This post is in response to a question regarding the speed of Maple 2023 on different computers. 

I'm asking users to suggest a few benchmark problems for Maple to calculate for testing.  Basic system information (Processor speed, RAM, video card etc..) perform the calculation, get the timing and then we can collect all the information into a chart where we can update it in the original post of this thread. 

All input is welcome, it doesn't have to be confined to Maple 2023.  We can expand to as many older versions as we wish. 

we have recieved lots of great sumissions, but we want your great submission and now you have more time.

The deadline for submissions to the Art Gallery and Showcase for the 2023 Maple Conference is rapidly approaching. We really want to see your art! It doesn't have to be incredibly impressive or sophisticated, we just want to see what our community can create! If you've been working on something or have a great idea, you still have a few days to get it together to submit.

Submission can be made by email to gallery@maplesoft.com but be sure to visit the visit our Call for Creative Works for details on the format of the submission.

The Proceedings of the Maple Conference 2022 are up at mapletransactions.org and I hope that you will find the articles interesting.  There is a brief memorial to Eugenio Roanes-Lozano, whom some of you will remember from past meetings. 

The cover image was the "People's Choice" from the Art Gallery, by Paul DeMarco.

This provides a nice excuse to remind you to register at the conference page for the Maple Conference 2023 and in particular to remind you to submit your entries for the Art Gallery.  See you there!  The conference will take place October 26 and 27, and features plenary talks by our own Laurent Bernardin and by Tom Crawford (Oxford, but more widely known as "The Naked Mathematician" for his incredibly popular YouTube videos on mathematical topics). See Tom Rocks Maths for more (or less :)

The deadline for submission to the Proceedings (which will again be published in Maple Transactions) will be Nov 27, one month after the conference ends.  We have put new processes in place to ensure a more timely publication schedule, and we anticipate that the Proceedings will be published in early Spring 2024.

What are planes? Are they aircraft that soar through the sky, or flat surfaces you'd come across in your geometry textbook? By definition yes, but they can be so much more. In the world of math, observing a system of equations with three variables allows us to plot them as planes in ℝ³. As we plot planes, these geometric entities can start intersecting, creating captivating visualizations. However, the intersection of planes is not just an abstract mathematical concept present only in the classroom. Throughout our daily lives, we come into contact with intersecting planes everywhere. Have you ever noticed the point where two walls and the floor in your room converge? That’s an intersection in its simplest form! And the line where the pages of a book are bound together? Another everyday intersection!
 

Room image: https://unsplash.com/photos/0H-aJ06IZw4, Book image: https://unsplash.com/photos/6H9H-tYPUQQ 

However, just seeing plane intersections is but a tiny piece of the puzzle. After all, how can we delve into the intriguing properties of these intersections without quantifying them? Enter the focus of Maple Learn's newest collection: Intersection of Planes. Not sure about how you can identify the different scenarios that three planes can form in ℝ³? Check out the eight documents that provide complete walk-throughs for solving each individual case that three planes can form! With cases ranging from three parallel and distinct planes to three planes forming a triangular prism to three planes intersecting in a line, you’ll gain a mastery of understanding the intersection of planes by the time you’re finished with the examples.

Once you’ve gained an understanding of how to identify and solve the cases that three planes can form, it’s time to test your knowledge! This quiz-like document takes you through the steps of solving for the intersection of three planes with guiding questions and comprehensive feedback. Once you successfully find the intersection or identify the case, you’ll be provided with an interactive 3D plot that allows you to see what the math you’ve been doing looks like. This opportunity to solve any of the 16 different possible systems of equations allows you to prove that you’re on another level!

With your newfound mastery of solving systems of equations, check out similar documents in the recently added linear algebra collection! Try calculating the volume of a parallelepiped or deriving the formula for the distance between a point and a plane. 

What are you waiting for? Gear up and join us on Maple Learn today! Whether you're diving deep into the world of linear algebra or merely dabbling, there’s a world of discovery waiting for you.

I just got the Maple kernel working in a Jupyter notebook : ).

No complaints here !

Access the Power of Maple in Jupyter

I was playing around with plotting volumes of revolution for calculus.  My opinion is that the defaults for Student[Calculus1][VolumeOfRevolution] could be improved by a couple simple changes.  My hope is that the people here can make my plots better to give Maplesoft a good idea of how to change the defaults.  

The standard code and output are

Download Volum_rev_2023_trial1.mw

Changing the surface style to patch and the surfce colors to different colors creates a plot that I find easier to interpret.

Download Volum_rev_2023_trial2.mw

What do you think about getting the defaults changed?  I hope someone can give better suggestions for the plot defaults.

Jill is walking on some trails after a long and stressful day at work. Suddenly, her stress seems to be lifted off her shoulders as her attention gets drawn to nature's abundant beauty. From the way the flowers blossom to the way the leaves grow on their stems, it is stunning.

When many think of mathematics, what comes to mind is often numbers, equations, and calculations. While these aspects are essential to math, they only scratch the surface of a profoundly creative discipline. Mathematics is much more than mere numerical manipulation. It is a rich and intricate realm that influences everything from art and science to philosophy and technology.

Just as Jill was stunned by the beauty of nature, you too can be amazed by the beauty of math! The golden ratio is one math concept that garners a reputation for being particularly beautiful, perhaps due to its presence in different parts of nature. You can explore it through some Maple Learn documents.

Check out the Fibonacci sequence and golden ratio document to better understand the golden ratio and its relationships. Perhaps, once you have a good grasp on the basics, you would like to check out the golden spiral document. Notice how the spiral that results resembles the outline of a nautilus shell and the arms of a spiral galaxy!

Nautilus shell image: https://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg -- Spiral galaxy image: https://www.cnet.com/pictures/natures-patterns-golden-spirals-and-branching-fractals/

Next, you may want to understand why the golden ratio is considered the most irrational number. You can do that by checking out the most irrational number document. Or you could explore this golden angle document to see how the irrationality of the number can be used to reproduce structures found in nature, such as the arrangement of seeds in a sunflower's centre!

Sunflower image: https://commons.wikimedia.org/wiki/File:Helianthus_whorl.jpg
 

That's all for this post! No worries, though. Maple Learn has hundreds of documents that can aid you in exploring the abundant beauty of math. Enjoy!

Perhaps you could consider a Coding theory Package.  I'm working on Coding theory at the moment.

It’s finally here. The mystical treasure that has long been rumoured to lie deep within the labyrinthine halls of Maple Learn is within your grasp at last. The ordeals ahead are treacherous, and most who have ventured in have never returned… but, armed with nothing but your wits and your curiosity, you know you’re prepared to conquer the trials that await you. Can you be the first to uncover the secrets of Maple Learn?

Surprise! We here at Maplesoft have decided to become game developers. Okay, maybe not really, but we do have one game that we’re excited to be sharing with you all. Introducing: The Treasure of Maple Learn. This series of documents mimics the style of a text-based adventure game, and takes you through a series of puzzles that challenge you to discover for yourself all of what Maple Learn has to offer. It was originally created by myself and a team of other co-op students during the 2021 Maplesoft Hackathon, and I’m very excited to be releasing this updated and polished version of the game. Finally, it’s time to set out on your quest to discover the legendary treasure that lurks within Maple Learn… if you dare.

If you don’t dare, don’t worry, we have other options. You can also check out our new video on Getting Started with Maple Learn, which takes you through everything you need to know to become a Maple Learn expert. And if that’s not enough learning Maple Learn for you, we also have an extensive collection of How-To documents. Want an in-depth look at how to use the plot window? How about an exploration of how to work with linear algebra? Or maybe you want to unleash your artistic side? We’ve got you covered.

So if you’re just getting started with Maple Learn and are looking for a tutorial, you’ve got options—we’ve got a quick video overview, tons of collections of in-depth documentation, and a quest through the treacherous depths of Maple Learn to uncover the secrets that lie within. Pick your poison! (But maybe watch out for literal poison in that labyrinth.)

Advanced Engineering Mathematics with Maple (AEM) by Dr. Lopez is such an art.

Mathematics and Control Theory talks easily in Maple...

Thanks Prof. Lopez. You are the MAN !!

Dr. Ali GÜZEL

The concept of “Maple Learn art” debuted on the MaplePrimes blog in December 2021.  Since then, we’ve come a long way with new Maple Learn features and ever-growing creative minds.  Creating art using mathematical expressions and shapes is a great way to hone both your mathematical skills and your creativity, and is the perfect break from a bout of studying or the like.

I started my own Maple Learn art journey over one year ago.  Let’s see how one’s art can improve over time using new and advanced features!

Art with Shapes, March 2022

This pi-themed pie is simple and cute, but could use some additional features:

Adding Shaded() around Maple Learn shape commands colors them in!

Fun fact: I hand-picked all of the coordinates for that pi symbol.  It was an arduous but rewarding process.  Nowadays, I recommend a new method.  When you create a table in Maple Learn with two number columns, the values are plotted as points.  These points can be clicked and dragged across the plot window, and the table updates automatically to display the new coordinates.  How can you use this to make art?

1. Create a table as described above.
2. Move the points with your mouse to create an outline of the desired shape.
3. Use the coordinates from your table in your geometry command.

Let’s apply these techniques in a newer piece: a full recreation of the spaghetti emoji!

Art with Shapes, August 2023

Would you look at that?!  Fully-shaded colors, a background, and lines of spaghetti noodles that weren’t painstakingly guesstimated combine to create a wonderfully improved piece of art.

Art with Animation, March 2022

Visit the document to see its animation.  Animation is an invaluable feature in Maple Learn, frequently utilized to observe how changing variables affect functions or model a concept.  We’ve harnessed its power for animated artwork!  This animation is cute, using parametric functions and more to change the image as the animation variable changes.  Like the previous piece, it’s missing a background, and the leaves overlap the stem awkwardly in some places.

Art with Animation, August 2023

This piece has a simple background made with a large black square, but it enhances the overall effect.

The animation here comes from piecewise functions, which display different values based on a given criterion.  In this case, the criterion is the current value of the animation variable.

There are 32 individual polygons in this image (including 8 really tiny ones along the edges!) and 8 rainbow colors.  Each color is associated with a different piecewise function, and displays four random squares in that color in each frame of the animation.

This image isn’t that much more advanced than the animated flower, but I think the execution has vastly improved.

Whether you’ve been following these blog posts since December 2021 or are new to Maple Learn, we hope you give Maple Learn art a try.

And don’t forget that Maple is also a goldmine of artistic potential.  Maple’s bountiful collection of packages such as Fractals, ColorTools, plottools and more are great places to start for math that is as aesthetically pleasing as it is informative.

This week, our staff participated in a series of art challenges using either Maple Learn or Maple itself, each featuring a suggested theme and suggested mathematical content.  Check out the challenges and some of our employees’ entries below, and try out a challenge for yourself!

Tuesday’s Art Theme: Pasta

Mathematical Content: Shapes

Example: Lazar Paroski’s spiraling take on spaghetti

Wednesday’s Art Theme: Nature

Mathematical Content: Fractals

Example: John May’s Penrose tiling landscape (in Maple!)

Thursday’s Art Theme: Disco

Mathematical Content: Animation

Example: Paulina Chin’s disco ball (in Maple!)

Friday’s Art Theme: Space

Mathematical Content: Color

Example: that’s today!  Who knows what our staff will create…?

We hope these prompts have inspired you! If you create some art you’re really proud of, consider submitting it to be featured in the 2023 Maple Conference’s Creative Works Showcase.

Space. The final frontier. A frontier we wouldn’t stand a chance of exploring if it weren’t for the work of one Albert Einstein and his theories of special relativity. After all, how are we supposed to determine at what speed an alien spaceship is traveling towards Earth if we can’t understand how Newtonian physics break down at high velocities? That is precisely the question that this Maple MathApp asks. Using the interactive tool, you can see how the relative velocities change depending on your reference point. Just what you need for the next time you see a UFO rocketing through the sky!

But what if you don’t have the MathApp on hand when the aliens visit? (So rare to travel anywhere without a copy of Maple on you, I know, but it could happen.) You’ll have to just learn more about special relativity so that you can make those calculations on the fly. And luckily, we have just what you need to do that: our new Maple Learn collection on modern physics, created by Lazar Paroski. Still not quite sure how to wrap your head around the whole thing? Check out this document on the postulates of special relativity, which explains and demonstrates some of the fundamentals of special relativity with lively animations.

Once you’ve gotten familiar with the basics, it’s time to get funky. This document on time dilation shows how two observers looking at the same event from different frames of reference can measure different times for that event. And of course once you start messing with time, everything gets weird. For an example, check out this document on length contraction, which explains how observers in different frames of reference can measure different lengths for the same moving object. Pretty wild stuff.

So now, armed with this collection of documents, we’ll all be ready for the next time the aliens come down to Earth—ready to calculate the relative speed of their UFOs from the perspectives of various observers. That’ll show ‘em!

Registration for Maple Conference 2023 is now open! This year’s conference will again be a free virtual event. Please visit our site to see more information about the event and to register.

Our call for presentations has now concluded, but it is not too late to submit to our Maple Conference Art Gallery and Creative Works Showcase.

The Agenda section, where you’ll find information about the conference format and an overview schedule, has been added. This will be updated as the details are finalized.  

The pendulum and the cantilever share simple-looking ordinary differential equations (ODEs), but they are challenging to solve:

This post derives solutions from Lawden and Bisshopp by Maple commands, which (to the best of my knowledge) have not been published providing not only results but also the accompanying computer algebra techniques. A tabulated format has been chosen to better highlight similarities and differences.

Both solutions have in common that in a first step, the unknown function is integrated and then in a second step the inverse of the unknown function (i.e., the independent variable) is integrated. Only in combination with a well-chosen set of initial/boundary conditions solutions are possible. This makes these two cases difficult to handle by generic integration methods.

Originally, I was not looking for this insight. I was more interested in an exact solution for nonlinear deformations to benchmark numerical simulation results.  Relatively quickly, I was able to achieve this with the help of this forum, but after that I was left with some nagging questions:

Why does Maple not provide a solution for the pendulum although one exists?

Why isn’t there an explicit solution for the cantilever when there is one for the pendulum?

Why is it so difficult to proof that elliptic expressions are equal?

Repeatedly, whenever there was time, I came back to these questions and got more and more a better understanding of the two problems and the overall context. It also required me to learn more of Maple, and I had to revisit fundamentals of functions, differential equations, and integration, which was entirely possible within Maples help system. Today, I am satisfied to the point that I think it is too much to expect Maple to provide a high-level general integration method for such problems.

I am also satisfied that I was able to combine all my findings scattered across many documents and Mapleprime questions into a single executable textbook-style document with hidden Maple code that:

Exclusively uses and manipulates equation expressions (no assignment operators := were required),

Avoids differentials that are often used in textbooks but (for good reasons) are not supported by Maple,

Exclusively applies high-level commands (i.e. no extraction of subexpression, manipulation
           and subsequent re-assembly of expressions was needed).

The solutions for the pendulum and the cantilever are substantially different although the ODEs and essential derivation steps are similar. I think that an explicit solution for the cantilever, as it exists for the pendulum, is impossible (using elliptic integrals and functions). I leave it open to comments: whether this is correct and whether it is attributable to the set of initial and boundary conditions, the different symmetry of the sine and cosine functions in the ODEs, or both. I hope that the tabular presentation will provide an easy overview, allowing to form an own opinion.

If you are patient enough to work through the table, you will find a link between the cantilever and the pendulum that you are probably not expecting. 

Finally, I have to give credit to Bisshopp, who was probably the first to provide a solution for the cantilever. The clarity and compactness on only 3 pages and the way how the inverse of functions was determined before the age of computers makes this paper worth studying. Also, Lawden has to be mentioned, who did the same on 3 pages for the pendulum in a marvelous book on elliptic functions and applications. It happens that he is overlooked in more recent publications and it’s unclear to me if he was the first who published an explicit solution. His book might be one of the last of its kind in this age of computers, and for that reason alone, it is worth enjoying as he enjoyed writing it.

Download Cantilever_and_pendulum_side_by_side_-_input_hidden.mw

Disability Pride Month happens every July to celebrate people with disabilities, combat the stigma surrounding disability, and to fight to create a world that is accessible to everyone. Celebrating disability pride isn’t necessarily about being happy about the additional difficulties caused by being disabled in an ableist society: as disabled blogger Ardra Shephard puts it, “Being proud to be disabled isn’t about liking my disability… [It] is a rejection of the notion that I should feel ashamed of my body or my disability. It’s a rejection of the idea that I am less able to contribute and participate in the world, that I take more than I give, that I have less inherent value and potential than the able-bodied Becky next to me.” The celebration started in the US to commemorate the passing of the Americans with Disabilities Act, which prohibits discrimination based on disability, and since then it has spread around the world.

So what does any of this have to do with us here in the math community? Well, while it’s easy to think of mathematics as an objective field of study that contains no barriers, the institutions and tools used to teach math are not always so friendly. For an obvious example, if there's a few steps leading up to your math classroom and you use a wheelchair, that's going to be a challenge. And that's just scratching the surface—there are countless ways to be disabled, many of which are invisible, and many of which make a typical classroom environment very challenging to learn in for a variety of different reasons. As well, it can be difficult for prospective mathematicians to ask for accommodations, because of both the stigma against disability and the systemic barriers to receiving the proper accommodations. Just ask Daniel Reinholz, a disabled math professor at San Diego State University, whose health forced them to drop out of several engineering courses during their undergraduate degree: “Throughout it all, I never had a notion that I could receive accommodation or support, or that I deserved it. (Even though I’ve never really fit into the “right” category of disabled to be accommodated, so who knows what difference it really would have made.)” While Daniel was lucky enough to find a path to mathematics that worked for them, not all disabled people currently have that path available to them. As math professor Allison Miller puts it in her AMS blog post about disability in math, “Success in mathematics should not depend on whether someone’s needs happen to mesh sufficiently well with institutional structures and spaces that have been designed to serve only certain kinds of minds and bodies.”

While we can’t make systemic changes on our own, we here at Maplesoft can still do our part to make tools for math that are something everyone can use and enjoy. As such, we’re excited to share that Maple Learn is now compatible with the screen reader NVDA. By using this screen reader, and with our extensive keyboard shortcuts that negate the need for a mouse, individuals with low or no vision can now use Maple Learn to help them explore mathematics. All you need to do is select “Enable Accessibility” from the hamburger menu, and you’ll be ready to go! Maple Learn also includes the colour palette CVD, which is designed to be accessible to colourblind users. To learn how to access the colour palettes, check out this How-To document.

There is still more work for us to be done to ensure that we’re doing our part to make math accessible to everyone. Not only are there still ways in which we’re working to improve the accessibility of our products, but we all as a math community need to strive towards recognizing the barriers we may have previously overlooked and finding ways to provide accommodation for all mathematicians. One organization, called Sines of Disability, is already working towards that very goal. They are a community of disabled mathematicians dedicated to dismantling the systemic ableism present in mathematics. For this Disability Pride Month, consider taking the time to check out these resources and learn more about this issue.