From a tweet by Tamás Görbe : plotting Chebyshev polynomials in polar coordinates leads to some interesting pictures.  Screenshot here, link to the worksheet (and some perhaps interesting puzzles) at the end.

ChebyshevRose.mw

Calling all fans of customizable documents! What am I saying, we’re all fans of customizable documents here. Well, we’re all in luck, then, because with our latest updates to Maple Learn you can tailor even more details of your documents to your exact specifications. Read on to see what’s new!

As we all know, graphs are not merely a method of communicating mathematical concepts, but are of course an art form that can be used to display both mathematical and aesthetic beauty. But sometimes, you may find a little something getting in the way of that beauty… those darn gridlines. Even the most elegant of graphs can be tarnished by this faint, criss-crossing lines. But have no fear! With our latest updates, you can fix this problem with the click of a button. Simply select “Plot Settings” from the graph controls to the right of the plot window, and set Axes to “None”. Finally, your graph is pristine. What’s more, that’s not the only new feature we’ve added to the Plot Settings menu. You can also set the axes to “Boxed”, allowing you to see the gridline labels no matter how from the origin you are on the graph. You can also manually set the boundaries of your axes! No more scrolling and zooming to get the perspective just right.

As if that wasn’t enough, we’ve also added another exciting feature that will help make your graphs look exactly as you want them. By clicking the small graph icon to the left of your expression, you can customize the colour of your plot! You can choose from a wide variety of pre-set colours, or you can use our colour selector to get the exact shade you want. Any custom colours will be temporarily added to the bottom of the colour palette, so you can be sure that your graphs are consistent. At last, you can rest assured that your Maple Learn graphs won’t clash with your outfit.

What’s more, if you’re a fan of graph customizability, then this is the set of updates for you. We’ve added two more features that will help make your graphs both pretty and easy to understand. Tired of trying to draw shapes, only to have each side be a different colour? Well, no more! We’ve adjusted the Segment command to accept as many coordinates as you’d like, allowing you to create polygons (or just funky zigzags) to your heart’s content! As well, we’ve introduced a new command: the Label command. Now you can add text right onto the plot window and label your graph as you see fit. Or maybe you could use the Maple Learn plot window to start drafting a best-selling novel. The possibilities are endless!

We also wanted to take a moment to highlight our Example Gallery. We’ve made some changes to make it easier to find the examples you’re looking for. And with over 400 documents and counting, we’re sure to have what you want! But, on the off-chance we don’t, let us know! We’d love to hear about what you’d like to see. And as always, that goes for both the Example Gallery and for any features you’d like in Maple Learn itself! We appreciate your feedback.

Dear all,

Reversion of series---computing a series for the functional inverse of a function---has been in Maple since forever, but many people are not aware of how easy it is.  Here's an example, where we are looking for "self-reverting" series---which I called "ambiverts".  Anyway have fun.

https://maple.cloud/app/5974582695821312/Series+Reversion%3A+Looking+for+ambiverts

PS There looks to be some "code rot" in the branch point series for Lambert W in Maple, which we encounter in that worksheet.  Or, I may simply have not coded it very well in the first place (yeah, that was mine, once upon a time).  Checking now.  But there is a workaround (albeit an ugly one) shown in that worksheet.

Dear all,

Recently we learned that the idea of "anti-secularity" in perturbation methods was known to Mathieu already by 1868, predating Lindstedt by several years.  The Maple worksheet linked below recapitulates Mathieu's computations:

https://github.com/rcorless/MathieuPerturbationMethod

Nic Fillion and I wrote a more general introduction to perturbation methods using Maple and you can find that paper at 

https://arxiv.org/abs/1609.01321

and the supporting Maple code in a workbook at 

https://github.com/rcorless/Perturbation-Methods-in-Maple

For instance, one of the problems solved is the lengthening pendulum and when we do so taking proper account of anti-secularity (we use renormalization for that one, I seem to remember) we get an error curve that is bounded over time.

Hope that some of you find this useful.

Welcome to Maplesoft Orientation Week!  We know what a difference math software can make when it comes to enhancing student learning, but we also know that everyone is very busy at the beginning of the school year! So our goal for this week is to make it easier for high school and university students to select the best math tool for their needs, and help them get on track for a great math year.  The week’s activities include free training on Maple and Maple Learn, discounts on Student Maple, live events with some of your favorite math TikTok personalities, and even the chance to win an iPad Air!  Check out all the activities now, and plan your week or tell your students.

Orientation week runs Mon. Sept. 20 – Fri. Sept. 24.

Hi everyone! It's been a remarkably long time since I posted on MaplePrimes -- I should probably briefly reintroduce myself to the community here. My name is Erik Postma. I manage the mathematical software group at Maplesoft: the team that writes most of the Maple-language code in the Maple product, also known as the math library. You can find a longer introduction at this link.

One of my tasks at Maplesoft is the following. When a request for tech support comes in, our tech support team can usually answer the request by themselves. But no single person can know everything, and when specialized knowledge of Maple's mathematical library is needed, they ask my team for help. I screen such requests, answer what I can by myself, and send the even more specialized requests to the experts responsible for the appropriate part of the library.

Yesterday I received a request from a user asking how to unwrap angles occurring in an expression. This is the general idea of taking the fact that , and similarly for the other trig functions; and using it to modify an expression of the form  to make it look "nicer" by adding or subtracting a multiple of  to the angle. For a constant, real value of  you would simply make the result be as close to 0 as possible; this is discussed in e.g. this MaplePrimes question, but the expressions that this user was interested in had arguments for the trig functions that involved variables, too.

In such cases, the easiest solution is usually to write a small piece of custom code that the user can use. You might think that we should just add all these bits and pieces to the Maple product, so that everyone can use them -- but there are several reasons why that's not usually a good idea:

• Such code is often too specialized for general use.
• Sometimes it is reliable enough to use if we can communicate a particular caveat to the user -- "this will not work if condition XYZ occurs" -- but if it's part of the Maple library, an unsuspecting user might try it under condition XYZ and maybe get a wrong answer.
• This type of code code generally doesn't undergo the careful interface design, the testing process, and the documentation effort that we apply to the code that we ship as part of the product; to bring it up to the standards required for shipping it as part of Maple might increase the time spent from, say, 15 minutes, to several days.

That said, I thought this case was interesting enough to post on MaplePrimes, so that the community can take a look - maybe there is something here that can help you with your own code.

So here is the concrete question from the user. They have expressions coming from an inverse Laplace transform, such as:

with(inttrans):
F := -0.3000*(-1 + exp(-s))*s/(0.0500*s^2 + 0.1*s + 125);
f := invlaplace(F, s, t)*u(t);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t-
#         49.98999900)-357.*cos(49.98999900*t-49.98999900))+.1680672269e-1*(-7.141428429*sin
#         (49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

I interpreted their request for unwrapping these angles as replacing the expressions of the form  with versions where the constant term was unwrapped. Thinking a bit about how to be safe if unexpected expressions show up, I came up with the following solution:

unwrap_trig_functions := module()
local ModuleApply := proc(expr :: algebraic, $)
  return evalindets(expr, ':-trig', process_trig);
end proc;

local process_trig := proc(expr :: trig, $)
  local terms := convert(op(expr), ':-list', ':-`+`');
  local const, nonconst;
  const, nonconst := selectremove(type, terms, ':-complexcons');
  const := add(const);
  local result := add(nonconst) + (
    if is(const = 0) then
      0;
    else
      const := evalf(const);
      if type(const, ':-float') then
        frem(const, 2.*Pi);
      else
        frem(Re(const), 2.*Pi) + I*Im(const);
      end if;
    end if);
  return op(0, expr)(result);
end proc;
end module;

# To use this, with f defined as above:
f2 := unwrap_trig_functions(f);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t+
#         .27548346)-357.*cos(49.98999900*t+.27548346))+.1680672269e-1*(-7.141428429*sin(
#         49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

Exercise for the reader, in case you expect to encounter very large constant terms: replace the calls to frem above with the code that Alec Mihailovs wrote in the question linked above!

Another series of updates to Maple Learn? It’s almost like we’re constantly working on Maple Learn to add more features and improve based on your feedback! Wild, right? Anyways, here’s some of the latest features we’ve added to Maple Learn.

First, we’re very excited to present our new Example Gallery. Not only does it have a shiny new design, but there are now over 400 example documents in just about every area of mathematics you can think of.  These documents are perfect for seeing how Maple Learn can be used to teach and explore concepts, and you can easily modify them to suit your own needs. We’re still working hard on improving the Example Gallery and its content, so let us know what you want to see!

We’ve also got some shiny new features in Maple Learn itself. Do you ever look at a graph and think, “Wow, this is great and all, but I sure would love if it had fewer straight lines and more circles?” I know I do. Luckily for both of us, Maple Learn now supports polar coordinates! Just click the round globe icon to see your plots transformed to the circular form you’ve always wanted them to be.

Looking to enhance the text portion of your documents, rather than the graphs? We’ve got just the thing for you—Maple Learn now supports bullet lists! Take your pick of numerical lists, alphabetical, or your traditional bullet point. If you’re looking to augment your document with a step-by-step process, a list of your favourite mathematical expressions, or you’re just feeling tired of using pen and paper for grocery lists, Maple Learn now has what you need.

Speaking of improving the layout of your documents, we now have an option for horizontal tables. The vertical tables can get a bit a long, especially for a short document, but with horizontal tables you can keep all your documents cozy and compact.

And as always, this is just a taste of what we’ve been up to. We’ve also improved a variety of features (including our new steps feature!) and fixed an assortment of bugs. And remember, we couldn’t do this without you! Please continue to let us know what you’d like to see in Maple Learn, and someday it could be your request featured in our post!

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.

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.

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.

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.

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…?)

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.

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!

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.

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.

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.

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!

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!
 

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: https://www.maplesoft.com/products/learn/examples/

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.

We’ve got a whole team of people, led by Senior Architect @pchin, who are working every day to make more examples like these. If there’s something you’d like to see, leave us a comment! We’d love to hear your ideas.

If you’re feeling inspired by all these examples and want to try your hand at creating something of your own using Maple Learn, check out the “How to Use Maple Learn” section at the end of the example gallery. Here you’ll find a collection of worksheets that will take you through the basic features of Learn, including “Using Sliders”, “Difference Between Equations and Assignments”, and “What Does the Light Bulb Do?”. With all this knowledge at your fingertips, you’ll be all set to create to your heart’s content!