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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  • Happy Valentine’s Day! Love is celebrated all around the world on this day, but did you know of some other love celebrations, and some of the mythology around the holiday?

    First of all, Cupid. We all know of the image of Cupid and his bow, shooting arrows to make couples fall in love. But where exactly did this come from?

    Cupid is a Latin deity, the son of Venus and Mars. With his parents being love and war, it’s no surprise that he ended up with a bow! In one legend, he shoots a golden arrow at Apollo, which makes him fall in love with a nymph. Unfortunately for Apollo, he also shoots a lead arrow at the nymph, making her repulsed by him.

    Roses are another popular tradition with Valentine’s Day. Red roses persist as a symbol of Aphrodite, the mother of Cupid, and are a symbol of love. Did you know you can draw them in Maple Learn with our geometry palette? See one rendition below of a stained glass rose. The link to the document is HERE.

    Now, there are a few other love traditions around the world. Did you know that not everyone celebrates love only on Valentine’s Day? There are other important days around the world, and some pre-date Valentine’s Day.

    For example, in China, the Miao people celebrate the Sister’s Meal Festival, likely our earliest form of a Valentine’s Day tradition in the world. This occurs in March. Young women make dyed rice representing the different seasons, and when the men come by to sing, they give them packages of the rice. Inside the rice are objects, each with different meanings. A pair of red chopsticks means the woman returns the man’s affection, while one red chopstick is a polite refusal. A clove of garlic or a chili pepper means a strong refusal, and pine needles mean that she is waiting for him to woo her.

    We’ve created a document to join in on the fun, even if you’re not participating in this Festival this year. Follow the link HERE to work with fraction tiles to pack your own rice packages, and your own responses to declarations of love. 

    We hope everyone has a lovely Valentine’s day!

    You heard us right! With the new update of Maple Learn, we’ve added a few more interesting features, perfect to keep your math learning going.

    Before we dig too far into these exciting features, we just have one quick thing to let you know about. We have updated the font sizes for Maple Learn text, adding 20 and 22 point font, and removing 36 and 120 point font.

    Now, let’s talk new features. First, we’ve added support for partial derivatives, allowing you to calculate derivatives for functions with two or more variables. How does this work? Well, take a look at our example document HERE. The button for entering a partial derivative is located in the functions palette. You can plot them too (shown below)!

    We’ve also added support for shaded Geometric Primitives. Remember our earlier post about MAPLE LEARN ART? Well, now you can color in your shapes! This allows for further math-related art, or ease of communication while teaching about area, or really, anything else you can think of! See how to use this HERE. In essence, with the shaded command, you can now place a geometric primitive inside the shaded command, which shades it! As well, you can assign a variable to a geometric primitive, and then place that inside the shaded command. This allows for a different color outline than the shaded section.

    Ever wanted to create a sequence in Maple Learn? Well, now you can easily, with our new sequence support. The syntax is simple, focusing on the start, end, and steps. See how to use this HERE. We hope this can be used for all kinds of documents!

    We hope you enjoy all the new features we’ve added to Maple Learn. Let us know in the comments what you think of them, and show us what you’re working on! Simply leave a comment with a link to a Maple Learn document, and we’ll gladly take a look at your ideas.

    We have just issued a critical fix to Maple, MapleSim, and Maple Flow running on macOS.

    We have heard from some users who were experiencing serious problems with doubled characters while using Maplesoft products on macOS, including these reports on MaplePrimes. Further investigation determined that these problems appear specifically on macOS 11 and macOS 12.  I am happy to report that we have now corrected the problem, and a patch is available. 

    Anyone who uses macOS 11 or macOS 12 should install this update immediately. We also strongly recommend that all macOS users install this update, to avoid problems that may be triggered by future updates to your operating system.

    To obtain this update:

    For those who have experienced problems, we apologize for the inconvenience and thank you for your patience while we worked to find a solution.

    Maple users may notice unexpected results when calculating standard deviations with weights.

    This is because the notion of weights used by Maple is not exactly the commonly used notion of repeated measurements.

    Maple uses the NAG library from the Numerical Algorithms Group to compute the standard deviation in the presence of weights. The formula that is used is given in their documentation: https://www.nag.com/numeric/cl/nagdoc_cl25/pdf/g01/g01aac.pdf.

     

    NULL

    restart

    with(Statistics)

    V := `<,>`(seq(i, i = 57 .. 77), undefined)

    _rtable[36893489755601713980]

    (1)

    W := `<,>`(2, 4, 14, 41, 83, 169, 394, 669, 990, 1223, 1329, 1230, 1063, 646, 392, 202, 79, 32, 16, 5, 2, 5)

    StandardDeviation(V, weights = W)

    HFloat(HFloat(undefined))

    (2)

    StandardDeviation(V, weights = W, ignore = true)

    HFloat(2.7274213984819053)

    (3)

    NULL

    Download standard-deviation-weights-help-example.mw

    Happy Lunar New Year to everyone here in the MaplePrimes community, as we enter the Year of the Tiger! There are different traditions followed in the many countries around the world where the Lunar New Year is celebrated. In my own Canadian-Chinese family, we usually cook a big meal and share with family members and friends. 

    The pandemic has made this year's celebration more muted, but I did cook a large batch of our favourite dumplings and made up several packages to take to friends. That led to the question: how many ways can I arrange 10 dumplings on a plate from the 3 kinds I made? Of course, that called for a Maple Learn document to compute the answer: A Counting Problem: Selecting Dumplings
     


    I was also interested in understanding the formula used in this computation, and so I created a second document showing a special case of this problem. By moving the sliders around, you can see how the "Stars and Bars" method for counting the ways one can choose a number of items from distinct bins works: Visualization the Stars and Bars Method.

    I hope you enjoy trying out these documents and I wish everyone good health, happiness and prosperity in the coming year!

    In November, I posted a message announcing that we have been working on an updated version of the Application Center, and invited comments from anyone wanting to check out the beta site. I received multiple comments, both as comments to that post, as well as directly, and we made a lot of changes based on the feedback. Thank you very much to everyone who responded.

    I am now very happy to report that the new Application Center is now open to the public!

    For those who aren't familiar with it, the Application Center has been around for over 20 years, and it provides a place for our user community to post and share their work. It includes over over 2,700 applications and examples covering a wide array of topics and disciplines, and all are freely available to download.

    The previous version of the Application Center was overdue for a refresh. And while we were in there applying a fresh coat of paint, we also took the opportunity to add some new features and capabilities that we hope you will enjoy. As a quick summary of what has changed:

    • The look and feel has been significantly updated. It is cleaner, more modern and easier to use.
    • In addition to search, user-created collections and tags make it easier than ever to find and discover content.
    • Logged-in users can customize the site by pinning their favorite collections and content.
    • Logged-in users can also take advantage of their community reputation to help maintain the content in MaplePrimes, and your contributions will now contribute to your reputation scores. For example, when someone likes one of your apps, your reputation score will be increased by 5.
    • In addition to Maple content, Maple Flow documents are also now included. The collection is very small right now, but it will grow quickly.

    There are plenty of other features and enhancements as well.

    So without further ado, I invite you to check out the Application Center and to continue to provide your comments and suggestions!

    Bryon

    When I was in middle school, I was really into puzzles.  At one point I attempted the Three Utilities Problem.  This famous problem is deceptively simple: three houses and three “utilities” (heating, water, and electricity) are represented by dots on a flat piece of paper.  The goal is to connect each house to the three utilities without crossing any lines.

    Figure 1: A starting setup.

    I spent hours drawing lines.  I eventually looked it up online, and the internet told me that the problem was impossible.  I didn’t believe it, and tried for several more hours until I was forced to accept its impossibility.  I still remember this intense stint of puzzling to this day.

        

    Figure 2: Cue twelve-year-old me saying “I’ll get it eventually…”

    Looking back, I wonder if this sparked my interest in graph theory.  I know now that the Three Utilities Problem is truly unsolvable.  I know that the graph’s formal name is K3,3 and I know a full graph theory proof explaining its nonplanarity.  Nevertheless, I still love this puzzle, and I’ve recently recreated it in Maple Learn.

    To do this, I created a table of x and y values and plotted all of them using the Point() command.  This allows the points to be fully click-and-drag-able.  Line segments joining two points automatically move with the points as well.  We then have a fully interactive graph directly in the Maple Learn plot window.  I can move the “houses” and “utilities” around all I want to try and solve the unsolvable.  I can also create other graphs to further explore planarity, paths, matchings, or any other aspects of the wide world of graph theory.

    If you want to check out the document for yourself, it can be found here

    A user wondered how to have Maple produce a desired form of a solution

    eq1 := `&sigma;__2` = P__2/(Pi*r^2)NULL

    NULL

    r := (1/2)*d

    NULL

    soln := `assuming`([solve(eq1, {d}, useassumptions)], [`&sigma;__2`::real, d > 0, P__2 > 0])

    {d = 2*(Pi*sigma__2*P__2)^(1/2)/(Pi*sigma__2)}

    (1)

    NULL

    Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

    Download question-better-spacing.mw

    We suggested the closest they might be able to get is using simplify like so:

     

    restart; eq1 := `&sigma;__2` = P__2/(Pi*r^2)
    ``

    ``

    r := (1/2)*d

    ``

    soln := `assuming`([solve(eq1, {d}, useassumptions)], [`&sigma;__2`::real, d > 0, P__2 > 0])

    {d = 2*(Pi*sigma__2*P__2)^(1/2)/(Pi*sigma__2)}

    (1)

    ``

    `assuming`([simplify(soln)], [sigma__2::real, P__2 > 0])

    {d = 2*P__2^(1/2)/(Pi^(1/2)*sigma__2^(1/2))}

    (2)

    NULL


    Download suggestion.mw

    Our user wondered about using PolynomialIdeals:

    1.  If we have n+1 polynomials,  f, g1,...,gn,  how to determine if  f  is in the ideal generated by  g1,...,gn?

    2.  If so, how to write  f  as a polynomial combination of   g1,...,gn? 

    We suggested that;

    The nicest interface to answer the first question is given by the ?PolynomialIdeals,Operators page: you can write

    with(PolynomialIdeals):
    with(Operators):
    J := <g1, g2, ..., gn>;
    f in J; # true or false
    

    To answer the second question, you need to use the lower level  package (which underlies the  package). This will also answer the first question for you. In particular the  command. You can write:

    (Edit Feb 1, 2022 - use  instead of 

    with(Groebner):
    G := [g1, g2, ..., gn];
    ord := tdeg(x,y,z); # replace x, y, z with the appropriate variables; you can also use other variable orders -- see ?Groebner,MonomialOrders
    
    b := Basis(G, ord);
    n := NormalForm(f, b, ord, 'Q');
    # if n = 0 then f is in the ideal; Q is the list of coefficients:
    f - add(Q[i] * b[i], i = 1 .. numelems(b)); # this will be equal to n.

    I’m looking for users’ favourite tips and tricks in Maple Learn. Specifically, small pieces of advice that most people don’t know about, but that helped you create better Maple Learn documents. For instance,

    • A favorite feature that you think is hard to discover;
    • Common techniques you use when creating documents;
    • Things about Maple Learn you wish you knew when you started.

    These tricks could be for newbies or for experienced users.

    To start off the discussion, let me share three of my own favorite tricks in Maple Learn.

    1. Using Documents from the Document Gallery

    Writing a Maple Learn document from scratch can seem overwhelming, especially for beginners. A much easier way to create documents is to start with a template from the Document Gallery.

    There are hundreds of Maple Learn documents in the Document Gallery, available here. Instead of writing Maple Learn documents from scratch, I like to search the gallery for documents relating to my topic. I then select a document, and just modify it slightly to get what I want.

    2. Toggling from Math Mode to Text Mode

    If you want to write text in a group element, it’s best to toggle to text mode (otherwise Maple Learn will treat your text as math).

    While this can be done using the toolbar, there is a nifty keyboard shortcut to toggle to text mode: place your cursor at the beginning of the group element, and press the space key.

    3. Using Double Arrows in Plots to Show Distance

    Here’s one for the advanced users. The Vector Command lets you draw arrows on a Maple Learn plot. Combine two such arrows of the same colour going in opposite directions, and you get a double arrow (see below), which I like to use to represent distances in my Maple Learn documents.

    Indeed, here is an example document where I use double arrows to provide a visualization of the product rule in calculus (plot pictured below). Notice how the double arrows (created using the vector command) represent distances in the plot.

    Comment your favourite tips and tricks down below!

    A user would like to know if it is possible to specify a data set say, x:=[1,2,3,4,5,6] and then extract a random sample from that data set, i.e. xsample:=[3,2,4] for a bootstrapping-type calculation.

    We suggested they use something like the following:

    restart; with(Statistics); my_data := [1, 2, 4, 5.5, 5.5, 6]; X := RandomVariable(EmpiricalDistribution(my_data)); s := Sample(X, 10); Bootstrap(Mean, X, samplesize = 4, replications = 10000)

    HFloat(3.9984625)

    (1)

    NULL

    Download array-random-sample.mw

     

    The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

    It prints quite well (with proper equipment).  I wish you all the best for 2022.

     

    Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.

    My Setup

    When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. 

    Here is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.

     

    Why I Chose Maple Learn

    My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. 

    Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.

    There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.

    Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.

    As always, it's just about drawings.
    The parametric equation of a circle has 3 variables and two equations. In 3-dimensional space, a circle is a spiral, but we only need one projection of this spiral into 2-dimensional space, and we also know how  the rest 2 it's projections on flat space look.
    If we look at the equation of the sphere in parametric form, we will see that these are 3 equations and 5 variables:
    x1 = sin(x4)*cos(x5); 
    x2 = sin(x4)*sin(x5); 
    x3 = cos(x4);
    And so I wanted to see how the remaining 9 projections of the sphere onto 3-dimensional space look. It is very easy to do this with Maple.
    SPHERE.mw

    Are you teaching a calculus course? Then use Maple Learn, Maplesoft’s free online product, to do so.

    Below are some examples of calculus documents you can create in Maple Learn.

     

    1. Documents Explaining Concepts with Interactive Visuals

    Example: Visualizing the Formal Definition of the Derivative

     

    2. Interactive Quizzes

    Example: The Product Rule: Practice Questions

     

    3. Documents Using Maple to Perform Complex Operations

    Example: Taylor Series Approximation Calculator

     

    Maplesoft’s learn content team has already created about 200 Maple Learn calculus documents! The full list is here. You can modify these documents easily, and use them to teach your calculus class as well.

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