Maplesoft Blog

The Maplesoft blog contains posts coming from the heart of Maplesoft. Find out what is coming next in the world of Maple, and get the best tips and tricks from the Maple experts.

Maple 2020 offers many improvements motivated and driven by our users.

Every single update in a new release has a story behind it. It might be a new function that a customer wants, a response to some feedback about usability, or an itch that a developer needs to scratch.

I’ll end this post with a story about acoustic guitars and how they drove improvements in signal and audio processing. But first, here are some of my personal favorites from Maple 2020.

Graph theory is a big focus of Maple 2020. The new features include more control over visualization, additional special graphs, new analysis functions, and even an interactive layout tool.

I’m particularly enamoured by these:

  • We’ve introduced new centrality measures - these help you determine the most influential vertices, based on their connections to other vertices
  • You now have more control over the styling of graphs – for example, you can vary the size or color of a nodebased on its centrality

I’ve used these two new features to identify the most influential MaplePrimes users. Get the worksheet here.

@Carl Love – looks like you’re the biggest mover and shaker on MaplePrimes (well, according to the eigenvector centrality of the MaplePrimes interaction graph).

We’ve also started using graph theory elsewhere in Maple. For example, you can generate static call graph to visualize dependencies between procedures calls in a procedure

You now get smoother edges for 3d surfaces with non-numeric values. Just look at the difference between Maple 2019 and 2020 for this plot.

Printing and PDF export has gotten a whole lot better.  We’ve put a lot of work into the proper handling of plots, tables, and interactive components, so the results look better than before.

For example, plots now maintain their aspect ratio when printed. So your carefully constructed psychrometric chart will not be squashed and stretched when exported to a PDF.

We’ve overhauled the start page to give it a cleaner, less cluttered look – this is much more digestible for new users (experienced users might find the new look attractive as well!). There’s a link to the Maple Portal, and an updated Maple Fundamentals guide that helps new users learn the product.

We’ve also linked to a guide that helps you choose between Document and Worksheet, and a link to a new movie.

New messages also guide new users away from some very common mistakes. For example, students often type “e” when referring to the exponential constant – a warning now appears if that is detected

We’re always tweaking existing functions to make them faster. For example, you can now compute the natural logarithm of large integers much more quickly and with less memory.

This calculation is about 50 times faster in Maple 2020 than in prior versions:

Many of our educators have asked for this – the linear algebra tutorials now return step by step solutions to the main document, so you have a record of what you did after the tutor is closed.

Continuing with this theme, the Student:-LinearAlgebra context menu features several new linear algebra visualizations to the Student:-LinearAlgebra Context Menu. This, for example, is an eigenvector plot.

Maple can now numerically evaluate various integral transforms.

The numerical inversion of integral transforms has application in many branches of science and engineering.

Maple is the world’s best tool for the symbolic solution of ODEs and PDEs, and in each release we push the boundary back further.

For example, Maple 2020 has improved tools for find hypergeometric solutions for linear PDEs.

This might seem like a minor improvement that’s barely worth mentions, but it’s one I now use all the time! You can now reorder worksheet tabs just by clicking and dragging.

The Hough transform lets you detect straight lines and line segments in images.

Hough transforms are widely used in automatic lane detection systems for autonomous driving. You can even detect the straight lines on a Sudoku grid!

The Physics package is always a pleasure to write about because it's something we do far better than the competition.

The new explore option in TensorArray combines two themes in Maple - Physics and interactive components. It's an intuitive solution to the real problem of viewing the contents of higher dimensional tensorial expressions.

There are many more updates to Physics in Maple 2020, including a completely rewritten FeynmanDiagrams command.

The Quantum Chemistry Toolbox has been updated with more analysis tools and curriculum material.

There’s more teaching content for general chemistry.

Among the many new analysis functions, you can now visualize transition orbitals.

I promised you a story about acoustic guitars and Maple 2020, didn’t I?

I often start a perfectly innocuous conversation about Maple that descends into several weeks of intense, feverish work.

The work is partly for me, but mostly for my colleagues. They don’t like me for that.

That conversation usually happens on a Friday afternoon, when we’re least prepared for it. On the plus side, this often means a user has planted a germ of an idea for a new feature or improvement, and we just have to will it into existence.

One Friday afternoon last year, I was speaking to a user about acoustic guitars. He wanted to synthetically generate guitar chords with reverb, and export the sound to a 32-bit Wave file. All of this, in Maple.

This started a chain of events that that involved least-square filters, frequency response curves, convolution, Karplus-Strong string synthesis and more. We’ll package up the results of this work, and hand it over to you – our users – over the next one or two releases.

Let me tell you what made it into Maple 2020.

Start by listening to this:

It’s a guitar chord played twice, the second time with reverb, both generated with Maple.

The reverb was simulated with convolving the artificially generated guitar chord with an impulse response. I had a choice of convolution functions in the SignalProcessing and AudioTools packages.

Both gave the same results, but we found that SignalProcessing:-Convolution was much faster than its AudioTools counterpart.

There’s no reason for the speed difference, so R&D modified AudioTools:-Convolution to leverage SignalProcessing:-Convolution for the instances for which their options are compatible. In this application, AudioTools:-Convolution is 25 times faster in Maple 2020 than Maple 2019!

We also discovered that the underlying library we use for the SignalProcessing package (the Intel IPP) gives two options for convolution that we were previously not using; a method which use an explicit formula and a “fast” method that uses FFTs. We modified SignalProcessing:-Convolution to accept both options (previously, we used just one of the methods),

That’s the story behind two new features in Maple 2020. Look at the entirety of what’s new in this release – there’s a tale for each new feature. I’d love to tell you more, but I’d run out of ink before I finish.

To read about everything that’s new in Maple 2020, go to the new features page.

Playing mini-golf recently, I realized that my protractor can only help me so far since it can't calculate the speed of the swing needed.  I decided a more sophisticated tool was needed and modeled a trick-shot in MapleSim.

To start, I laid out the obstacles, the ball and club, the ground, and some additional visualizations in the MapleSim environment.

 

When running the simulation, my first result wasn't even close to the hole (similar to when I play in real life!).

 

The model clearly needed to be optimized. I went to the Optimization app in MapleSim (this can be found under Add Apps or Templates  on the left hand side).

 

Inside the app I clicked "Load System" then selected the parameters I wanted to optimize.

 

For this case, I'm optimizing 's' (the speed of the club) and 'theta' (the angle of the club). For the Objective Function I added a Relative Translation Sensor to the model and attached a probe to the Vector Norm of the output.

 

Inside the app, I switched to the Objective Function section.  Selecting Probes, I added the new probe as the Objective Function by giving it a weight of 1.

 

 

Scrolling down to "Execute Parameter Optimization", I checked the "Use Global Optimization Toolbox" checkbox, and clicked Run Parameter Optimization.

 

Following a run time of 120 seconds, the app returns the graph of the objective function. 

 

Below the plot, optimal values for the parameters are given. Plugging these back into the parameter block for the simulation we see that the ball does in fact go into the hole. Success!

 

 

Mini_golf_Global_Optimization.msim