MaplePrimes Posts

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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  • Maple Learn is a great tool for checking the answer to your math problems, but what happens when your answer is wrong and you don’t know why? Knowing there’s a mistake doesn’t actually tell you what that mistake is. Luckily for you, Maple Learn’s newest feature is here to help you out: steps! Now, with the click of a button, you can see full, step-by-step solutions to a wide variety of problems. Instead of endlessly pouring over your work to find that one misplaced negative sign, you can check the steps to quickly and easily spot where you went wrong. Plus, if you’re having trouble figuring out how to approach a problem, you can sneak a peek at the first few steps to get the ball rolling. Full solutions are an invaluable learning tool, and we’re excited to be able to share them with our users.

    A screenshot of Maple Learn showing the derivative of an equation. Next to the derivative is a button labeled Steps, with a graphic of a pair of footsteps.

    Getting the steps is simple. When you perform an operation using the Context Panel, you’ll see a “Steps” button appear next to the solution when steps are available. Just click this button! This will take you to a new Maple Learn document showing you a full, detailed solution. Plus, if you want to bring the steps into another document, you can then click the “Copy to Clipboard” button. Checking your solution has never been easier!

    What sorts of problems do we have steps for, you might ask? Good question! The answer is a resounding “most of them”. Are you a high schooler? We’ve got steps for factoring, expansion, and solving both equations and linear systems. Doing calculus? Derivatives, integrals, limits, and even solving differential equations all have full solutions available. How about linear algebra? Absolutely! We provide steps for Gauss-Jordan elimination, matrix inversion, finding eigenvalues and eigenvectors, and calculating the determinant! And that’s just a taste of what Maple Learn can do. We’re working constantly to expand our roster of steps, so let us know what you want to see!

    I hear what some of you must be thinking: “But what about when I don’t have my computer with me? I never know when I’m going to need a step-by-step solution to a math problem!” If that’s you, then check out the Maple Calculator! The Maple Calculator provides full solutions just like Maple Learn, and you can carry it around in your pocket for math-on-the-go. With Maple Learn and the Maple Calculator on your side, no math problem can stop you now.

    A manipulator, in which 3 degrees of freedom are provided by changing the length of the links and one degree of freedom, is provided by turning. Only 4 degrees of freedom. Solved using Draghilev's method. In one case, the length of the manipulator link could be expressed through the value of the 3rd coordinate. The lengths of the other two links are considered generalized coordinates. In this case, it is still obtained polynomial equations, as for the usual coordinates.
    I was asked to make an example of the movement of such a manipulator using Maple. (Automatically, this is an example of solving an inverse kinematics problem.)
    four_degrees_of_freedom_from_Sabina.mw

    I am happy to announce that registration for Maple Conference 2021, to be held Nov. 2-5, is now open! The event is once again virtual and free this year. On our home page, you can find information about our keynote presentations. Our keynote speakers this year are Dr. Veselin Jungic, Dr. Evelyne Hubert and Dr. Laurent Bernardin.

    The Agenda & Event Format page contains preliminary information about the event and will be updated as the agenda develops. This page describes two add-on workshops that are also free of charge: "Maple Programming: Beyond the Basics" and "Advanced Problem Solving with Regular Chains".

    You can register for both the conference and the add-on workshops here: Maple Conference 2021. I hope to see you all in November!

    MacDude posted a worksheet for creating help files using the makehelp command that I found very useful.  However, his worksheet created a table of contents that organized the command help pages under a single folder.  I wanted to create a help file table of contents with the commands organized into sub-folders under the main application folder. ie. Package Name,Folder Name, command. The help page for makehelp is not very informative; in particular the example that shows (purportedly) how to override the existing help pages with your own help file is very misleading.  Also, the description of the parameters to the browser option of the makehelp command is too vague. I needed an error message to tell me that the browser option expects parameters in the form List(Name,String).  In the end, I was able to get a folder/sub-folder structure using a structure [`Folder Name`,`Subfolder Name`,"Command"].  Sub-folders are sorted alphabetically. If anyone has a need, the attached worksheet shows how I created the table of contents structure. 

    Our grand quest to expand and improve Maple Learn is marching steadily along, and we wanted to share with you some of what we’ve been working on! We’ve added some exciting new features that we hope you’ll enjoy.

    First up, we’ve added a new command: the Shaded command. This allows you to shade the area beneath a curve—perfect for helping students understand and visualize integrals. It also looks pretty cool, if I do say so myself.

    A screenshot of Maple Learn featuring a cosine function with the area under the curve coloured in.

    We’ve also added a few new symbols to our roster. You can now enter the not-equals sign through the Numbers and Operators menu, and we’ve added the upper-case Greek alphabet to the Greek symbols menu. Now you can write your documents entirely in Greek! (Or you can just use them as symbols.)

    If you’d rather keep the Latin alphabet, but do want to shake things up a bit, we’ve got just the thing for you: you can now choose either a Serif or Sans Serif font. With that and our other text editing tools, you’ll be able to customize the design of your document to your heart’s content.

    If you’re one of our users who requested support for mixed fractions, today is your lucky day! Maple Learn now fully supports mixed fractions, and you can convert between mixed and improper fractions using the Context Panel.

    A screenshot of Maple Learn showing 3 and 5/7 being converted to 26/7, and 11/9 being converted to 1 and 2/9.

    We also wanted to take the time to mention some of the bugs we’ve fixed based on user feedback. Thanks to you, we have now:

    • Fixed tooltips for floor and ceiling functions
    • Resolved the issue of Maple Learn slowing when using asin(x) in equations
    • Fixed typesetting bug when entering inequalities with fractions
    • Added more support for dealing with units in tables and equations

    Thank you to everyone who has sent in their feedback. Your reports are what allowed us to fix these issues. If you ever have feedback for us, whether it’s a bug you’ve found or a feature you’d like to see, use the “Flag a Problem” button to let us know. Maybe it’ll be your suggestion you see here next!

    A few weeks ago, some of our sales and marketing representatives decided to spice up some emails with some whimsical poetry. We sent them out to a selection of people, but we thought they were too fun not to share with everyone else! After all, what better way to talk about math products than through poetry? So without further ado, we’re proud to present our collection of mathematical verses:

    I.

    Math teachers and students, hear this tale of mine

    Maple Learn will help you, and it’s online

     

    The interface is freeform, the plots a delight

    With Maple behind it, you know they are right

     

    Solve problems from calculus? Easily done!

    Algebra, matrices, even trig becomes fun.

     

    Solve line by line, or all in one go

    With Maple Learn, you work fast or work slow

     

    Applications are endless, the basic version is free

    Fully unlock it for just a small fee

     

    Are you a teacher, from small school or great hall?

    Maple Learn Premium is free when you call!

     

    II.

    Maple Learn is great, as I hope you recall

    But when it comes to math products, that’s not all

     

    Do you have a math problem right before your eyes?

    Pull out your phone, is what I advise

     

    A click of your camera, a solution shown to you

    Solutions, graphs, and even steps too!

     

    Integrals, matrices, factoring, and more

    Maple Calculator solves problems galore

     

    And when find you have even more to do

    The problem in the picture reaches Maple Learn too!

     

    Teaching these days can be quite a task

    Our products can help you, you’ve only to ask

     

    III.

    My final approach, I’ll disturb you no more

    Just one final poem for you is in store

     

    On Maple Learn, there’s much more I could say

    But instead, here are examples with which you can play

     

    And Maple Calculator too, please don’t forget it

    Give it a try, I know you won’t regret it.

     

    My poems are now done, my inspiration depleted

    Thanks for your patience as by my poems, you were greeted

     

    We hope you had as much fun reading that as we did writing it. Stay tuned for next week, where we’ll be posting Maple Learn: The Musical! (Just kidding. Unless…?)

    In this simple example, we are going to learn how to Plot Isocline & Trajectory to examine stability of a dynamical system with Lyapunov Stability Theorem in Maple.

    iso.mw

    Download iso.mw

    You should be familiar with Dynamical Systems and Linear Control.

    This content would be more useful for students who are studying

    >> Linear Control &

    >> ODE's Theory

    I have a linear ctrl course this semester & I was trying to solve such problems. Finally I did.

    Hope to enjoy

    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

    Abastract

    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

    Ponencia_UNTumbes.pdf

    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.

    Download perpetual-motion-machine-corrected.mw

    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).

     

    Download proper_divisor.mw

    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.

    restart:
    with(Statistics):
    
    GeomRV := RandomVariable(Geometric(1/2)):
    f := unapply(ProbabilityFunction(GeomRV, n), n):
    
    AnotherGeomRV := Distribution(
          'ProbabilityFunction'=f,
          'Support'=0..infinity,
          'DiscreteValueMap'=(n->n),
          'Type'=discrete
    ):
    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):

    restart:
    with(Statistics):
    
    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(
          'ProbabilityFunction'=g,
          'Support'=0..infinity,
          'DiscreteValueMap'=(n->n),  # is wanted
          'Type'=discrete
    ):
    ProbabilityFunction(AnotherGeomRV, 2);
                     1/8
    ProbabilityFunction(AnotherGeomRV, Pi);
                      0
    

    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.

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