfyingly simpler.

### MUSIC to my ears

We’ve dramatically increased the scope of the signal processing package.

My favorite addition is the MUSIC function. With some careful tuning, you can generate a pseudo power spectrum at frequencies smaller than one sample.

First generate a noisy data set with three frequencies (two frequencies are closer than one DFT bin).

with(SignalProcessing):
num_points:= 2^8:
sample_rate := 100.0:
T := Vector( num_points, k -> 2 * Pi * (k-1) / sample_rate, 'datatype' = 'float[8]' ):
noisy_signal:=Vector( num_points, k -> 5 * sin( 10.25 * T[k] ) + 3 * sin( 10.40 * T[k] ) - 7 * sin( 20.35 * T[k] )) + LinearAlgebra:-RandomVector(num_points, generator=-10..10):
dataplot(noisy_signal, size = [ 800, 400 ], style = line)

Now generate a standard periodogram

Periodogram( noisy_signal, samplerate = sample_rate, size = [800, 400] )

This approach can’t discriminate between the two closely spaced frequencies.

And now the MUSIC pseudo spectrum

MUSIC( noisy_signal, samplerate = sample_rate, dimension = 6, output = plot );

### Molecules

The Maple Quantum Chemistry Toolbox from RDMChem, a separate add-on product to Maple, is a powerful environment for the computation and visualization of the electronic structure of molecules. I don’t pretend to understand most of what it does (more knowing nods are required). But I did get a kick out of its new molecular dictionary. Did you know that caffeine *binds to adenosine receptors in the central nervous system (CNS), which inhibits adenosine binding*? Want to know more about the antiviral drug remdesivir? Apparently it looks like this:

### Step-by-Step

We put a lot of work into resources for students and educators in this release, including incorporating study guides for Calculus, Precalculus, and Multivariate Calculus, a new student package for ODEs, and the ability to obtain step-by-step solutions to even more problems. But my favourite thing out of all this work is the new SolvePractice command in the Grading Tools package. Because it lets you build an application that does this:

I like this for three main reasons:

- It lets students practise solving equations in a way that actually helps them figure out what they’ve done wrong, saving them from a spiral of frustration and despair
- The same application can be shared via Maple Learn for students to use in that environment if they don’t have Maple
- The work we did to create that “new math entry box” can also be used to create other Maple applications with unknown numbers of inputs (see DocumentTools). I’m definitely planning on using this feature in my own applications.

### LaTeX

Okay, yes, we know. Up until recently, our LaTeX export has been sadly lacking. It definitely got better last year, but we knew it still wasn’t good enough. This year, it’s good. It’s easy. It works. And it’s not just me saying this. The feedback we got during the beta period on this feature was overwhelmingly positive.

That’s just the tip of the Maple 2021 iceberg of course. You can find out more at What’s New in Maple 2021. Enjoy!