Do you have a Chromebook?  Are you a student or a teacher looking for the mighty power of Maple, but find yourself limited by your web-only computer? Well, have no fear, because Maple Learn is here!

As a web-based application, Maple Learn is fully supported by Chromebooks. You can create graphs, perform and check calculations, and share documents all within the comfort of your own browser. No need to download any kind of software—just go to learn.maplesoft.com to get started!

Students, if you’re looking for some use for your school-provided Chromebook and wondering how it can help you learn instead of just weighing down your backpack, Maple Learn can help. It’s the perfect, all-inclusive tool to help you learn, visualize, and check your math. And, if you’re looking to brush up on all that math you forgot over the summer, you can check out the Maple Learn Example Gallery, home to hundreds of examples and explanations of a wide variety of math concepts. And it’s all accessible on your Chromebook!

Here's a podcast that covers a few topics that get discussed on MaplePrimes.
 

We all like finding the right tool for the job. In the Sep 2021 episode of the Engineering Matters Podcast “#127 – Tools for Thinking” you can discover how far engineers have come in their quest for better tools.

It features contributions from several members of the Maplesoft team as they discuss how the user experience shapes the adoption of engineering software tools.

The hosts have fun describing some early calculation hacks - from early Sumerian farmers using their fingers as tally counters, to the paper calculus notebooks of the 1850s used by historical engineering figures like Isambard Kingdom Brunel. What starts as a necessity gets improved over time to save them mental effort – all driven by the way users interact with the tool.

This episode gives a behind-the-scenes look at some of the decisions that shaped the engineering product that is now Maple Flow from its roots in Maple. Maplesoft CEO Laurent Bernardin describes the spark of innovation in the late 1970s, when two professors at the University of Waterloo developed Maple. “The two professors got together, realising that there was a need in math education for a tool to help with calculations and setting out to create that tool. And Maple was born quickly, was adopted across universities around the globe.”

As engineers typically work in ways far removed from the regular academic setting, Product Manager Samir Khan weighs in on the shift that comes from a different user base: “Different tools have different design intents,” says Khan. “Some tools are designed for programmers such as code development environments, like Visual Studio. Some environments are aimed at mathematicians, people who need precise control over the mathematical structure of their equations, and some environments are designed for engineers who simply want to throw down a few equations on a virtual whiteboard and manipulate them and get results.”

The conversation also touches on the design of the GUI itself. Margaret Hinchcliffe, Maple’s Senior GUI Developer expresses the importance of smoothing the user experience - drilling down and taking “the typical tasks that people want to do the most, and make those the most immediate. So really focusing on how many keystrokes do they need to do this task?”.

Ironically the idea of the paper notebook still has features that are desirable. Khan muses on the idea that Maplesoft has “taken the first step with having a virtual whiteboard, but Maple Flow still relies on keyboard and mouse input”. He offers suggestions for what may be next in the industry: “It’d be interesting to see if we can take advantage of modern advances in deep learning and AI to imitate what humans are doing and interpreting handwritten mathematics.”

You can listen to the entire podcast (~30 min) here: https://engineeringmatters.reby.media/2021/09/30/the-evolution-of-tools-for-thinking/

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

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.

... 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.

I am a high school Teacher in Denmark, who have been using Maple since version 12, more than 12 years ago. I suggested it for my school back then and our math faculty finally decided to purchase a school license. We are still there. We have watched Maple improve in a lot of areas (function definitions, context panels, graphically etc., etc ). Often small changes makes a big difference! We have been deligted. We we are mostly interested in improvements in GUI and lower level math, and in animations and quizzes. I have also been enrolled as a beta tester for several years yet. 

One of the areas, which is particually important is print and export to pdf, because Danish students have to turn in their papers/solutions at exams in pdf format! I guess the Scandinavian countries are ahead in this department. They may quite possible be behind in other areas however, but this is how it is. 

Now my point: Maplesoft is lacking terrible behind when regarding screen look in comparison with print/export to pdf. 

I am very frustrated, because I have been pinpointing this problem in several versions of Maple, both on Mapleprimes and in the beta groups. Some time you have corrected it, but it has always been bouncing back again and again! I have come to the opinion that you are not taking it seriously? Why?

Students may loose grades because of missing documentations (marking on graphs etc.). 

I will be reporting yet another instance of this same problem. When will it stop?

Erik

 

Download Wirtinger_Derivatives.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

I’m very pleased to announce that the Maple Calculator app now offers step-by-step solutions. Maple Calculator is a free mobile app that makes it easy to enter, solve, and visualize mathematical problems from algebra, precalculus, calculus, linear algebra, and differential equations, right on your phone.  Solution steps have been, by far, the most requested feature from Maple Calculator users, so we are pretty excited about being able to offer this functionality to our customers. With steps, students can use the app not just to check if their own work is correct, but to find the source of the problem if they made a mistake.  They can also use the steps to learn how to approach problems they are unfamiliar with.

Steps are available in Maple Calculator for a wide variety of problems, including solving equations and systems of equations, finding limits, derivatives, and integrals, and performing matrix operations such as finding inverses and eigenvalues.

(*Spoiler alert* You may also want to keep a look-out for more step-by-step solution abilities in the next Maple release.)

If you are unfamiliar with the Maple Calculator app, you can find more information and app store links on the Maple Calculator product page.  One feature in particular to note for Maple and Maple Learn users is that you can use the app to take a picture of your math and load those math expressions into Maple or Maple Learn.  It makes for a fast, accurate method for entering large expressions, so even if you aren’t interested in doing math on your phone, you still might find the app useful.

I make a maple worksheet for generating Pythagorean Triples Ternary Tree :

Around 10,000 records in the matrix currently !

You can set your desire size or export the Matrix as text ...

But yet ! I wish to understand from you better techniques If you have some suggestion ?

the mapleprimes Don't load my worksheet for preview so i put a screenshot !

Pythagoras_ternary.mw

Pythagoras_ternary_data.mw

Pythagoras_ternary_maple.mw

The order in which expressions evaluate in Maple is something that occasionally causes even advanced users to make syntax errors.

I recently saw a single line of Maple code that provided a good example of a command not evaluating in the order the user desired.

The command in question (after calling with(plots):) was

animate(display, [arrow(<cos(t), sin(t)>)], t = 0 .. 2*Pi)

This resulted in the error:

Error, (in plots/arrow) invalid input: plottools:-arrow expects its 3rd argument, pv, to be of type {Vector, list, vector, complexcons, realcons}, but received 0.5000000000e-1*(cos(t)^2+sin(t)^2)^(1/2)
 

This error indicates that the issue in the animation is the arrow command

arrow(<cos(t), sin(t)>)

on its own, the above command would give the same error. However, the animate command takes values of t from 0 to 2*Pi and substitutes them in, so at first glance, you wouldn't expect the same error to occur.

What is happening is that the command 

arrow(<cos(t), sin(t)>)

in the animate expression is evaluating fully, BEFORE the call to animate is happening. This is due to Maple's automatic simplification (since if this expression contained large expressions, or the values were calculated from other function calls, that could be simplified down, you'd want that to happen first to prevent unneeded calculation time at each step).

So the question is how do we stop it evaluating ahead of time since that isn't what we want to happen in this case?

In order to do this we can use uneval quotes (the single quotes on the keyboard - not to be confused with the backticks). 

animate(display, ['arrow'(<cos(t), sin(t)>)], t = 0 .. 2*Pi)

By surrounding the arrow function call in the uneval quotes, the evaluation is delayed by a level, allowing the animate call to happen first so that each value of t is then substituted before the arrow command is called.

Maple_Evaluation_Order_Example.mw

Download Godel_universe_and_Tedrads.mw

Hi,
Some people using the Windows platform have had problems installing MapleCloud packages, including the Maplesoft Physics Updates. This problem does not happen in Macintosh or Linux/Unix, also does not happen with all Windows computers but with some of them, and is not a problem of the MapleCloud packages themselves, but a problem of the installer of packages.

I understand that a solution to this problem will be presented within an upcoming Maple dot release.

Meantime, there is a solution by installing a helper library; after that, MapleCloud packages install without problems in all Windows machines. So whoever is having trouble installing MapleCloud packages in Windows and prefers not to wait until that dot release, instead wants to install this helper library, please email me at physics@maplesoft.com. 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

There is an interesting preprint here, on a method for integration of some pseudo-elliptic integrals.

It was mentioned in a (sci.math.symbolic) usenet thread, which can be accessed via Google Groups here.

Inside the paper, the author mentions that the following is possible for some cases -- to first convert to RootOf form.

Download int_pe.mw

I’m extremely pleased to introduce the newest update to the Maple Companion. In this time of wide-spread remote learning, tools like the Maple Companion are more important than ever, and I’m happy that our efforts are helping students (and some of their parents!) with at least one small aspect of their life.  Since we’ve added a lot of useful features since I last posted about this free mobile app, I wanted to share the ones I’m most excited about. 

(If you haven’t heard about the Maple Companion app, you can read more about it here.) 

If you use the app primarily to move math into Maple, you’ll be happy to hear that the automatic camera focus has gotten much better over the last couple of updates, and with this latest update, you can now turn on the flash if you need it. For me, these changes have virtually eliminated the need to fiddle with the camera to bring the math in focus, which sometimes happened in earlier versions.

If you use the app to get answers on your phone, that’s gotten much better, too. You can now see plots instantly as you enter your expression in the editor, and watch how the plot changes as you change the expression. You can also get results to many numerical problems results immediately, without having to switch to the results screen. This “calculator mode” is available even if you aren’t connected to the internet.  Okay, so there aren’t a lot of students doing their homework on the bus right now, but someday!

Speaking of plots, you can also now view plots full-screen, so you can see more of plot at once without zooming and panning, squinting, or buying a bigger phone.

Finally, if English is not you or your students’ first language, note that the app was recently made available in Spanish, French, German, Russian, Danish, Japanese, and Simplified Chinese. 

As always, we’d love you hear your feedback and suggestions. Please leave a comment, or use the feedback forms in the app or our web site.

Visit Maple Companion to learn more, find links to the app stores so you can download the app, and access the feedback form. If you already have it installed, you can get the new release simply by updating the app on your phone.

The ideas here are to allow 3D plotting commands such as plot3d to handle a `size` option similarly to how 2D plotting commands do so, and for the plots:-display command to also handle it for 3D plots.

The size denotes the dimensions of the inlined plotting window, and not the relative lengths of the three axes.

I'd be interested in any new problems introduced with this, eg. export, etc.

Download 3Dsize_hotedit.mw

If this works fine then it might be a candidate for inclusion in an initialization file, so that it's
automatically available.