This is still a work in progress, but might be of use to anybody interested in Maxwell's Equations :-)

Examining_Maxwells_Equations.mw

Since we are getting many questions on how to create Math apps to add to the Maple Cloud. I wanted to go over the different GUI aspects of how you go about creating a Math App in Maple. The following Document also includes some code examples that are used in the the Math App but doesn't go into them in detail. For more details on the type of coding you do in a Math App see the DocumentTools package help page.

Some of the graphical features of the Math app don't display on Maple Primes so I'd recommend downloading this worksheet from here: HowToMathApp.mw to follow along.

How to make a Math App (An example of using the Document Tools).   This Document will provide a beginners guide on one way to make a Math app in Maple. It will contain some coding examples as well as where to find different options in the user interface. Step 1 Insert a Table     •  When making a Math App in Maple I often start with a table. You can enter a table by going to Insert > Table...      •  I often make the table 1 x 2 to start with as this gives an area for input and an area for the output (such as plots).   Add a plot component to one of the cells of the table     •  From the Components  Palette you can add a Plot Component . Add it to the table by clicking and dragging it over.     Add another table inside the other cell     •  In the other cell of the table I'll add another table to organize my use of buttons, sliders, and other components. Add some components to the new table     •  From the Components Palette I'll add a slider, or dial, or something else for interaction.   •  You may also want a Math region for an area to enter functions and a button to tell Maple to do something with it.   Arrange the Components to look nice     •  You can change how the components are placed either by resizing the tables or changing the text orientation of the contents of the cells.   Write some code for the interaction of the buttons.     •  Using the DocumentTools  package there are lots of ways you can use the components. I often will start writing my code using a code edit region  as it provides better visualization for syntax. On MaplePrimes these display as collapsed so I will also include code blocks for the code.   Let's write something that takes the value of the slider and applies it to the dial     •  Note that the names of the components will change in each section as they are copies of the previous section.   with(DocumentTools): with(DocumentTools): sv:=GetProperty('Slider2',value); SetProperty('Dial2',value,sv); •  This code will only execute when run using the  button. Change the value of the slider below then run the code above to see what happens.   Move the code 'inside' the slider     •  Instead of putting the code inside the code edit region where it needs to be executed, we'll next add the code to the value changed code of the slider.   •  Right click the Slider then select "Edit Value Changed Code".     •  This will open the code editor for the Slider     •  Enter your code (ensuring you're using the correct name for the slider and dial).   •  Notice that you don't need to use the with(DocumentTools): command as "use DocumentTools in ... end use;" is already filled in for you.   •  Save the code in the Slider and hit the  button inside it once. •  Now move the slider.   •  On future uses of the App you won't need to hit  as the code will be run on startup. Add some more details to your App     •  Let's make this app do something a bit more interesting than change the contents of a dial when a slider moves.   •  The plan in the next few steps is to make this app allow a user to explore parameters changing in a sinusoidal expression.   •  I'm going to add a second Math Component, put the expression into both then uncheck the box in the context panel that says "Editable".   •  To make the Math containers fit nicely I'll check the Auto-fit container box and set the Minimum Width Pixels to 200.   Add code to change the value of phi in the second Math Container when the Slider changes     Note: Maple uses Radians for trigonometric functions so we should convert the value of phi to Radians. use DocumentTools in   use DocumentTools in phi_s:=GetProperty(Slider5,value); expr:= GetProperty(MathContainer6,expression); new_expr:=algsubs(phi=phi_s*Pi/180,expr); SetProperty(MathContainer7,expression,new_expr); end use: Make the Dial go from 0 to 360°     •  Click the Dial and look at the options in the context panel on the right.   •  Update the values in the Dial so that the highest position is 360 and the spacing makes sense for the app.   Have the Dial update the theta value of the expression     •  Add the following code to the Dial   use DocumentTools in use DocumentTools in theta_d:=GetProperty(Dial7,value); phi_s:=GetProperty(Slider7,value); #This is added so that phi also has the value updated expr:= GetProperty(MathContainer10,expression); new_expr0:=algsubs(theta=theta_d*Pi/180,expr); new_expr:=algsubs(phi=phi_s*Pi/180,new_expr0); #This is added so that phi also has the value updated SetProperty(MathContainer11,expression,new_expr); end use:   •  Update the value in the slider to include the value from the dial   use DocumentTools in   use DocumentTools in theta_d:=GetProperty(Dial7,value); #This is added so that theta also has the value updated phi_s:=GetProperty(Slider7,value); expr:= GetProperty(MathContainer10,expression); new_expr0:=algsubs(theta=theta_d*Pi/180,expr); #This is added so that theta also has the value updated new_expr:=algsubs(phi=phi_s*Pi/180,new_expr0); SetProperty(MathContainer11,expression,new_expr); end use:   Notice that the code in the Dial and Slider are the same     •  Since the code in the Dial and Slider are the same it makes sense to put the code into a procedure that can be called from multiple places.   Note: The changes in the code such as local and the single quotes are not needed but make the code easier to read and less likely to run into errors if edited in the future (for example if you create a variable called dial8 it won't interfere now that the names are in quotes).     UpdateMath:=proc()  UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial8','value'); #Get value of theta from Dial phi_s:=GetProperty('Slider8','value'); #Get value of phi from slider expr:= GetProperty('MathContainer12','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression SetProperty('MathContainer13','expression',new_expr); # Update expression end use: end proc:   •  Now change the code in the components to call the function using .   •  Since the code above is only defined there it will need to be run once (but only once) before moving the components. Instead of leaving it here you can add it to the Startup code by clicking  or going to Edit > Startup code.  This code will run every time you open the Math App ensuring that it works right away.   •  The startup code isn't defined in this document to allow progression of these steps.   Make the button initialize the app     •  Since the startup code isn't defined in this document we are going to move this function into the button.   UpdateMath:=proc()   UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial9','value'); #Get value of theta from Dial phi_s:=GetProperty('Slider9','value'); #Get value of phi from slider expr:= GetProperty('MathContainer14','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression SetProperty('MathContainer15','expression',new_expr); # Update expression end use: end proc: •  First click the button to rename it, you'll see the  option in the context panel on the right. Then add the code above to the button in the same way as the Slider an Dial (Right click and select Edit Click Code).   Now it is easy to add new components     •  Now if we want to add new components we just have to change the one procedure.  Let's add a Volume Gauge to change the value of A.   •  Click in the cell containing the Dial, the context panel will show the option to Insert a row below the Dial. •  Now drag a Volume Gauge into the new cell.   •  Click in the cell and choose the alignment (from the context panel) that looks best to you. In this case I chose center:     Update the procedure code for the Gauge     •  Add two lines for the volume gauge to get the value and sub it into the expression UpdateMath:=proc() UpdateMath:=proc() local theta_d, phi_s, expr, new_expr, new_expr0; use DocumentTools in theta_d:=GetProperty('Dial11','value'); #Get value of theta from the Dial phi_s:=GetProperty('Slider11','value'); #Get value of phi from the Slider A_g:=GetProperty('VolumeGauge1','value'); #Get value of A from the Guage expr:= GetProperty('MathContainer18','expression'); new_expr0:=algsubs('theta'=theta_d*Pi/180,expr); # Put value of theta in expression new_expr1:=algsubs('phi'=phi_s*Pi/180,new_expr0); # Put value of phi in expression new_expr:=algsubs('A'=A_g,new_expr1); # Put value of A in expression SetProperty('MathContainer19','expression',new_expr); # Update expression end use: end proc: •  Now add UpdateMath();   to the Gauge.   Plot the changing expression     •  Make a procedure to get the value in the second Math Container and plot it   PlotMath:=proc() PlotMath:=proc() local expr, p; use DocumentTools in expr:=GetProperty('MathContainer21','expression'); p:=plot(expr,'t'=-Pi/2..Pi/2,'view'=[-Pi/2..Pi/2,-100..100]): SetProperty('Plot14','value',p) end use: end proc: •  Put this procedure in the Initialize button and the call to it in the components.   Tidy up the app     •  Now that we have an interactive app let's tidy it up a bit.   •  The first thing I'd recommend in your own app is moving the code from the initialize button to startup code. In this document we choose to use the button instead to preserve earlier versions.   •  You can also remove the borders around the components by clicking in the table and selecting "Interior Borders" > "None" and "Exterior Borders" > "None" from the context panel. Now you have a Math App     •  You can upload your Math App to the Maple Cloud to share with others by going to "File" > "Save to Cloud".   •  I'd recommend also including a description of what your app does. You can do this nicely using another table and Text mode.

HowToMathApp.mw

When re-initializing a module (for example, while executing its ModuleApply), you'd likely want to re-initialize all of the remember tables and caches of its procedures. Unfortunately, forget(thismodule) (a direct self reference) doesn't work (I wonder why not?), and it doesn't even tell you that it didn't work. You could do forget(external name of module) (an indirect self reference), but I consider that not robust because you'd need to change it if you change the external name. Even less robust is forget~([procedure 1, procedure 2, submodule 3, ...]). Here's something that works and is robust:

forget~([seq(x, x= thismodule)])[]

Or, using Maple 2019 or later syntax,

forget~([for local x in thismodule do x od])[]

Both of these handle submodules and ignore non-procedures. Both handle both locals and exports.

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.

Download log_misinterpretation2.mw

One of the forums asked a question: what is the maximum area of a triangle inscribed in a given ellipse x^2/16 + y^2/3 - 1 = 0? It turned out to be 9, but there are infinitely many such triangles. There was a desire to show them in one of the possible ways. This is a complete (as far as possible) set of such triangles.
(This is not an example of Maple programming; it is just an implementation of a Maple-based algorithm and the work of the Optimization package).
MAX_S_TRIAN_ANINATION.mw

This app shows the modeling and simulation of DNA carried out entirely in Maple. The mathematical model is inserted through the combination of trigonometric functions. It shows the graphs of the curvature vs time for its interpretation. Made for engineering and health science students.

MV_AC_R3_UNI_2020.mw

Lenin Araujo Castillo

Ambassador of Maple

I have recently taken some questions about MaplePrimes reputation scores, and coincidentally, there was a discussion about it within MaplePrimes yesterday. I wanted to address these issues, and thought that doing so as a separate post made sense.

Reputation was added back in 2010 as a mechanism to track how fellow users value your contributions, and I believe it has largely worked. It's become a great way to acknowledge the time and effort our members put into the community, and I know that many of you greatly value the scores that you have earned. I also know that it is never fun to see it drop, even by just a few points.

To be clear, there are only two ways to lose reputation:

• If someone upvoted your answer/reply and then later rescinded the upvote
• If someone marked your answer as the "best" answer, and then later changed their vote to another answer

This means you can only lose reputation points if someone undoes an action that gave you points in the first place. This is going to happen occasionally. For example, the user may have voted your answer “best”, but as the discussion continued, someone else posted a different solution that the user felt was even better. So you can expect to see small fluctuations from day to day, but the overall trend will be upward. 

That said, members get understandably concerned when their reputation drops, and want to know why. We have always been able to track when reputation changed, but “why it changed” was obscured. Starting today, we have added enhanced logging for reputation shifts. This will allow us to better diagnose the causes when a member is concerned about a change to their reputation points. As well, in the very unlikely event that there is malicious behavior on MaplePrimes, this will give also us the data we need to take action to protect the community.  

With the new features added to the Student[LinearAlgebra] package I wanted to go over some of the basics on how someone can do Linear Algebra in Maple without require them to do any programming.  I was recently asked about this and thought that the information may be useful to others.
 

This post will be focussed towards new Maple users. I hope that this will be helpful to students using Maple for the first time and professors who want their students to use Maple without needing to spend time learning the language.
 

In addition to the following post you can find a detailed video on using Maple to do Linear Algebra without programming here. You can also find some of the tools that are new to Maple 2020 for Linear Algebra here.

The biggest tools you'll be using are the Matrix palette on the left of Maple, and the Context Panel on the right of Maple.

First you should load the Student[LinearAlgebra] package by entering:

with(Student[LinearAlgebra]);

Once you have a Matrix you can use the context panel on the right to apply a variety of operations to it:

The Student Linear Algebra Menu will give you many linear algebra commands.

You can also access Maple's Tutors from the Tools Menu

Tools > Tutors > Linear Algebra

?Student[LinearAlegbra]

Maple_for_Beginners.mw

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

Over the past weeks, we have spoken with many of our academic customers throughout the world, many of whom have decided to continue their academic years online. As you can imagine, this is a considerable challenge for instructors and students alike. Academia has quickly had to pivot to virtual classrooms, online testing and other collaborative technologies, while at the same time dealing with the stress and uncertainty that has resulted from this crisis.

We have been working with our customers to help them through this time in a variety of ways, but we know that there are still classes and students out there who are having trouble getting all the resources they need to complete their school year. So starting today, Maple Student Edition is being made free for every student, anywhere in the world, until the end of June. It is our hope that this action will remove a barrier for instructors to complete their Maple-led math instruction, and will help make things a bit more simple for everyone.

If you are a student, you can get your free copy of Maple here.

In addition, many of you have asked us about the best way to work on your engineering projects from home and/or teaching and learning remotely during this global crisis. We have put together resources for both that you can use as a starting point, and I invite you to contact us if you have any questions, or are dealing with challenges of your own. We are here to support you, and will be very flexible as we work together through these uncertain times.

I wish you all the best,

Laurent
President & CEO

Download Vectors_and_Spherical_coordinates_in_tensor_notation.mw

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

A way of cutting holes on an implicit plot. This is from the field of numerical parameterization of surfaces. On the example of the surface  x3 = 0.01*exp (x1) / (0.01 + x1^4 + x2^4 + x3^4)  consider the approach to producing holes. The surface is locally parameterized in some suitable way and the place for the hole and its size are selected. In the first example, the parametrization is performed on the basis of the section of the initial surface by perpendicular planes. In the second example, "round"  parametrization. It is made on the basis of the cylinder and the planes passing through its axis. Holes can be of any size and any shape. In the figures, the cut out surface sections are colored green and are located above their own holes at an equidistant to the original surface.
HOLE_1.mwHOLE_2.mw