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.

Today we are pleased to announce the release of Maple 2018.

For many people, today is just another day in March. It’s not like the release of a new version of a software product is a world-shaking event. But for us here at Maplesoft, these first few days after the latest version of Maple is released are always a bit more special. There’s always a nervous energy whenever we release Maple and everyone else gets to see what we’ve been pouring our efforts into for the past year.

I’m not going to start this post by calling the latest version of Maple “game-changing” or “cutting edge” or any other marketing friendly platitude. I’m well aware that the latest version of Maple isn’t going to change the world.

What I would say though is that with every new release of software comes an opportunity. Every new software release is an opportunity to re-evaluate how that software has evolved to better suit your needs and requirements. So… if you've been sitting on the sidelines and watching version after version go by, assuming that it won't affect you, that's wrong! There's a lot that you could be missing out on.

The way that these release announcements usually work is that we try to amaze and astound you with a long list of features. Don’t worry, I’ll get into that in a bit. But first I wanted to walk through a simple exercise of release arithmetic.

I’ll start with one of those basic truths that has always been hiding in plain sight. The build number # for Maple 2018 is 1298750. Here at Maplesoft, every time our developers make a change to Maple this build number goes up by 1. These changes are sometimes small and sometimes very big; they can be as small as fixing a documentation typo or they can constitute implementing a major feature spread across numerous files in our source tree.

I have come to look at these build numbers in a slightly different way. I look at build numbers as representing all of the small to large sized steps our developers take to get you from one version to the next (or put another way, how many steps behind you are if you are using the older versions). With that in mind, let’s do some quick math:

If you are using Maple 2017 (2017.0 was build # 1231047), there have been 1298750 – 1231047 = 67703 steps since that release (these numerous "steps" are what built the "long list" of features below). If you’re using Maple 2016 (#1113130) this number grows to 185620. And so it goes… Maple 2015 (#1022128) = 276622 steps, Maple 18 (#922027) = 376723, Maple 17 (#813473) = 485277, you get the idea. If you’re using a really old version of Maple – there’s a good chance that we have fixed up a bunch of stuff or added something that you might find interesting in the time since your last upgrade!


Every new release of Maple adds functionality that pushes Maple into new domains, rounds out existing packages, fills gaps, and addresses common user requests. Let's explore some additions:


Clickable Math - a.k.a. math that looks like math and can be interacted with using your mouse - has evolved. What was once a collection of operations found in the right-click or main menu items or in interactive smart-popups or in many additional dialogs, has been brought together and enhanced to form the new Context Panel.

We can summarize the Context Panel as follows: Enter an expression and relevant operations that you can apply to that expression appear in a panel on the right side of your screen. Easy, right? It's a great change that unlocks a large part of the Maple library for you.

The addition of the Context Panel is important. It represents a shift in the interaction model for Maple – you’ll see more and more interaction being driven through the context panel in future releases. Already, the changes for the Context Panel permeate through to various other parts of Maple too. You’ll see an example in the Units section below and here’s another for coding applications.

The Context Panel also gives you access to embedded component properties – this makes it much easier to modify parts of your application.

There’s much more we can say about the Context Panel but in the interest of keeping this post (somewhat) concise I’ll stop there. If you are interested and want to see more examples, watch this video.


Coding in Maple - For many of us, using the Maple coding language is fundamental; it's just what we do. Whether you write a lot of procedures, or modify the start-up code for your worksheet, or put a sequence of commands in a code edit region, or include a button or slider in your application, you’ll find yourself using Maple’s code editing tools.

For Code Edit Regions and the Maple Code Editor, there’s automatic command completion for packages, commands, and even file paths.

maplemint has been integrated into the Code Editor, providing code analysis while you write your code.

mint and maplemint have been unified and upgraded. If you’ve never heard of these before, these are tools for analysing your Maple code. They provide information on procedures, giving parameter naming conflicts, unreachable code, unused parameters or variables, and more. Mint is available for use with external text files and maplemint runs directly inside of Maple.

For more, I’ve got another video.


For many engineers and scientists, units are intrinsically linked with calculations. Here's something else in Maple 2018 that will improve your everyday experience – units are now supported in many core routines such as in numeric equation solving, integration, and optimization.

Here’s a quick example of using units in the int command with some thermophysical data:

We define an expression that gives the pressure of methane as a function of the specific volume V.

P := ThermophysicalData:-Property("pressure", "methane", "temperature" = 350*Unit('K'), "density" = 1/V):
-(int(P, V = 1.0*Unit('m'^3/'kg') .. .5*Unit('m'^3/'kg'), numeric));

You'll also find unit formatting in the Context Panel.

Near and dear to my heart, data analysts also have some occasion to rejoice. Maple 2018 finally adds an Interpolate command that supports irregular data! This is one of those items that users have been requesting for a long time and I'm very happy to say that it's finally here.

Furthering the data story, there are new sources for thermochemical data as well as updates to ensure that existing datasets for thermophysical data and scientific constants are up to date.


If you're interested in protecting your content in Maple, listen up:

You can now encrypt procedures; anyone can use your code, but they can't see the source!

You can also lock your Maple documents - effectively protecting them from accidental changes or other unintended modifications.



Of course, I won't leave mathematics out of this. As always, there’s a ton of new and updated stuff here.

There's a new computational geometry package. There are improvements across all fields of mathematics including group theory, graph theory, integration, differential equations and partial differential equations. And there's a ton of new work in Physics (many of you who have been following the Physics project will already know about these).

You can recreate some of the visualizations above as follows:

Here’s an example of the new VoronoiDiagram Command:

m := LinearAlgebra:-RandomMatrix(40, 2):
ComputationalGeometry:-VoronoiDiagram(m, showpoints, symbol = solidcircle, symbolsize = 7,colorregions=ColorTools:-GetPalette("Dalton"));

Here’s another change that I’ve seen mentioned several times on MaplePrimes – the ability to control the  border of arrows:

plots:-display(plottools:-arrow([0, 0], [2, 2], 0.5e-1, .2, .1, border = false, color = "DarkGrey", legend = "A+B"),
                       plottools:-arrow([0, 0], [1, 2], .15, .3, .15, border = false, color = "Crimson", legend = "A"),
                       plottools:-arrow([1, 2], [2, 2], .15, .3, .15, border = false, color = "CornflowerBlue", legend = "B"),
                   size = [600, 400]);

You can rotate Tickmarks in plots using the rotation option. Some plots, such as those in the TimeSeriesAnalysis package, use rotation by default.

ts := TimeSeriesAnalysis:-TimeSeries([7, 23, 21, 19, 13, 46, 42, 30, 31, 26, 19, 9, 16, 26, 17, 33, 31, 46, 42, 35, 45, 30, 11, 17, 23, 20, 15, 36, 31, 55, 49, 39, 36, 28, 12, 11, 21, 23, 27, 33, 36, 49, 42, 37, 33, 45, 12, 7, 23, 32, 25, 42, 27, 52, 50, 34, 41, 40, 16, 14], frequency = monthly, startdate = "2005-09");
TimeSeriesAnalysis:-SeasonalSubseriesPlot(ts, startingperiod = 9, seasonnames = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"], space = .25, size = [800, 400]);


I’ll also mention some updates to the Maple language – items that the readers of this forum will likely find useful.

Dates and Times – Maple 2018 adds new data structures that represent dates and times. There are numerous functions that work with dates and times, including fundamental operations such as date arithmetic and more advanced functionality for working with Calendars.

today := Date();

Year( today ), DayOfMonth( today ), Month( today );

Date arithmetic:

One_year_ago := today - 365*Unit(d);


Until - An optional until clause has been added to Maple's loop control structure.

Here's an example, the following code finds the next prime number after 37 and then terminates the loop.

n := 37;

do n := n+1 until



As always with these posts, we can't cover everything. This post is really just the beginning of the story. I would love to spend another couple of pages describing the inner-workings of every single improvement to Maple 2018 for you; however I'd rather you just try these features yourself, so go ahead, get out there and try out Maple 2018 today. You won't be disappointed that you did.

We’re kicking off 2018 right, with another Meet Your Developers interview! This edition comes from Erik Postma, Manager of the Mathematical Software Group.

To catch up on previous interviews, search the “meet-your-developers” tag.

Without further ado…


  1. What do you do at Maplesoft?
    I’m the manager of the mathematical software group, a team of 7 mathematicians and computer scientists working on the mathematical algorithms in Maple (including myself). So my work comes in two flavours: I do the typical managerial things, involving meetings to plan new features and solve my team’s day to day problems, and in the remaining time I do my own development work.
  2. What did you study in school?
    I studied at Eindhoven University of Technology in the Netherlands. The first year, I took a combined program of mathematics and computer science; then for the rest of my undergrad, I studied mathematics. The program was called Applied Mathematics, but with the specialization I took it really wasn’t all that applied at all. Afterwards I continued in the PhD program at the same university, where my thesis was on a subject in abstract algebra (Lie algebras over finite fields).
  3. What area(s) of Maple are you currently focusing on in your development?
    I’ve spent quite a bit of time over the past two years making the facilities for working with units of measurement in Maple easier to use. There is a very powerful package for doing this that has been part of Maple for many years, but we keep hearing from our users it’s difficult to use. So I’ve worked on keeping the power of the package but making it easier to use.
  4. What’s the coolest feature of Maple that you’ve had a hand in developing?
    This was actually working on a problem in a part of the code that existed long before I started with Maplesoft. We have a very clever algorithm for drawing random numbers according to a custom, user-specified probability distribution. I wrote about it on MaplePrimes in a series of four blog posts, here. I’ve talked at various workshops and the like about this algorithm and how it is implemented in Maple.
  5. What do you like most about working at Maplesoft? How long have you worked here?
    I love working at the crossroads of mathematics and computer science; there aren’t many places in the world where you can do that as much as at Maplesoft. But the best thing is the people I work with: us mathematicians are all crazy in slightly different ways, and that makes for a very interesting working environment.
  6. Favourite hobby?
    Ultimate frisbee. I captain a mixed (i.e., coed) team called The Clockwork. (We play in orange jerseys – it references the book/movie A Clockwork Orange.) We play in a couple of local leagues, and some of the other members also work here. We don’t win much – but we work hard and have fun!
  7. What do you like on your pizza?
    Mushrooms. Mushrooms on everything!
  8. What’s your favourite movie?
    Probably Black Book, a dark movie about the Dutch resistance in the second world war from 2006, directed by Paul Verhoeven. I think what I like best about it is that it highlights the moral shades of grey in even so morally elevated a group as the resistance.
  9. What skill would you love to learn? Why?
    I’d love to learn to speak Russian! I’m trying, but I have a very hard time with it. It would allow me to communicate with my in-laws more easily; they speak Russian.
  10. Who’s your favourite mathematician?
    Oh, so many to choose from! I’m torn between:
  • Ada Lovelace (1815-1852), known as the first programmer.
  • Felix Klein (1849-1925), driving force behind a lot of research into geometries and their underlying symmetry groups.
  • Wilhelm Killing (1847-1923), a secondary school teacher who made big contributions to the theory of Lie algebras.

Or wait, can I choose my wife?

My September 9, 2016, blog post ("Next Number" Puzzles) pointed out the meaninglessness of the typical "next-number" puzzle. It did this by showing that two such puzzles in the STICKELERS column by Terry Stickels had more than one solution. In addition to the solution proposed in the column, another was found in a polynomial that interpolated the given members of the sequence. Of course, the very nature of the question "What is the next number?" is absurd because the next number could be anything. At best, such puzzles should require finding a pattern for the given sequence, admitting that there need not be a unique pattern.

The STICKELERS column continued to publish additional "next-number" puzzles, now no longer of interest. However, the remarkable puzzle of December 30, 2017, caused me to pull from the debris on my retirement desk the puzzle of July 15, 2017, a puzzle I had relegated to the accumulating dust thereon.

The members of the given sequence appear across the top of the following table that reproduces the graphic used to provide the solution.

It turns out that the pattern in the graphic can be expressed as 100 – (-1)k k(k+1)/2, k=0,…, a pattern Maple helped find. By the techniques in my earlier blog, an alternate pattern is expressed by the polynomial

which interpolates the nodes (1, 100), (2, 101) ... so that f(8) = -992.

The most recent puzzle consists of the sequence members 0, 1, 8, 11, 69, 88; the next number is given as 96 because these are strobogrammatic numbers, numbers that read the same upside down. Wow! A sequence with apparently no mathematical structure! Is the pattern unique? Well, it yields to the polynomial

which can also be expressed as

Hence, g(x) is an integer for any nonnegative integer x, and g(6) = -401, definitely not a strobogrammatic number. However, I do have a faint recollection that one of Terry's "next-number" puzzles had a pattern that did not yield to interpolation. Unfortunately, the dust on my desk has not yielded it up.

In the beginning, Maple had indexed names, entered as x[abc]; as early as Maple V Release 4 (mid 1990s), this would display as xabc. So, x[1] could be used as x1, a subscripted variable; but assigning a value to x1 created a table whose name was x. This had, and still has, undesirable side effects. See Table 0 for an illustration in which an indexed variable is assigned a value, and then the name of the concomitant table is also assigned a value. The original indexed name is destroyed by these steps.


At one time this quirk could break commands such as dsolve. I don't know if it still does, but it's a usage that those "in the know" avoid. For other users, this was a problem that cried out for a solution. And Maplesoft did provide such a solution by going nuclear - it invented the Atomic Variable, which subsumed the subscript issue by solving a larger problem.

The larger problem is this: Arbitrary collections of symbols are not necessarily valid Maple names. For example, the expression  is not a valid name, and cannot appear on the left of an assignment operator. Values cannot be assigned to it. The Atomic solution locks such symbols together into a valid name originally called an Atomic Identifier but now called an Atomic Variable. Ah, so then xcan be either an indexed name (table entry) or a non-indexed literal name (Atomic Variable). By solving the bigger problem of creating assignable names, Maplesoft solved the smaller problem of subscripts by allowing literal subscripts to be Atomic Variables.

It is only in Maple 2017 that all vestiges of "Identifier" have disappeared, replaced by "Variable" throughout. The earliest appearance I can trace for the Atomic Identifier is in Maple 11, but it might have existed in Maple 10. Since Maple 11, help for the Atomic Identifier is found on the page 


In Maple 17 this help could be obtained by executing help("AtomicIdentifier"). In Maple 2017, a help page for AtomicVariables exists.

In Maple 17, construction of these Atomic things changed, and a setting was introduced to make writing literal subscripts "simpler." With two settings and two outcomes for a "subscripted variable" (either indexed or non-indexed), it might be useful to see the meaning of "simpler," as detailed in the worksheet

Many of you enjoyed our profile on one of our developers, Paulina Chin, so we’re happy to bring you another one!

Today, we’ll be talking with John May, Senior Developer of Maple. Let’s get started.

  1. What do you do at Maplesoft?
    Until recently I was consulting on-site at the NASA Jet Propulsion Laboratory helping people there more effectively solve their engineering problems using Maplesoft products.  But my main job that I am back to full time now is the development and maintenance of various parts of the Maple library.
  2. What did you study in school?
    I studied both Pure and Applied Mathematics at the University of Oregon,  focusing a lot on Abstract Algebra.  In graduate school, I specialized more in computation mathematics like computer algebra and numerical analysis.  My Ph.D. work focused on effective numerical algorithms for problems in polynomial algebra – with implementations in Maple!
  3. What area(s) of Maple are you currently focusing on in your development?
    Right now I am focused on addressing complaints I’ve gotten from engineers about the usability of units with other parts of the math library.
  4. What’s the coolest feature of Maple that you’ve had a hand in developing?
    A lot of the cool things I’ve built live pretty deep in the internals of Maple.  I’ve done a lot of meta-heuristic tuning to seamlessly integrate high-performance libraries into top-level Maple commands.

    I had a lot of fun developing a lot of the stuff for manipulation and visualization of colors in the ColorTools package.
  5. What do you like most about working at Maplesoft? How long have you worked here?
    I started working at Maple in 2007, but I’ve been a Maple user since 1997.  I love being part of the magic that brings powerful algorithmic mathematics to everyone.  The R&D team is also full of eccentric nerds who are great fun to work with.
  6. Favourite hobby?
    It varies by the season, but right now it is prime for mountain biking in southern California.  I ride my local trails a couple times a week, and when I get I chance, I love to get away on epic bikepacking adventures (like this one:  this is me: ).
  7. What do you like on your pizza?
    Anything and everything. Something different every time. My all-time favorite pie my from grad school days is the “Rio Rancho” from the dearly departed That’s Amore Pizza (which was next to the comic book store and across the street from North Carolina State University).  It was an olive oil and mozzarella pizza with chopped bacon that was covered in sliced fresh roma tomatoes and drizzled with ranch dressing when it came out of the oven. 
  8. What’s your favourite movie?
    It’s really hard to pick just one.  So, I’ll go with the safe answer and say the greatest movie of all time, and “Weird Al” Yankovic’s only foray into movies, UHF, is my favorite.
  9. What skill would you love to learn? (That you haven’t already) Why?
    Another hard one.  I feel like I’ve dabbled in lots of things that I would like to get better at.  At the top of the list is probably unicycling.  I’d love to get good enough to play Unicyle Football or do Muni (mountain unicyling).
  10. Who’s your favourite mathematician?


The Perimeter Institute for Theoretical Physics (PI) is a place where bold ideas flourish. It brings together great minds in a shared effort to achieve scientific breakthroughs that will transform our future. PI is an independent research center in foundational theoretical physics.

One of the key mission objectives of Perimeter is to provide scientific training and educational outreach activities to the general public. Maplesoft is proud to be part of this endeavor, as PI’s Educational Outreach Champion. Maplesoft’s contributions support Perimeter’s Teacher Network training activities, core educational resources, development of online course material, support of events such as the EinsteinPlus workshop for high school teachers, the International Summer School for Young Physicists (ISSYP), and other initiatives.

The annual International Summer School for Young Physicists (ISSYP) is a two-week camp that brings together 40 exceptional physics-minded students from high schools across the globe to PI. The program covers many different topics in physics such as quantum mechanics, special relativity, general relativity, and cosmology. Each year students receive a complimentary copy of Maple, and use the product to practice and strengthen their math skills. The program receives an average of three-hundred applications from students in grades eleven and twelve from around the world. Competition is intense, and students who are chosen for the program are extremely bright and advanced for their age; however there is some variation in their level of math and physics knowledge. . Students are asked to review a “math primer” document to prepare them with the background needed for the program.The ISSYP program now uses Möbius, Maplesoft’s online courseware platform to administer this primer. With Möbius, PI has moved from a pdf document primer to fully online material, which has motivated more students to complete the material and be more engaged in their courses. The interactivity and engagement that technology provides has made the summer program more productive and dynamic.

EinsteinPlus is a one-week intensive workshop for Canadian and international high school teachers that focuses on modern physics, including quantum physics, special relativity, and cosmology. EinsteinPlus also provides unique opportunities to learn some of the latest developments in physics from expert researchers at the forefront of their fields. Maplesoft proudly supports this workshop by giving teachers access to and training in Maple.


Perimeter Institute also organizes a lively program of seminars, regularly exposing researchers and students to current ideas in the wider theoretical physics community. The talks provide content outside of, but related to, core disciplines.  Recently Maplesoft’s own physics expert Dr. Edgardo Cheb-Terrab conducted a lecture and training session at PI on Computer Algebra for Theoretical Physics.

Dr. Edgardo Cheb-Terrab is the force behind the algorithms and Maple libraries of the ODE and PDE symbolic solvers, the MathematicalFunctions package (an expert system in special functions) and the Physics package, among other things.  

In his talk at PI, the Physics project at Maplesoft was presented and the resulting Physics package was illustrated through simple problems in classical field theory, quantum mechanics and general relativity, and through tackling the computations of some recent Physical Review papers in those areas.   In addition there was a hands-on workshop where attendees were offered four choices of activity:  follow the mini-course; explore items of the worksheet of the morning presentation; or bring their own problems so that Dr. Cheb-Terrab could guide them on how to tackle it using the Physics package and Maple in general.

As a company that strives to continuously improve student learning, and empower instructors and researchers with the tools necessary to compete in an ever changing and demanding educational environment, Maplesoft’s partnership with the Perimeter Institute allows us to do just that. We take great pride and joy in bringing our technology to outreach programs for students and teachers, making these opportunities a more productive and dynamic experience for all.


I write shell scripts that call Maple to automate frequent tasks. Because I prefer writing Maple code to shell code, I've created a Maple package, Bark, that generates a shell script from Maple source code. It provides a compact notation for defining both optional and positional command-line parameters, and a mechanism to print a help page, from the command-line, for the script. The optional parameters can be both traditional single letter Unix options, or the more expressive GNU-style long options.

As an example, here is the Maple code, using Bark, for a hello-world script.

hello := module()
    Parser := Bark:-ArgParser(NULL
                              , 'prologue' = ( "Print `Hello, World!'" )
                              , 'opts' = ['help' :: 'help' &c "Print this help page"]
    ModuleApply := proc(cmdline :: string := "")
        Bark:-ArgParser:-Parse(Parser, cmdline);
        Bark:-printf("Hello, World!\n");
    end proc;
end module:

The following command creates and installs the shell script in the user's bin directory.

Bark:-CreateScript("hello", hello
                   , 'add_libname' = Bark:-SaveLib(hello, 'mla' = "hello.mla")

The hello script is executed from the command-line as

$ hello
Hello,  World!

Pass the -h (or --help) option to display the help.

$ hello -h
Usage: hello [-h|--help] [--]

Print `Hello, World!'

Optional parameters:
-h, --help Print this help page

CreateScript creates two files that are installed in the bin directory: the shell script and a Maple archive file that contains the Maple procedures. The shell script passes its argument in a call to the parser (a Maple procedure) saved in the archive file (.mla file). Here's the created shell script for the hello command:

#!/usr/bin/env sh
CMD_LINE=$(echo $0; for arg in "$@"; do printf '%s\n' "$arg"; done)
echo "hello(\"$CMD_LINE\");" | "$MAPLE" -q -w2 -B --historyfile=none -b '/home/joe/bin/hello.mla'

I've used Bark on Linux and Windows (with Cygwin tools). It should work on any unix-compatible OS with the Bash shell. If you use a different shell that does not work with it, let me know and I should be able to modify the CreateScript command to have options for specific shells.

Bark is available on the MapleCloud. To install it, open the MapleCloud palette in Maple, select packages in the drop-down menu and go to the New tab (or possibly the Popular tab). You will also need the TextTools package which is also on the MapleCloud. The intro page for Bark has a command that automatically installs TextTools. Alternatively, executing the following commands in Maple 2017 should install both TextTools and Bark.


The source for a few useful scripts are included in the examples directory of the installed Bark toolbox. Maple help pages are included with Bark, use "Bark" as the topic.

I am pleased to announce that a new release of Maple T.A., our online testing and assessment system, is now available. Maple T.A. 2017 includes significant enhancements to learning management system integration, as well as security, performance, and other improvements. These same improvements are also available in a new version of the  Maple T.A. MAA Placement Test Suite.  For more information, see What’s New in Maple T.A. 


As you know, the MapleCloud is a good way to share all sorts of interactive documents with others, in private groups or so they are accessible to everyone. We recently posted some new content that I thought people might be particularly interested in: a collection of Maple Assistants.


Up until now, Maple Assistants were only available from within Maple, but now you can take advantage of these powerful tools wherever you are, using your web browser.


Code Generation  - Translate Maple code to C, Java, Python, R, and more

Scientific Constants – Explore over 20000 values of physical constants and properties of chemical elements, including units and uncertainty values

Special Functions – Explore the properties of over 200 special functions, including the Hypergeometric, Bessel, Mathieu, Heun and Legendre families of functions.

Units Converter – Convert between over 500 units of measurement. (In addition to the standard stuff, you can find out how many fortnights old you are, or how long your commute is in furlongs!)

Since 2002, the Texas A&M Math Department has sponsored a Summer Educational Enrichment in Math (SEE-Math) Program for gifted middle school students entering the 6th, 7th or 8th grade under the direction of Philip Yasskin and David Manuel.  Students spend two weeks exploring ideas from algebra, geometry, graph theory, topology, and other mathematical topics. 

The program’s primary goal is to help students find excitement in the discovery of mathematics and science concepts, and to provide them with the knowledge and confidence to continue their studies in math and science related fields. “I love working with the bright young kids who come to SEE-Math, they keep me young,” said Yasskin, one of the programs directors.

Maplesoft has been a sponsor of SEE-Math for many years and are happy to see the students explore math at this young age. Research into the importance of early math skills shows that children who are taught math early and learn the basics at a young age are set up for a lifetime of achievement in all aspects of their academic performance.  Every year, Maplesoft commits time, funds and people to various organizations to enhance the quality of math-based learning and discovery and to encourage students to strengthen their math skills.

One of the major activities of the SEE-Math program, and something the students really enjoy doing, is creating computer animations in Maple. The kids are divided into 3 groups; the Euler group is mostly made up of 6th graders with a few younger, the Fibonacci group is mostly 6th and 7th graders, and the Gauss group is 7th and 8th graders.

 Here are the 2017 first place winners from each group and their animations:

Euler Group - Nigel M "Buckets"

Fibonacci Group - Gabriel M "Skillz"

Gauss Group - Michael C - "Newton's Castle"



To learn more about this program visit:

While many of us in North America were getting re-acquainted with the Fall routine, Maplesoft was involved in a major event, the Maple T.A. and Möbius User Summit. In the past, the Summit has alternated locations between Europe and North America, but following the success of last year’s Summit in Vienna, Austria, we recently broke new ground and expanded the reach of the event to include more countries around the world in order to localize the themes and to meet the growing demand from educators to take learning online.

The first event, organized by Cybernet, took place in China. The second of five events on the calendar took place in London, England. Held from September 7-8, this installment was a major stop in the tour, drawing many residents of the UK to hear talks from some of our strongest proponents of Möbius in Europe. The London Summit drew several delegates from the UK alone, many of whom were completely new contacts for us! Other attendees came from as far away as Russia, Pakistan, Sri Lanka, and Australia, as well as some from Sweden, Denmark, Italy and the Netherlands. The turnout was brilliant!

Make progress or make excuses

The bulk of the London Summit was divided into three driving themes: Showcasing the Successful Delivery of Online Education; Best Practices for Digital Testing and Assessment; and Creating Engaging and Interactive Online STEM Content. Each theme consisted of 3 user presentations delivered by representatives from renowned institutions like University of Manchester, University of Birmingham, London Imperial College, University of Waterloo, Chalmers University of Technology, and more.

Maplesoft Application Engineer Surak Perera may have inadvertently set the tone for the day when he kicked off theme 1 with a quote from Tony Robbins: Make progress, or make excuses. One thing’s for sure – excuses were nowhere to be found at One Moorgate Place. The audience was captivated and engaged, and wasted no time bouncing questions and ideas off of our presenters. In fact, they were so eager to learn from our Maple T.A. and Möbius users that Jonny Zivku, Maple T.A. Product Manager, had to interject several times in order to keep the schedule moving! Each presentation reinforced the ability of Maple T.A. and Möbius to be used for diverse purposes such as distance education or analyzing incoming students, and in a range of subjects including multidisciplinary engineering cohorts, or simply core mathematics. Each presenter demonstrated that these tools can take you as far as the user’s mind is willing to be stretched.


Evening Reception

As heads were getting full and bellies were getting empty, the group left the luxuries of modern day and stepped back into what must have felt like a scene from Downton Abbey in the Main Reception Room of the venue. On the menu was the most culturally appropriate dish: fish and chips! Oh, and don’t forget the tea and wine!

There was no better way to wrap up the Summit than with Steve Furino’s interactive presentation and open discussion “Collecting Data about Collecting Data.” Small group discussion enabled the attendees to reconcile their inspiration from Day 1 with the practicality of putting it into practice once they return to their schools.

Overall, the London Summit was a smashing hit. The centralized location drew attendees who had a lot of common experiences which made for optimal discussion. The final question posted was the most revealing of everyone’s experience: where will the Summit be next year?

While that’s not yet decided, the Toronto Summit – the next stop in the Summit Series – is just a fortnight away (November 2-3). So for now, we’re saying “Cheers” to jolly good times in London, and “Can I get a double-double, eh” to Toronto!

Until then, you can experience the London Summit as if you were there with the full presentation proceedings and videos. They’re now available on our website!

The Railway Challenge is a competition designed by the Institute of Mechanical Engineers (IMechE), aimed at engaging young engineers with the rail industry.  The challenge, now in its seventh successive year, brings together teams of university students, as well as apprentices and graduates working in industry across the world to test their business knowledge, design ability and technical skills in a live test environment.

The Railway Challenge at Sheffield (RCAS) is an extracurricular student-led activity within the Mechanical Engineering department at the university of Sheffield, that designs, codes and manufactures a 10 1/4 inch gauge miniature locomotive to compete in the IMechE’s  Railway Challenge.  The locomotive is assessed in accordance with a set of strict rules and a detailed technical specification, such as traction, ride comfort, and a business case. The locomotives are tested live at a competition, which takes place in June at the Stapleford Miniature Railway in Leicestershire, where several categories of winners and an overall Railway Challenge champion is crowned.

The team consists of around twenty members, and students studying Mechanical Engineering and even cross discipline can get involved as soon as they come to the University, getting into to the design of components within the suspension or braking systems for example, before proceeding to manufacture and test; allowing the students to experience all the stages of an engineering product as well as skills gained by working in the team such as effective communication, time management and financial planning.

Last year the team was granted a sponsorship from Maplesoft, and as a result, huge improvements were made within the team. Overall the team jumped from finishing in 7th place to in the summer winning the maintainability challenge and finishing in 4th place overall – mostly down to the electronics working for the first year ever!


Using Maplesoft’s donation the team switched form a central CRIO control system to a distributed network using I2C protocols and Arduino hardware. This did away with some of the electrical teething problems the team has suffered in previous years. It also introduced our Mechanical Engineers to coding that they would otherwise not do in their course.

This year Maplesoft have again sponsored RCAS. The team is hoping to use the licenses to perform their structures calculations in an easy way to keep track of them for use in the design report. They are also hoping to use MapleSim for dynamics modelling, to assist with suspension design, and designing any electronics or control elements, such as filter design and motor control.

We’re so excited to bring you guys #MapleOfficeHours! This is a program we’ve designed for students (but open to everyone) to connect via social media for help with Maple. Maple can play a really important part in your courses and can sometimes be intimidating for new users. We get it, there’s a lot of ground to cover. With #MapleOfficeHours, we will use social media as a live Q&A platform to help you figure out how to use Maple for your homework, assignments and more. Having trouble with a command or function? #MapleOfficeHours. Need help finding a specific resource or app? #MapleOfficeHours. You get the idea…

Just like the office hours your professors hold, #MapleOfficeHours is going to be available on a regular basis for support. More events will be scheduled soon, but look out for Twitter chats, mini-webinars, Facebook live events and more. Once we get going, we’d love to hear your feedback on what other types of events we can offer and what topics you’d like to see covered.

Our first #MapleOfficeHours event will be a live Twitter chat. On October 16th at 2PM EDT, I will be joined with Maple Product Manager, @DanielSkoog and Tech Support Team Lead, Dr. Matt Calder to answer as many questions about Maple that we can possibly fit into an hour’s time.

To join the Twitter chat, use the hashtag #MapleOfficeHours when posting your questions and/or mention us with @maplesoft.

Looking forward to seeing everyone at our first #MapleOfficeHours event on October 16th, 2PM EDT!

We’ve just released a major new version of MapleSim. The MapleSim 2017 family of products provides new and improved model development and analysis tools, expands modeling scope, introduces new deployment options, and strengthens toolchain connectivity.  Here are some highlights:

  • The new Initialization Diagnostics App further simplifies the initialization task by helping you determine how your initial values are computed and what you need to do to adjust them.
  • The new Modal Analysis App helps you explore and understand the natural vibration modes of your mechanism, so you can determine how to reduce the vibration in the final product. 
  • Over 100 new components include expansions to the Electrical and Magnetic libraries.
  • A new Modelica® code editor makes it easier to create Modelica-based custom components.
  • The MapleSim Heat Transfer Library from CYBERNET, a new add-on component library, provides a comprehensive view into heat transfer effects in your model, enabling you to refine your  design to improve performance and avoid overheating.
  • The new MapleSim Explorer product provides a cost-effective deployment solution that allows you to make MapleSim models available to more people in your organization.


There’s more, of course.  See What’s New in MapleSim for lots more details.


A project that I have been working on is adding some functionality for Cluster Analysis to Maple (a small part of a much bigger project to increase Maple’s toolkit for exploratory data mining and data analysis). The launch of the MapleCloud package manager gave me a way to share my code for the project as it evolves, providing others with some useful new tools and hopefully gathering feedback (and collaborators) along the way.

At this point, there aren’t a lot of commands in the ClusterAnalysis package, but I have already hit upon several interesting applications. For example, while working on a command for plotting clusters of points, one problem I encountered was how to draw the minimal volume enclosing ellipsoid around a group (or cluster) of points. After doing some research, I stumbled upon Khachiyan’s Algorithm, which related to solving linear programming problems with rational data. The math behind this is definitely interesting, but I’m not going to spend any time on it here. For further reading, you can explore the following:

Khachiyan’s Algorithm had previously been applied in some other languages, but to the best of my knowledge, did not have any Maple implementations. As such, the following code is an implementation of Khachiyan’s Algorithm in 2-D, which could be extended to N-dimensional space rather easily.

This routine accepts an Nx2 dataset and outputs either a plot of the minimum volume enclosing ellipsoid (MVEE) or a list of results as described in the details for the ‘output’ option below.

MVEE( X :: DataSet, optional arguments, additional arguments passed to the plotting command );

The optional arguments are as follows:

  • tolerance : realcons;  specifies the convergence criterion
  • maxiterations : posint; specifies the maximum number of iterations
  • output : {identical(data,plot),list(identical(data,plot))}; specifies the output. If output includes plot, then a plot of the enclosing ellipsoid is returned. If output includes data, then the return includes is a list containing the matrix A, which defines the ellipsoid, the center of the ellipse, and the eigenvalues and eigenvectors that can be used to find the semi-axis coordinates and the angle of rotation, alpha, for the ellipse.
  • filled : truefalse; specifies if the returned plot should be filled or not


#Minimum Volume Enclosing Ellipsoid
MVEE := proc(XY, 
              {tolerance::positive:= 1e-4}, #Convergence Criterion
              {maxiterations::posint := 100},
              {output::{identical(data,plot),list(identical(data,plot))} := data},
              {filled::truefalse := false} 

    local alpha, evalues, evectors, i, l_error, ldata, ldataext, M, maxvalindex, n, ncols, nrows, p1, semiaxes, stepsize, U, U1, x, X, y;
    local A, center, l_output; #Output

    if hastype(output, 'list') then
        l_output := output;
        l_output := [output];
    end if;


    ldata := Statistics:-PreProcessData(XY, 2, 'copy');

    nrows, ncols := upperbound(ldata);
    ldataext := Matrix([ldata, Vector[column](nrows, ':-fill' = 1)], 'datatype = float');

    if ncols <> 2 then
        error "expected 2 columns of data, got %1", ncols;
    end if;

    l_error := 1;

    U := Vector[column](1..nrows, 'fill' = 1/nrows);

    ##Khachiyan Algorithm##
    for n to maxiterations while l_error >= tolerance do

        X := LinearAlgebra:-Transpose(ldataext) . LinearAlgebra:-DiagonalMatrix(U) . ldataext;
        M := LinearAlgebra:-Diagonal(ldataext . LinearAlgebra:-MatrixInverse(X) . LinearAlgebra:-Transpose(ldataext));
        maxvalindex := max[index](map['evalhf', 'inplace'](abs, M));
        stepsize := (M[maxvalindex] - ncols - 1)/((ncols + 1) * (M[maxvalindex] - 1));
        U1 := (1 - stepsize) * U;
        U1[maxvalindex] := U1[maxvalindex] + stepsize;
        l_error := LinearAlgebra:-Norm(LinearAlgebra:-DiagonalMatrix(U1 - U));
        U := U1;

    end do;

    A := (1/ncols) * LinearAlgebra:-MatrixInverse(LinearAlgebra:-Transpose(ldata) . LinearAlgebra:-DiagonalMatrix(U) . ldata - (LinearAlgebra:-Transpose(ldata) . U) . LinearAlgebra:-Transpose((LinearAlgebra:-Transpose(ldata) . U)));
    center := LinearAlgebra:-Transpose(ldata) . U;
    evalues, evectors := LinearAlgebra:-Eigenvectors(A);
    evectors := evectors(.., sort[index](1 /~ (sqrt~(Re~(evalues))), `>`, ':-output' = ':-permutation'));
    semiaxes := sort(1 /~ (sqrt~(Re~(evalues))), `>`);
    alpha := arctan(Re(evectors[2,1]) / Re(evectors[1,1]));

    if l_output = [':-data'] then
        return A, center, evectors, evalues;
    elif has( l_output, ':-plot' ) then
            x := t -> center[1] + semiaxes[1] * cos(t) * cos(alpha) - semiaxes[2] * sin(t) * sin(alpha);
            y := t -> center[2] + semiaxes[1] * cos(t) * sin(alpha) + semiaxes[2] * sin(t) * cos(alpha);
            if filled then
                p1 := plots:-display(subs(CURVES=POLYGONS, plot([x(t), y(t), t = 0..2*Pi], ':-transparency' = 0.95, _rest)));
                p1 := plot([x(t), y(t), t = 0..2*Pi], _rest);
            end if;
        return p1, `if`( has(l_output, ':-data'), op([A, center, evectors, evalues]), NULL );
    end if;

end proc:


You can run this as follows:


                plots:-pointplot(M, symbol=solidcircle,symbolsize=15)],



As it stands, this is not an export from the “work in progress” ClusterAnalysis package – it’s actually just a local procedure used by the ClusterPlot command. However, it seemed like an interesting enough application that it deserved its own post (and potentially even some consideration for inclusion in some future more geometry-specific package). Here’s an example of how this routine is used from ClusterAnalysis:


X := Import(FileTools:-JoinPath(["datasets/iris.csv"], base = datadir));

kmeans_results := KMeans(X[[`Sepal Length`, `Sepal Width`]],
    clusters = 3, epsilon = 1.*10^(-7), initializationmethod = Forgy);

ClusterPlot(kmeans_results, style = ellipse);



The source code for this is stored on GitHub, here:

Comments and suggestions are welcomed.


If you don’t have a copy of the ClusterAnalysis package, you can install it from the MapleCloud window, or by running:



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