The first day of Maple Conference 2022 is coming up on November 2 and it's not too late to register! Please go to our conference home page and click on the "Register Now" button. This is a free virtual event open to all.

The schedule is available on the conference agenda page.

Come join us to see recent developments in research, education and applications, find out about new and upcoming features in our products, talk to Maplesoft staff and other members of the Maple community and view (and vote on) Maple and Maple Learn artwork.

We hope to see you at the conference!

It seems to me that Draghilev's method can be applied quite successfully to the solution of Diophantine equations. Here is a simple example where we find two solutions at the intersection line of two ellipsoids:
  x1^2-x1*x2+x2^2+x2*x3+x3^2-961=0;
  (x1-3)^2+10*x2^2+x3^2-900=0;
Solutions: (11, -4, -26) and (10, 1, 29).
 

Based on the text of the program, it is possible to solve various examples with Diophantine equations.
3d_1.mw

Explanations.
f3 is an auxiliary equation for finding the starting point, NPar is a procedure that implements the Draghilev method, the red color of the text is the place where the integer values of the points on the integral curve are filtered.

 Can be compared with the solution of the isolve function
 

 restart:
  f1 := x1^2-x1*x2+x2^2+x2*x3+x3^2-961;
  f2 := (x1-3)^2+10*x2^2+x3^2-900;
  isolve({f1, f2})

Any chance to have "Evaluate->Remove Output From Worksheet" become active and usable when one is still running something in the worksheet?  May be in 2023 version?

This is something that has been missing in Maple for ages.

Maple definitely slows down when the worksheet becomes full of output (from print messages) when a command has been running for long time. Now there is no way to remove the output in the worksheet until the command completes which can take hours. May be this slow down because the scrolling/writing to the worksheet slows down, and this affects how long it takes to complete as the engine is waiting for the frontend to finish writing to the worksheet?. I do not know. I just know Maple slows down when this happens.

I do not understand why Maple can't implement this. Is there a tehnical reson which will make removing current output in the worksheet not possible while a command is running?

We have just released the 2022.2 updates for Maple and MapleSim. These updates are freely available to all customers who have the 2022 version of these products.

Maple 2022.2 includes improvements to worksheet performance, the math engine, and more. As always, we recommend that all Maple 2022 users install this update. It is available through Tools>Check for Updates in Maple, and is also available from our website on the  Maple 2022.2 download page, where you can also find more details.

The MapleSim 2022.2 family of products offers an enhanced user experience through an expansion of the modeling libraries, a range of new productivity features, and several new options requested by users. See the MapleSim 2022.2 update page for details on new features, and for instruction on how to obtain your update.

Physics is a very diverse field with a vast array of different branches to focus on. One of the most interesting areas of physics is optics - the study of light.

It's common to think of light as some super-fast form of matter that just bounces around at 300,000 km/s and never slows down. However, light can actually slow down when it moves through different substances. Imagine dropping a baseball from the air into a deep pool of water. It would slow down, right? Well, what happens for light isn't too different.

We call the air or the water in the previous example 'mediums' (or media). Light moves through each of these mediums differently. For example, light moves close to the speed of light in vacuum, 299 792 458 m/s, in air, but it moves considerably slower in water, closer to 225 000 000 m/s. Take a look at Indices of Refraction for more details on how we can quantify this change in speed and Dispersion for some information on the role that the wavelength of light plays.

So light slows down when it enters a medium with a higher refractive index. It also speeds up when it moves from a higher refractive index to a lower one. But did you know that it also bends? Unlike in the example of the baseball falling into the pool, light that changes speeds moving between mediums will also change direction.

Snell's Law is our way of determining how much light bends between mediums. Try playing around with the values of the indices of refraction and the incident angle and see what effect that has on the refracted ray. Is there a combination of parameters for which the refracted ray disappears? The answer can be found in Critical Angle and Total Internal Reflection.

Want to learn about how principles from optics can be applied in the real world? See Fiber Optics - Main Page for information on one of optics' most impactful applications.

Welcome back to another Maple Learn blog post! We know it is midterm season, and we’re here to help. Maple Learn can be used to study in many different ways, and I’m sure you’ve already tried some of them. One way is making your notes in Learn, or making your own examples, but have you taken a look at our document gallery? We have a wide range of subjects and types of documents, so let’s take a look at some documents!

I’m going to start by talking about the documents in the gallery which are content learning focused, then move into practice problems and a special document for studying.

First, let’s look at some calculus content learning documents! The calculus collection is our largest, reaching over 250 documents and still counting. The two documents I’ve picked from this category are our documents on the Fundamental Theorem of Calculus and a Visualization of Partial Derivatives. See a screenshot of the visualisations for each document below!

Are there other subjects you’d like to look at? Well, take a look at our list below!

Algebra: Double Vertical Asymptote Slider Graph

Graph Theory: Dijkstra’s Algorithm for Shortest Paths

Economics: Increase in Demand in a Market

Chemistry: Combined Gas Law Examples

Biology: Dihybrid Cross Punnett Squares

Physics: Displacement, Velocity, and Acceleration

We have many other subjects for documents, of course, but they wouldn’t fit in this post! Take a look at our entire document gallery for the others.

Another class of documents we have are the practice problems. Perfect for studying, we have practice problems ranging from practicing the four color theorem, to practicing mean, median, and mode, to even practicing dihybrid cross genotypes!

Now for, in my opinion, our most useful document for the midterm season: A study time calculator!

This document allows you to put in the amount you want to study each class over the day or week, and breaks down visually what that would look like.  

This allows you to make sure you’re taking enough time for breaks and sleep, and not overloading yourself. Feel free to customise the document to make it work better for you and your study style!

We hope you enjoyed this post, and that we could help you study! Let us know below if there’s anything else you’d want to see to support you during midterms and exams.

The search query in the new Maple Application center is broken.  There is no advanced search options and a search for mapleflow or maple flow brings up 0 results.  There should at least be one found, for example the search should have at least brought up The Liquid Volume in a Partially-Filled Horizontal Tank".

Maple, please fix.

Maple allows to extract, manipulate, and optimize equations from a MapleSim model. Code can be generated from the equations in various programming languages. To verify the code, C code can be imported back into the original MapleSim model and compared to the model.

This verification step is not an everyday task, but it is advisable before the code is used elsewhere (e.g., in a controller). This post summarizes helpfull links and provides an additional example with equations that are too large to be efficiently verified by code review.

Comparison to a physical model is demonstrated here on an older version of MapleSim (~2015). In newer versions the import has changed (basics are described in Tutorial 6.6: Using the External C Code/DLL Custom Component App). An external C compiler must be set-up to make the import work.

The attached MapleSim model verifies against an optimized custom component. Instead of manually entering and modifying the code as described in the Tutorial 6.6, the model uses a Maple worksheet that programmatically generates C code from Maple equations and modifies the C code (sets C definitions and parameters) to be usable for MapleSim’s External C/Library Block App.

The Maple worksheet to generate and modify C code has been improved in many details with support from MaplePrime users for which I would like to express my thanks.

C_code_generation_of_optimised_code_for_MapleSim.mw

C_code_generation_of_optimised_code.msim

Have you heard the news yet? Maple Learn has had a major update! You may be wondering what this means, and what all the shiny new features are. Let’s go through them together.

First, as with many updates, we’ve improved performance with Maple Learn. Longer documents will load and perform faster, requiring less computing power for operations, and as a result your browser will be more responsive. Performance on Chromebooks is also improved.

Operations that previously would have needed to be refreshed now automatically calculate. Up until now, if you performed a menu operation on an expression and then changed the value of the expression, the result would turn orange to warn you that the result was no longer valid. You would then have to refresh manually. Now, this is no longer the case, the orange refresh button has been removed from Maple Learn, and results are never out of date.

The plot window, inline plots, and the context panel are all resizable now. This means that, for example, if you’re presenting using Maple Learn, you can enlarge the plot window to be the focus of the presentation, and shrink the context panel out of the way. Take a look at the difference, with our animation of it in action!

Sliders are also more flexible now! Bounds for sliders can be expressed in terms of variables or symbols like π. As well, you can now animate sliders, animating the graph. This allows for more interactivity in documents. See the old view on the left, and the new view on the right! Make sure to take a look at an example of the animated slider below the views as well. 

You can also now snap groups to a grid, allow them to automatically adjust their position as other groups adjust. This ensures better alignment of groups. It also allows you to easily rearrange elements of your documents.

Next, Maple Learn could handle 3D plots before, but now Maple Learn supports 3D parametric plots!

Finally, Maple Learn now has printing! This means you can print out your Maple Learn documents, with two options: to print just the canvas, or to print just the plot. This was requested by many users.

Multiple selection is also possible, allowing you to select multiple cells in a group by holding down the Ctrl/Command key while clicking and dragging.

That’s all for the updates in this version, but keep an eye out for our other updates! For more details, please take a look at our What’s New In Maple Learn page. We hope you enjoy our new features, and let us know if there are any more features you’d like to see in Maple Learn below.

 This interactive electronic textbook, in the form of Maple worksheets, is released in its sixth edition, 2021 August.  This book has two major divisions, mathematics for chemistry -- the mathematics that any instructor of a course in chemistry would wish a student thereof to understand and to be able to implement, and mathematics of chemistry, in the sense of the classic volumes by Margenau and Murphy -- mathematical treatments of particular topics in chemistry from an introductory post-secondary level to a post-graduate level. The content, which includes not only chapters in previous editions that have been revised but also additional chapters on quantum mechanics, molecular spectrometry and advanced chemical kinetics, has been collected during two decades, with many contributions from other authors, acknowledged in particular locations.  Each chapter includes not only explanatory treatments but also illuminating examples and exercises with chemical applications where practicable.

Mathematics for chemistry      0  introduction to Maple commands

                                                 1  numbers, symbols and elementary functions

                                                 2  plotting, geometry, trigonometry and functions

                                                 3  differential calculus

                                                 4  integral calculus

                                                 5  multivariate calculus

                                                 6  linear algebra

                                                 7  differential and integral equations

                                                 8  probability, statistics, regression and optimisation

Mathematics of chemistry       9  chemical equilibrium

                                                10  group theory

                                                11  graph theory

                                                12  quantum mechanics in three parts -- models, atoms and molecules

                                                13  molecular spectrometry

                                                14  Fourier transforms

                                                15  advanced chemical kinetics

                                                16  dielectric and magnetic properties

The content freely available at https://www.maplesoft.com/applications/view.aspx?SID=154267 includes also a published report on teaching mathematics with symbolic software and an interactive periodic chart that yields information about particular chemical elements and their isotopic variants.

            The nature of this electronic interactive textbook makes it applicable with an instructor in a traditional setting, or computer laboratory, for which the material of mathematics for chemistry could be reasonably covered in three or four semesters, but even for self study.  The chapters on quantum mechanics and Fourier transforms are available as separate textbooks in the same format.

Mathematical visualizations are beautiful representations of technical phenomena.  From the visual “perfection” of the golden spiral to the pattern generation of fractals, so many works of art can be boiled down to formulas and equations.  Such is the case with N.G. de Bruijn’s medallion and frieze patterns.  Given two starting values, two lines of mathematical formulae produce a recursive sequence of complex numbers.  We can associate these numbers with the four cardinal directions, following the steps on a plot to produce beautiful patterns.  The patterns are of two different types, the closed medallion or repeating frieze, depending on the starting values.

When you need a complex math visualization, Maple is a perfect place to go.  A demonstration of medallion and frieze patterns is available in the Maple Application Center, in which you can vary the starting values and watch the outcome change, along with more detailed background information.  However, there’s an even simpler way to explore this program with the help of Maple Learn.  Maple Learn has the same computational power as Maple, streamlined into an easy-to-use notebook style.  

Maple Learn includes many core features, and anything missing can be ported in through Maple.  This is done using Maple’s DocumentTools:-Canvas package.  The package contains the necessary procedures to convert Maple code into a “canvas”, which can be opened as a Maple Learn sheet.  This makes the whole document look cleaner and allows for easy sharing with friends.

The medallion and frieze document, along with the additional contextual information, is now also available in Maple Learn’s Document Gallery, home to over one thousand example documents covering calculus, geometry, physics, and more.

Who else likes art?  I love art; doodling in my notebook between projects and classes is a great way to pass the time and keep my creativity sharp.  However, when I’m working in Maple Learn, I don’t need to get out my book; I can use the plot window as my canvas and get my drawing fix right then and there.

We’ve done a few blog posts on Maple Learn art, and we’re back at it again in even bigger and better ways.  Maple Learn’s recent update added some useful features that can be incorporated into art, including the ability to resize the plot window and animate using automatically-changing variables.

Even with all the previous posts, you may be thinking, “What’s all this?  How am I supposed to make art in a piece of math software?”  Well, there is a lot of beauty to mathematics.  Consider beautiful patterns and fractals, equations that produce surprisingly aesthetically interesting outputs, and the general use of mathematics to create technical art.  In Maple Learn, you don’t have to get that advanced (heck, unless you want to).  Art can be created by combining basic shapes and functions into any image you can imagine.  All of the images below were created in Maple Learn!

There are many ways you can harness artistic power in Maple Learn.  Here are the resources I recommend to get you started.

1. I’ve recently made some YouTube videos (see the first one below) that provide a tutorial for Maple Learn art.  This series is less than 30 minutes in total, and covers - in three respective parts - the basics, some more advanced Learn techniques, and a full walkthrough of how I make my own art.
2. Check out the Maple Learn document gallery art collection for some inspiration, the how-to documents for additional help, and the rest of the gallery to see even more Maple Learn in action!

Once you’re having fun and making art, consider submitting your art to the Maple Conference 2022 Maple Learn Art Showcase.  The due date for submission is October 14, 2022.  The Conference itself is on November 2-3, and is a free virtual event filled with presentations, discussions, and more.  Check it out!

I have polished up findings with custom components to share it here:

Optimized code generated with Maple’s codegen package cannot be used in the same way as it was possible with older versions of MapleSim’s Custom Component Template.

Intermediate variables `tx` (where x is an integer) of the optimized code are interpreted as physical parameters in the current template version and not as variables. This makes sense and is more consistent with MapleSim’s definition of variables and parameters, but leads to errors in MapleSim.

The attached model shows how optimized code can be generated for the current template and compares an older, still working (!) template with the new one.

The attached worksheet contains commands to programmatically generate optimized code for the current Custom Component Template.

CustomComponentTemplates_comparision.msim

Optimized_code_for_custom_component_template.mw

Have you ever wondered about the people behind the scenes at Maplesoft? What about the students who help design the products?

This week, we thought we’d introduce ourselves. We are some of the co-op students at Maplesoft, who in between studying believe that Math Matters.

I’ll go first. My name is Pleiades, I’m 21 and my pronouns are they/them. I am a product management intern at Maplesoft, working with Maple Learn and Maple Calculator. I'm not a math student, but my favorite thing about math is how expressive its language is. Mathematical equations and symbols can be used to express incredibly complex ideas, and even if you don't understand the sense, you can still read the "words". My favorite thing about working for Maplesoft is the flexibility. I have many different types of tasks, and I’m able to learn so many different things.

Keep reading, and find out more about my fellow students below!

Quality Assurance:

Hello, my name is Matilda (she/her)! I am 19 years old, studying physics and astronomy at the University of Waterloo. I am part of the QA team here at Maplesoft, working as a quality assurance analyst co-op. I find math fascinating as it is a broad field that can be challenging, but also invokes a lot of creativity. As I am a new addition at Maplesoft, I am excited to work with the various Maple products.  I am looking forward to meeting new students and individuals, and to help grow not only myself but the company further. 

My name is Kat, I’m 20 and my pronouns are she/her. In my spare time, I enjoy reading and rock climbing. I am a QA analyst at Maplesoft, mostly working on Maple 2023. I am a student at UW studying mathematical physics and I would like to also minor in astronomy/astrophysics. My favorite thing about math is the objectivity of it, how there is a set structure and logical solution to any problem. I especially like calculus and trigonometry. I’m excited to be at Maplesoft because I will be learning everything about Maple from the inside perspective, which is used in many 300 and 400-level applied math courses that I will be taking at UW. I also really like the office environment and my coworkers.

Development:

Hey, my name is Paul C, I am 22 years old, and I am working as a Web and Mobile developer with Steve Metzger for the next 4 months. At the University of Waterloo, I study Mathematical Physics, though, I love the Computational Mathematics courses I’ve taken at UWaterloo. As for the world of Mathematics, I have always been fond of how everything can be thoroughly proven through basic arguments and logic. I am very excited to be working at Maplesoft, as I have for a long time been intrigued as to how Maple, Symbolab, and WolframAlpha function. So, this position is finally giving me the opportunity to truly explore how such software is developed.

Sales:

My name is Robin, I’m 21 years old and my pronouns are he/him. I am currently working as a Business Operations Analyst at Maplesoft, working with the sales department. I am a candidate of Bachelors of Business Administration at Wilfrid Laurier University with a minor in Economics and a specialization in Finance. My favorite thing about math is how it is present everywhere. Numbers help us understand world and Math helps us understand the number. My favorite part about working at Maplesoft is the extremely positive culture that we work in. Rather than competing with other people in the department, sales team has a very healthy approach towards work and are always there to help out each other.

Content Creation:

My name is Nikolas (he/him), I’m 20 years old and I’m an undergraduate physics student at the University of Waterloo. I’m part of the math content team at Maplesoft, focussing on creating new content for Maple Learn. The thing I like most about math is that while it may be a very objective discipline, it still involves an incredible amount of creativity. My favourite part of working at Maplesoft is the chance to share what I’ve learned about physics and math through Maple Learn content.

Good morning, afternoon, or evening!  I'm Miles (age 23, he/him), and I'm a UW mathematics student majoring in combinatorics and optimization and minoring in biology.  This term at Maplesoft, I work in content development for Maple Learn, which involves creating examples for the Maple Learn Document Gallery, working on special requests for users, and more.  My favorite thing about math is the fact that it is the analytical backbone of so many other areas of research.  You may think of biological research as performing experiments or medical trials, but behind the scenes, data entry and analysis are key to finding valuable conclusions and discoveries.  Biology is my particular favorite, of course, but there are countless fields of study with these mathematical aspects.

I'm looking forward to expanding my skillset and repertoire of tasks at Maplesoft.  This is my second term working here; last term I got my bearings as a content developer and am looking forward to so much more.  More advanced documents and workshops/presentations are on the horizon! :D

Download New_arbitrary_constants_and_functions.mw

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