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MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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  • With most software, it can take time to learn all the ins and outs and little tricks that make using the software easier. Have you ever learned a new keyboard shortcut for a software you’ve been using for years and found it so useful that you’re kicking yourself not learning it earlier? I certainly have. We thought we’d take the time to highlight five tips and tricks for using Maple Learn, so that you can skip the kicking stage and go straight to the using the cool trick stage!


    1. Convert math to text

    Here’s the trick that I probably use the most: You can press the spacebar in an empty cell to convert it to text. Just like that! No fiddling with menus, no starting to type and then backtracking as you realize all your words are turning into variables. Just a quick space at then beginning, and then you can type as much text as you’d like. Click the text icon on the left to change it back to math if you change your mind.

    An empty math cell in Maple Learn, followed by an arrow and

    2. Assigning variables

    Have you ever wanted to assign a value to a variable? Who hasn’t? And luckily, Maple Learn makes it easy to do just that. Just use “:=”. For example, you could say “a:=4”. The variable ‘a’ will now have a value of 4 for that group and all subsequent groups. What’s more, a slider will appear, so that you can adjust the value and see how it affects the rest of the document. You can change the range of the slider using the slider settings (that’s the gear) or disable the slider using the Quick Actions menu (that’s the lightbulb). You can also select “Parameterize …” from the Quick Actions menu when you have an expression that contains variables, and sliders will be automatically created for those variables. Another trick to variable assignments is that if you have a table, you can use the header of your table as a variable that contains all the values in that column. No extra work necessary, Maple Learn does this automatically!

    A screenshot of Maple Learn showing a parameterized expression with sliders for each variable. There is also a table with a single column. In the next group, the label of that column is shown to be equal to all the values in that column.

    3. Order of execution

    One handy feature about Maple Learn is that once you’ve assigned values to variables, you can use those variables again for all the groups that come after it. But hold on, I hear you say. How is that order determined? The Maple Learn canvas is dynamic and doesn’t have a set order to it, so which groups are “after”? Well, I’m glad you asked! The small grey number in the top left-hand corner of the group tells you its place in the order. Maple Learn evaluates any assignments according to this order, which means that a variable assigned in group 3 can be used in any group after 3, but not in groups 1 and 2. The order is determined based on where the groups are on the page, starting with 1 in the top-right corner and moving left to right, top to bottom across the page. That means that if you want to change a group’s place to earlier in the order of execution, all you have to do is move the group higher or to the left! The numbers (and thus the order of execution) will update automatically. Handy.

    A screenshot of Maple Learn with the group numbers circled in red. The variable defined in group 1 is accessible in groups 2 and 3, and the variable defined in group 2 is accessible in group 3.

    4. “Reset document” vs. “Clear document”

    You may have noticed two seemingly similar buttons in the toolbar: “Reset document” and “Clear document”. Here’s a little secret: they do actually do different things! Say you’re looking at a shared document, like one of the ones in our Example Gallery. You can mess around with it as much as you’d like: change values, add groups to the canvas, zoom around on the graph, whatever suits your fancy. But, if you decide that you don’t like your changes and want to go back to the original document, you can hit “Reset document” and presto! Back to the original. And “Clear document” will, of course, clear the document.

    A labelled screenshot of the Reset and Clear buttons in Maple Learn.

    5. Using the keyboard

    Are you the type of person who would rather use three keyboard commands to perform a single action than go anywhere near a mouse? Well, you’re in luck, because Maple Learn has several keyboard commands you can use to input functions without even thinking about looking at a menu. You can use standard keyboard math notation and Maple Learn will automatically format it as you would expect: ^ for exponents, * for multiplication, / for division, and so on. What’s more, you can enter “sqrt()” to write a square root symbol, and you can type in any trig function and Maple Learn will treat it as that function! You can see a full list of keyboard shortcuts here. All these things are also available through the palette menus, so a variety of workflows are supported.

    An image showing how sqrt(3x^4)/2 is displayed in math notation in Maple Learn.

    So there you have it, our top five tricks for using Maple Learn. If you’re looking for a more detailed guide on how to use Maple Learn, check out the How-To pages at the bottom of our Example Gallery. And if you have any tips you’ve found useful for using Maple Learn, let us and your fellow MaplePrimes users know in the comments!

    Using Python and MapleSim versus Basic Science Teaching in Times of Pandemic


    In the following research work entitled Use of Python and MapleSim against the teaching of Basic Sciences in times of pandemic, due to the social immobility imposed by the government, we saw the need to use scientific software to train our students with modern approaches. The purpose is to raise the learning achievement in the subjects of Mathematics and Physics for engineering. The methodology we used was native syntax programming and graphic component programming. The results that we obtained in modeling and simulation are quite exact, with respect to the traditional results. Finally, all the material can be updated and managed at any time because it is available on maplecloud.

    Keywords: Python, MapleSim, modeling, simulation


    Lenin AC

    Ambassador Maple

    Has this ever happened to you? You’re using Maple Learn, and having a grand old time, but suddenly! The horror! You notice a bug! Of course, it’s a shocking experience to realize that our products are not, in fact, flawless, but unfortunately it’s true. There are bugs. But, what’s this? There’s a glimmer of hope on the horizon… the Flag a Problem button! By using the Flag a Problem button, you can let us know about the problem you found, and with the power of our mighty development team, we’ll fix it! Yes, with our forces combined… we can defeat all of these bugs!

    A picture of the Flag a Problem button with glowing rays surrounding it.

    In all seriousness, we really do appreciate your feedback. Whether you’ve spotted a bug or are looking for a new feature, let us know! We’re constantly updating and improving Maple Learn, and user feedback is a hugely important part of this process. For example, we had a user suggest that Maple Learn treat Δt as a single entity, as in physics that notation is used to mean a change in time rather than Δ times t. And we’re happy to announce that this is now a feature! Here’s just a taste of some of the other things we’ve changed based on user feedback:

    • Can now use the Context Panel to evaluate operations with matrices
    • Maximum number of intersection points shown has increased to 20
    • Intersection points now shown for parametric equations and circles
    • Using the Context Panel no longer scrolls the page
    • Quick Actions menu no longer parameterizes the f of f(x)
    • Fixed display bug for inverse trig functions

    Evidently, not every piece of feedback we get is a feature request. Sometimes there’s bugs! And we want to hear about those too. In all honesty, I think it’s pretty neat to see the bugs I’ve reported being fixed. It wasn’t too long ago that I noticed a small error with tables—when the header of the table had a subscript, pressing the down arrow jumped to the next group instead of the next row. I reported it, and now it’s fixed! I can’t help but feeling a little smug, like I’m the one who fixed it. Of course, the credit for the actual code goes to our developers. But it is also true that they wouldn’t have fixed it if no one had pointed it out. Truly, teamwork makes the dream work. And if you want to feel smug about the bug you pointed out being fixed, or the feature you asked for being added, then head on over to that Flag a Problem button. Let us know what you want to see and we’ll listen. What’s more, we’ll be making more posts every now and then to let you know about what’s new with Maple Learn and what we’ve changed based on your feedback. That way you have something to print out and frame on your wall as proof of the contribution you’ve made to Maple Learn! (Or I suppose you could just read it. But where’s the fun in that?)

    Some misguided individuals insist that perpetual motion machines are impossible. Here is a proof that they are wrong!

    One of these units hooked up to an electrical generator should be enough to supply all your household electrical needs as well as charge your Tesla in the garage.

    If you build one and find out that it doesn't work as demonstrated here, then surely you must have misread the specs. Try it again and again until you succeed.


    In the context of analyzing physical systems I often have to plot results in the form of y=f(x,a,b,c,…). Here the plot variables x and y are physical quantities and the system parameters a,b,c… can have units as well.

    After substitution of parameters the expression f(x,a,b,c,…) can be plotted using plot(f(x,a,b,c,…),x_range). Unit choice and labeling of the abscissa work already well when x_range is given in the format x=x0..x1 (where x0 and x1 have a value and a unit). This is already a huge improvement since labeling and unit conversion errors on the abscissa are almost impossible.

    Also, the units on the ordinate are correctly displayed. However, if the depended variable y is desired to be displayed on the ordinate it must be added by hand using the label option. In doing so the display units and labels of both axes must be re-entered by hand. This re-entering step is a source of labeling and conversion errors.

    To improve ordinate labeling and to reduce conversion errors I would love to see two improvements:

    • A plot option that would allow unit conversion of plot axes. I.e. telling Maple in which units a physical quantity has to be displayed and forcing a rescaling of the values of the physical quantities.
    • With less priority and additional to expressions, the plot command should also accept equations in the form of y=f(x) as input. This would lead to a very compact syntax that produces content rich and, more importantly, correct plots of physical quantities. Wrong labeling and conversion errors would be very unlikely.

    Overall, I am very pleased by Maples unit functionality. I have been reluctant to switch from my old work style of using names as unit placeholder and self-made conversion sets. But now I feel that the likelihood of producing unit conversion errors with my old work style has become higher than using Maples units.

    I can only encourage interested users to give units a try. Its good!  For me it has turned out to be time worth invested.

    I also hope that Maplesoft continues their efforts of providing more unit functionalities. It’s a big task but calculations with physical quantities are also a big differentiator.  

    Over the last few months, we’ve had the honour of working with some fantastic online content creators who share our goals of helping make math accessible to students. We wanted to take a moment to highlight some of the great things they’ve done and how they’ve been able to use Maple Learn and the Maple Calculator to help explain math concepts to their audiences. Whether you’re looking to learn or searching for ways to make math engaging to others, these content creators are worth checking out!

    Much as some may complain about “attention spans these days”, there is definitely merit in being able to clearly explain high school level math in under a minute. If you’re looking for tips and tricks to help you understand math concepts, look no further than Justice the Tutor, whose TikTok is full of easy-to-understand videos explaining how to solve a wide variety of problems. You can check out his video on solving systems of equations here.

    I think it’s fair to assume that most people reading this like math, but all of us are multi-faceted individuals—so who’s also into drag? Online Kyne is, and she explains tons of math concepts in a fun, engaging, and sparkly way. Check out her video on 3D plots (and her matching 3D-glasses-themed eye makeup) here!

    If you’re looking for more ways to have fun with math, check out Tom Rocks Math, run by the University of Oxford’s Dr Tom Crawford. He rose to fame with his “Naked Mathematician” series, but even his clothed videos explain difficult math topics in ways that are clear and accessible. You can see how he tackles a complex topic like partial differentiation here.

    Whether you’re looking for a refresher or to learn something new, Dr Trefor Bazett’s YouTube channel has everything from cool math facts to complete courses on calculus, linear algebra, and more. If you don’t mind feeling called out for that one dumb mistake you made on a test once, this video on common algebra mistakes is a great resource for both students and teachers. What’s more, we’re excited to announce that Dr Trefor Bazett will be hosting a Maplesoft webinar where he’ll be discussing how to design effective interactive learning activities! The webinar will be on June 15, and you can sign up here. This promises to be a fascinating talk and a great way to get tips from someone whose online presence exemplifies his skill at getting people to engage with math, so we hope you’ll check it out.

    These content creators are just the tip of the iceberg. We’ve also been working with Bobby Seagull, a math teacher and author, and TikTok personalities nerdynas and tamerxi, whose student-centric content is both fun and useful. For our Japanese audiences, you can also check out Kantaro Suzuki’s videos on solving a variety of math problems, and Takumi’s video where he brought in other YouTubers to compete in a puzzle challenge using the Maple Calculator!

    We’re so thrilled to see how these amazing content creators are using Maple Learn and the Maple Calculator to create new content and engage with their audiences. It’s very exciting for us to be working with so many people who share our goals of making math accessible and interesting, and we love seeing what they’ve done with our products. Whether you’re a student looking to further understand your courses, a teacher looking to find more ways to engage with your students, or just someone who wants to learn more about math, these videos are all a fantastic resource. It’s clear that all these content creators have a passion for math, and as people who share that passion, we’re so happy to be working with them to help others find their own interest in math.

    Hi again all

    You can enjoy this simple Maple code to find the proper divisors of a given positive integer (whole number).



    here  some_proper_divisor_examples_3.pdf   file

    Hope this helps

    Matt Anderson


    ... and two suggestions to the development team

    POINT 1
    In ?DiscreteValueMap (package Statistics) it's given an example concerning rhe Geometric distribution along with this comment:
    "The Geometric distribution is discrete but it necessarily assumes integer values, so (bold font is mine) it also does not have a DiscreteValueMap"

    This sentence seems to indicate that "because a distribution is discrete over the set of integers, it cannot have a DiscreteValueMap", some sort of logical implication...

    But my feeling is that the Geometric distribution (or any other discrete distribution) does not have a DiscreteValueMap because this attribute has just not been specified when defining the distribution.

    GeomRV := RandomVariable(Geometric(1/2)):
    f := unapply(ProbabilityFunction(GeomRV, n), n):
    AnotherGeomRV := Distribution(
    DiscreteValueMap(AnotherGeomRV , n);

    Thus having the set of natural numbers as support doesn't imply that DiscreteValueMap cannot exist.

    Suggestion 1: modify the ?DiscreteValueMap help page so that it no longer suggests that some discrete distributions cannot have a .DiscreteValueMap 


    POINT 2
    I think there exists a true problem with the definition of discrete distributions in Maple: the ProbabilityFunction of a (discrete) random variable) takes non zero values outside their definition set.
    For instance

    ProbabilityFunction(GeomRV, Pi);  # something non null

    To ivercome this problem I defined a new Geometric distribution this way (not entirely satisfying):

    GeomRV := RandomVariable(Geometric(1/2)):
    f := unapply(ProbabilityFunction(GeomRV, n), n):
    g := n -> (1-ceil(n-floor(n)))*f(n)    # (1-ceil(n-floor(n))) = 1 if n in Z, 0 otherwise
    AnotherGeomRV := Distribution(
          'DiscreteValueMap'=(n->n),  # is wanted
    ProbabilityFunction(AnotherGeomRV, 2);
    ProbabilityFunction(AnotherGeomRV, Pi);

    PS: None of the statistics based upon the  ProbabilityFunction (Mean, Variance, ... ) is correctly computed with the previous construction. This could be easily overcome by completing this definition, just as its done in Maple, for all the requires statistics, for instance 

    AnotherGeomRV := Distribution(
          'Mean'=1   # or more generally (1-p)/p form Geometric(p)

    Suggestion 2: modify the way discrete distributions are defined in Maple in order to avoid ProbabilityFunction to return wrong values.

    We’ve been working hard on Maple Learn since its release, and we wanted to share some of the many updates we’ve made. If there was a feature you were looking for that we didn’t have, it might be time to check again! Here’s just a taste of some of the things we’ve been working on.

    Given its name, perhaps it’s not surprising that our focus with Maple Learn is to help students learn math. That’s why we’ve improved many of Maple Learn’s math capabilities, to give students the best experience we can. We’ve added support for piecewise functions and vector norms/magnitudes, and made many improvements to tables based on user feedback. Are you more of a statistician? Well, you’re in luck, because we’ve also added various statistics options to the Context Panel, which allow you to calculate mean, median, linear regression, and more. We’ve also made a handful of improvements to evaluation and assignment that we hope will make Maple Learn more intuitive for users.

    Maple Learn isn’t just about math, though—it’s about making math accessible. That means communicating clearly, so luckily, we’ve added several new text editing features to help you do just that. You can now use bold, italics, underline, hyperlinks, and changeable font sizes and colours. You can even collapse the plot window and Context Panel if you need a larger workspace or if your problem doesn’t require them. Now your documents will be both easy to follow and stylish!

    Speaking of stylish documents, we’ve also made various improvements to how functions can be visualized. There are a couple I’d like to point out to you: You can plot points by adding values to a table! What’s more, you can then move these points around the plot and your table will update automatically. You can also add points and other geometric plot primitives like line segments and vectors using the commands Point, Segment, and Vector. As well, if you have multiple functions plotted, you can see the intersection points by clicking the “Show special points” button. If points aren’t your style, we’ve also added support for some more types of plots, such as parametric plots. When working with differential equations, you can also plot the vector field for that equation. To learn how to use these features and more, check out the “How To” section at the bottom of our Example Gallery. We’re working on more help documentation everyday to help you use Maple Learn to its full potential.

    Finally, we’ve made a handful of miscellaneous changes that should help improve your overall experience with Maple Learn. For example, users can now save a copy of their document. We’ve also translated many of our examples to different languages, and are working on translating more everyday. We hope that all these changes and updates will help you get the most out of Maple Learn. If there are features you’d like to see, don’t hesitate to let us know. We add improvements to Maple Learn regularly, so keep an eye out for future updates on Primes!

    We have just released an update to Maple, Maple 2021.1.

    Maple 2021.1 includes improvements to plotting, export to PDF and LaTeX, the user interface, the mathematics engine, and more. We strongly recommend that all Maple 2021 users install these updates.

    This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2021.1 download page, where you can also find more details.

    In particular, please note that this update includes fixes to the sometimes missing plotting toolbar, the misplaced plot annotations on export, and a workbook saving problem, all reported on MaplePrimes.

    Thanks for the feedback!


    We’re excited to announce the release of MapleSim 2021! The MapleSim 2021 family of products lets you build and explore models more easily than ever, with improved simulation performance and 3-D visualizations, new ways to share models with those who don’t use MapleSim, and a host of new and expanded component libraries. Improvements include:

    • Improved performance for large models that allows you to take advantage of the fastest simulations yet – no matter how complex your design is.
    • More realistic 3-D visualizations with the ability to define dynamic shape sizes, such as spheres and cylinders that expand or contract over the course of the simulation, so components are realistically represented throughout.
    • Expanded modeling scope for machine builders, with a new pneumatics component library and expanded hydraulics support, as well as improved visualizations in the MapleSim Ropes and Pulleys Library add-on.
    • New simulation and analysis features in MapleSim Insight, a standalone product in the MapleSim family that provides anyone in your organization with access to powerful simulation-based debugging and 3-D visualization capabilities that connect directly to common automation platforms.

    See What’s New in MapleSim 2021 for more information about these and other improvements!

    The deadline to submit a presentation proposal for the Maple Conference 2021, to be held Nov. 2-5, 2021, has been extended to June 13, 2021.

    We invite submissions of proposals for presentations on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. All presenters will be given the option of submitting a full paper, which will undergo peer review, and if accepted, be included in the conference proceedings.

    More about the themes of the conference, how to submit a presentation proposal, and the program committee can be found here: Call for Presentations.

    We hope to see you at Maple Conference 2021!

    HI Maple Primes people and other interested parties,

    I was a teacher for more that ten years.  Most of my teaching was at community college level.

    Although I am not a biological father, my extended family is important to me.

    I graduated from university two times with special diplomas.  The next two years (99 to 01) were hectic for me.  After that I went to see about females, and now I am in the happily married club.

    I'm glad I kept my Maple 13 student version software because like my father, I like to make computer code.


    Mathematical truth will outlast the stars in the sky.  but government and good behavior will always kick the ass of any expression.

    Consider this 






    When we first launched Maple Learn in January, there were only a handful of examples in the Example Gallery. Today, due to customer requests, we have 57 examples and the number grows every week. You can check out the gallery here:

    The gallery is full of both practical and fun examples showing how you can use Maple Learn to work with all kinds of math. One great example is this worksheet on Logarithmic and Archimedean spirals made by our Sales Account Manager, @Oliver K. You can learn a bit about each type of spiral and adjust the sliders to see how the different parameters change the visualization. It’s a great tool for introducing students (or anyone who likes cool graphs!) to these types of spirals and for helping them understand the math behind them.