Last year, I read a fascinating paper that presented evidence of an exoplanet, inferred through the “wobble” (or radial velocity) of the star it orbits, HD 3651. A periodogram of the radial velocity revealed the orbital period of the exoplanet – about 62.2 days.
I found the experimental data and attempted to reproduce the periodogram. However, the data was irregularly sampled, as is most astronomical data. This meant I couldn’t use the standard Fourier-based tools from the signal processing package.
I started hunting for the techniques used in the spectral analysis of irregularly sampled data, and found that the Lomb Scargle approach was often used for astronomical data. I threw together some simple prototype code and successfully reproduced the periodogram in the paper.
After some (not so) gentle prodding, Erik Postma’s team wrote their own, far faster and far more robust, implementation.
This new functionality makes its debut in Maple 2019 (and the final worksheet is here.)
From a simple germ of an idea, to a finished, robust, fully documented product that we can put in front of our users – that, for me, is incredibly satisfying.
That’s a minor story about a niche I’m interested in, but these stories are repeated time and time again. Ideas spring from users and from those that work at Maplesoft. They’re filtered to a manageable set that we can work on. Some projects reach completion in under a year, while other, more ambitious, projects take longer.
The result is software developed by passionate people invested in their work, and used by passionate people in universities, industry and at home.
We always pack a lot into each release. Maple 2019 contains improvements for the most commonly used Maple functions that nearly everyone uses – such as solve, simplify and int – as well features that target specific groups (such as those that share my interest in signal processing!)
I’d like to to highlight a few new of the new features that I find particularly impressive, or have just caught my eye because they’re cool.
Of course, this is only a small selection of the shiny new stuff – everything is described in detail on the Maplesoft website.
Edgardo, research fellow at Maplesoft, recently sent me a recent independent comparison of Maple’s PDE solver versus those in Mathematica (in case you’re not aware, he’s the senior developer for that function). He was excited – this test suite demonstrated that Maple was far ahead of its closest competitor, both in the number of PDEs solved, and the time taken to return those solutions.
He’s spent another release cycle working on pdsolve – it’s now more powerful than before. Here’s a PDE that Maple now successfully solves.
Maplesoft tracks visits to our online help pages - simplify is well-inside the top-ten most visited pages. It’s one of those core functions that nearly everyone uses.
For this release, R&D has made many improvements to simplify. For example, Maple 2019 better simplifies expressions that contain powers, exponentials and trig functions.
Increment and Decrement Operators
Everyone who touches Maple uses the same programming language. You could be an engineer that’s batch processing some data, or a mathematical researcher prototyping a new algorithm – everyone codes in the same language.
Maple now supports C-style increment, decrement, and assignment operators, giving you more concise code.
Display of Large Data Structures
We’ve made a number of improvements to the interface, including a redesigned start page. My favorite is the display of large data structures (or rtables).
You now see the header (that is, the top-left) of the data structure.
For an audio file, you see useful information about its contents.
I enjoy creating new and different types of visualizations using Maple's sandbox of flexible plots and plotting primitives.
Here’s a new feature that I’ll use regularly: given a name (and optionally a modifier), polygonbyname draws a variety of shapes.
In other breaking news, I now know what a Reuleaux hexagon looks like.
Local Peaks of a Data Set
Since I can’t resist talking about another signal processing feature, FindPeakPoints locates the local peaks or valleys of a 1D data set. Several options let you filter out spurious peaks or valleys
I’ve used this new function to find the fundamental frequencies and harmonics of a violin note from its periodogram.
A Complete Guide for Tensor Computations using Physics
Speaking of passionate developers who are devoted to their work, Edgardo has written a new e-book that teaches you how to use tensor computations using Physics. You get this e-book when you install Maple 2019.
The new LeastTrimmedSquares command fits data to an equation while not being signficantly influenced by outliers.
In this example, we:
- Artifically generate a noisy data set with a few outliers, but with the underlying trend Y =5 X + 50
- Fit straight lines using CurveFitting:-LeastSquares and Statistics:-LeastTrimmedSquares
LeastTrimmedSquares function correctly predicts the underlying trend.
We try to make every release faster and more efficient. We sometimes target key changes in the core infrastructure that benefit all users (such as the parallel garbage collector in Maple 17). Other times, we focus on specific functions.
For this release, I’m particularly impressed by this improved benchmark for factor, in which we’re factoring a sparse multivariate polynomial.
On my laptop, Maple 2018 takes 4.2 seconds to compute and consumes 0.92 GiB of memory.
Maple 2019 takes a mere 0.27 seconds, and only needs 45 MiB of memory!
Day and Night Terminator App
I’m a visualization nut, and I always get a vicarious thrill when I see a shiny new plot, or a well-presented application.
I was immediately drawn to this new Maple 2019 app – it illustrates the transition between day and night on a world map. You can even change the projection used to generate the map. Shiny!
So that’s my pick of the top new features in Maple 2019. Everyone here at Maplesoft would love to hear your comments!