Maple’s Code Generation makes it possible to translate your Maple code to various other programming languages including C, Python, and several others. In Maple 2015, we added a new Code Generation target to one of my other personal favourite languages, R. R is a programming language designed for statistical computing and graphics, so no code translation from Maple to R would be complete without attempting to translate as many commands as possible from Maple’s Statistics package. 

Translating code from one language to another is tricky business. Maple 2015 represented the first time that any Code Generation target language added the ability to translate commands from the Statistics package. With R, we found that many common statistics commands had almost a one-to-one mapping, such as Statistics:-Mean = mean, but several others were much more complicated, including several commands for dealing with probability functions that did not have direct mappings due to differences in how the systems handle symbolic probability functions.

A list of statistics commands that can be translated from Maple to R can be found here.

In addition to assisting me recall the correct syntax in R, having worked with CodeGeneration[R] for several months now, I find that one of my most common uses for Maple’s code generation to R is simply to pass data between the systems. A simple example:

 CodeGeneration:-R( LinearAlgebra:-RandomMatrix( 5, 2 ) );

translates to the following in R:

 cg <- matrix(c(-4,27,8,69,99,29,44,92,-31,67),nrow=5,ncol=2)

To see a couple more short examples, here’s a short video that I recorded on Code Generation to R:

A little known fact about Code Generation is that the translation files can be viewed in from the “samples” directory in your Maple install directory. Similar to many of Maple’s packages, you can view all of the source code that Code Generation uses for its translations. For example, you can view the translations for the commands that I mentioned above from the “FunctionTable.mm” file inside of your “%MapleInstallDir%/ samples/CodeGeneration/R” directory.

Should you have any feedback on this translation, or any other, please feel free to contact us. We’re also on the hunt for our next code generation targets, so let us know what other languages you would like to see added as Code Generation targets.

A wealth of knowledge is on display in MaplePrimes as our contributors share their expertise and step up to answer others’ queries. This post picks out one such response and further elucidates the answers to the posted question. I hope these explanations appeal to those of our readers who might not be familiar with the techniques embedded in the original responses.

Before I begin, a quick note that the content below was primarily created by one of our summer interns, Pia, with guidance and advice from me.

MaplePrimes member Thomas Dean wanted 1/2*x^(1/2) + 1/13*x^(1/3) + 1/26*x^(45/37)  to become  0.5*x^0.500000 + 0.07692307692*x^0.333333 + 0.03846153846*x^1.216216216  using the evalf command.

Here you can see the piece of code that Thomas Dean wrote in Maple:

eq:=1/2*x^(1/2) + 1/13*x^(1/3) + 1/26*x^(45/37);
evalf(eq);

Carl Love replied simply and effectively with a piece of code, using the evalindets command instead:

evalindets(eq, fraction, evalf);

As always, Love provided an accurate response, and it is absolutely correct. But for those just learning Maple, I wanted to provide some additional explanation.

The evalindets command, evalindets( expr, atype, transformer, rest ), is a particular combination of calls to eval and indets that allows you to efficiently transform all subexpressions of a given type by some algorithm. It encapsulates a common "pattern" used in expression manipulation and transformation.

Each subexpression of type atype is transformed by the supplied transformer procedure. Then, each subexpression is replaced in the original expression, using eval, with the corresponding transformed expression.

Note: the parameter restis an optional expression sequence of extra arguments to be passed to transformer. In this example it was not used.

I hope that you find this useful. If there is a particular question on MaplePrimes that you would like further explained, please let me know. 

Here are some tips and tricks - ranging from keyboard shortcuts to the newest features - that will help you get the most out of MapleSim 2015.

1. Quickly run your simulation by pressing F5. Similarly, toggle between the Main Window and Visualization Window by press F6.
   
   
2. Maintaining an organized and clean model layout is made easier by using the Reroute Connections tool. Select the connection lines or components and press CTRL+D (or using the Edit menu, Reroute Connections) to have MapleSim automatically reroute the connections.
   
   
3. While creating your MapleSim model, components and connections can be enabled or disabled by selecting the desired item(s) and using the disable/enable button (  ) or the keyboard shortcut CTRL+E.
   
   
4. Use the Model Tree palette in MapleSim to help manage, navigate, and search a model quickly. Items within the model tree include: components, probes, parameters, and attachments. Simply select the desired view using the drop-down menu. The Model Tree palette is found under the Project tab.
   
   
5. Automatically remove any unreferenced subsystems or custom components using the Prune Model tool. Especially useful for large models or models with multiple modifications, this tool will automatically identify and removes unused shared subsystems or custom components that appear within the Definitions tab, Components palette. The Prune Model function can be performed by clicking the Edit menu, and selecting Prune Model.
   
   
6. Set the MapleSim’s Visualization Window to always on top by toggling the anchor button (  ) in the upper left corner of the Visualization Window.
   
   
7. Automatically scale the model diagram to fit in the viewable area by pressing CTRL+T to gain a complete look at the model. Then return to a default zoom by pressing CTRL+0 (zero). This is also accessible using the View menu.
   
   
8. To group components into a subsystem, select the desired components, right-click and select Create Subsystem or press CTRL+G.
   
   
9. For quick access to get help on a particular component, right-click on it and select help. Similarly, selecting a component within the workspace and pressing F2 will bring up the help page for that component.
   
   
10. View the Modelica code behind the visible system/subsystem/component, click Code View (  ) in the Navigation Tool bar. Then, to switch back to Diagram Mode click the icon (  ) in the Navigation Tool bar.
    
    
11. Automatically compare two models by using the compare tool, found under the Tools menu Compare Models.
    
    
12. Attach important files to a MapleSim model to keep content in one place. Attachments can be Maple worksheets or others such as pdfs, Excel, Word, STL files, etc. These files are found under the Project Tab, Attachments palette. Attach a file by, right-clicking the category and selecting Attach File or clicking the Edit menu Attach File.

I hope you find these useful! Do you have any tips that you would add to this list?

The first instalment in the Hollywood Math webinar series will be returning live this September 17^th! It will be presented by Daniel Skoog, our Maple Product Manager.

Over its storied and intriguing history, Hollywood has entertained us with many mathematical moments in film. John Nash in “A Beautiful Mind,” the brilliant janitor in “Good Will Hunting,” the number theory genius in “Pi,” and even Abbott and Costello are just a few of the Hollywood “mathematicians” that come to mind.

During this webinar we will present a number of examples of mathematics in film, including those done capably, as well as questionable and downright “creative” treatments. See relevant, exciting examples that you can use to engage your students, or attend this webinar simply for its entertainment value. Have you ever wondered if the bus could really have jumped the gap in “Speed?” We’ve got the answer! Anyone with an interest in mathematics, especially high school and early college math educators, will be both entertained and informed by attending this webinar.

To join us for the live presentation, click here to register.

A wealth of knowledge is on display in MaplePrimes as our contributors share their expertise and step up to answer others’ queries. This post picks out one such response and further elucidates the answers to the posted question. I hope these explanations appeal to those of our readers who might not be familiar with the techniques embedded in the original responses.

Before I begin, a quick note that the content below was primarily created by one of our summer interns, Pia, with guidance and advice from me.

The Question: why is 2*cos(x)^2-1 simpler than 1-2*sin(x)^2

The author, nm, asked why 2*cos(x)^2-1  was simpler than 1-2*sin(x)^2 according to Maple. nm wrote:

I looked at help trying to understand why Maple thinks 2*cos(x)^2-1 is simpler than 1-2*sin(x)^2 but did not see it. I was expecting to see cos(2*x) as a result.

Preben Alsholm answered nm’s question by recommending the use of the combine command to obtain the result he was expecting to see, as well as a further explanation on how the simplify command works. Alsholm wrote:

Use combine to obtain what you want:
combine(1-2*sin(x)^2);

simplify has a general preference for cos over sin. That doesn't mean however, that it turns sin into cos at all costs:

simplify(sin(x));
##Try also
simplify(1-2*sin(x)^2,size);

simplify doesn't necessarily get you the simplest result in the common sense of the word 'simplify'. Try as another example

expand((x+y)^3);
simplify(%);
factor(%);

As always, Alsholm provided an accurate, thoughtful response. But for those just learning Maple, I thought some additional explanation could be helpful.

Let’s talk more about the simplify command and combine function

The simplify command applies simplification rules to an expression. Its parameters can be any expression.

The combine function applies transformations which combine terms in sums, products, and powers into a single term. For many functions, the transformations applied by combine are the inverse of the transformations that are applied by expand. For example, consider the well-known identity:

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

The combine function applies the identity from right to left, whereas the expand function does the reverse.

I hope that you find this useful. If there is a particular question on MaplePrimes that you would like further explained, please feel free to contact me.

On this week I asked Maplesoft Customer Service for help. Here is our correspondence
(Only the purchase code and e-mail addresses are censored. PS. Also the last name of Kari was deleted by Bryon Thur on 28.08.2015.).
I think this is of interest for many Maple users. I have got some experience contacting
with Kaspersky Antivirus (They helped me by the use of indices of my comp.) and ABBYYLingvo
(They helped to install an ABBYYLingvo vocabulary on my phone.) so I can compare and
make conclusions.


From:
Sent: August-15-15 4:44 AM
To: Maplesoft Customer Service
Subject: Customer Service Request: (Web) Installation questions

Hello,
After upgrading my Windows 7 HB 32-bit to Windows 10 I cannot uninstall my Maple 16 PE.
 It cannot be uninstalled by neither Start/Parameters/System/Applications nor
Uninstall in C/ProgramFiles/Maple 16.
The Uninstall option is not seen in Maple 16 as application.
Also the overinstallation of Maple 16 does not work.
Waiting for your feedback.
Sincerely,
Markiyan Hirnyk
------------------------------------------------------------------------------------------------------

Dear Markiyan Hirnyk,

Thank you for contacting Maplesoft.

Maple 16 is not officially supported on Windows 10 but I have added an activation to your
existing Maple 16 Personal Edition purchase code: XXXXXXXXXXXXXXXX to see if reactivating
your license fixes the issue.  If reactivating doesn't give you access to Maple 16, please
send me the exact wording of any error messages that you receive so that I can send
 the information to our Technical Support Team so that they can investigate further.

Kind regards,

Kari
Maplesoft
Customer Service
-----------------------------------------------------------------------------------------------------------
Hello Kari,
Unfortunately, neither the  reactivation of my Maple 16 PE by XXXXXXXXXX nor its uninstallation
do not succeed for me. See the error communications in the attached screens (both in one file) screens_1_2.docx.
It should be noticed that Maple V Release 4 works on Windows 10 of my comp without any problems.
Regards,
Markiyan Hirnyk

--------------------------------------------------------------------------------------------------------
Hi Markiyan Hirnyk,

Thanks for your response.
I am forwarding your information to our Technical Support Team.
A representative will contact you soon.
Kind regards, Kari
Maplesoft Customer Service
------------------------------------------------------------------------------------------------------------
Hello Markiyan,

This error is usually caused by a Windows permissions setting. To fix this, please do the following:

1. Ensure that all Maple programs are completely closed.
2. Click on your Start Menu and go to the 'Programs' > 'Maple 16' > 'Tools' folder.
3. Right click the 'Activate Maple' icon and choose 'Run as administrator'.
4. Activate Maple using your purchase code and this should fix your issue.

Please let me know if you continue to experience any troubles.

Regards,

Chris
Technical Support Analyst
--------------------------------------------------------------------------------------------------------
Hello Chris,
Following your directions, I have just reactivated Maple 16, but my problem is not solved.
To shed light on the situation, my Maple 16.02 works properly,
but I cannot uninstall it after upgrading to Windows 10 Home 32bit.
See the screens in the attached file screen.docx .
Regards,
Markiyan Hirnyk
----------------------------------------------------------------------------------------
Hello Markiyan,
If you are seeing error messages about Maple still being open,
 I would suggest you try to restart your PC and then attempt the uninstall again to ensure
that you do not have any lingering Maple programs running. Please let me know
if you still see this message after restarting.

Regards,

Chris
Technical Support Analyst
------------------------------------------------------------------------------------------------------
Hello Chris,
This does not help too. My guess is execution failure when Maple 16 was installing.
Because of that reason the Maple 16 installer did not create Maple uninstaller in my Maple 16.
 See the attached screen of the uninstall folder in C:/ Program Files/ screen_3.docx.
Regards,
Markiyan Hirnyk
--------------------------------------------------------------------------------------------------------
Hello,
If you think that you have a corrupted installation, I recommend that you reinstall Maple
using the new Maple 16.02 installer link provided below.
 This version of the installer was created to get around the Windows 8 installation issues and
 may be of help to you in Windows 10 as well, though again please be aware that
 we do not officially support Windows 10 yet.
Here are the steps to reinstall Maple:
1. Click on the Start Menu > Control Panel > Programs and Features ( or Add/Remove Programs).
 Find ‘Maple 16’ in the list and uninstall it. If this is not possible, move on to the next step and continue.
2. Restart your computer.
3. Click on the Start Menu > Computer > Local Disk C: > Program Files.
If there is a folder here called ‘Maple 16’, please delete it.
4. Download the installer for Maple 16 from the following link:
        http://www.maplesoft.com/downloads/?d=C75DEBEC838C08BB1DCCED0440B49503&pr=Maple16
5. Make sure to download the correct version for your operating system, i.e. Windows version and 32 or 64-bit.
6. Install Maple by right clicking the installation file and choosing ‘Run as administrator’.
I hope that this helps to resolve the issues that you’re having and if it does not,
contact us and we can further investigate for you.

Regards,
Chris
Technical Support Analyst
--------------------------------------------------------------------------------------------------------
 Hi Chris,
My problem with Maple 16 is solved. I completely uninstalled it by Uninstall Tool 3.4, not using brute force. After that I installed Maple 16 by the distributive suggested by you. That's all right.
Regards,
Markiyan Hirnyk
---------------------------------------------------------------------------------------------------------
Alright, that is good to hear. Please let us know if you run into any further issues with your installation.
Regards,
Chris
Technical Support Analyst

In addition to providing access to powerful tools for mathematical computation, Maple has been designed to help you work quickly and efficiently. Here are 10 useful short-cuts when working with Maple:

1. Use F5 to switch between Text and 2D Math input modes in Maple.

2. Use F2 (Control+? for Macintosh) to quickly bring up Maple Help information for anything that you have typed in your document.

3.  Automatic Command Completion can be used when you don't want to type in the full name of a Maple command. To use, begin typing the first few letters of the command name, and press CTRL+Space (Esc or Command+Shift+Space for Macintosh, CTRL+Shift+Space for Linux).  A list of possible completions will display; click the one you want.

4. The Shift+Enter key combination lets you continue entering math or commands on a new line without executing that line. 

5. If you want more than a single command to be executed at once, you must separate them with a semi-colon or colon.

6. When you click inside a set of commands in Math mode, the dash line indicates the boundaries of the input region; all commands in this region will execute together in sequence.

7. To increase the size of a piecewise function, add a new row.  Place the cursor on the last row, and press CTRL+Shift+R (Command+Shift+R for Macintosh). These shortcut keys also work to add rows to matrices.

8. An easy way to insert a Greek letter is to first press CTRL+Shift+G (Command+Shift+G for the Macintosh). The next letter typed will appear in Greek.

9. Sometimes you may want to insert symbols above or below another character, for example, to enter a vector arrow. To insert a symbol above (called "overscript"), press CTRL+Shift+["] (Command+Shift+["] for Macintosh) and then type in your symbol (or insert it from a palette).

For example, typing "x" then holding down CTRL+Shift and pressing ["] allows you to insert a symbol above the x, such as 

10. Compute or recompute the entire Maple worksheet when you have changed expressions that affect subsequent Maple commands.  Press Ctrl + Shift + Enter (Command + Shift + Enter in Macintosh) or click the execute worksheet icon. 

Are there any short-cuts that you would add to this list?

As an educator, you surely know that giving students more involved problems in an online assessment tool provides challenges, both for students and instructors. Only marking the final answer doesn’t necessarily provide an understanding of the student’s capabilities, and it penalizes students that make a small mistake in part of their solution.

This webinar will demonstrate how to create separate questions with multiple steps that can be linked or chained together. Question chaining allows instructors to mark subsequent questions based on the correct answer or the answer provided by students in previous parts.

To join us for the live presentation, please click here to register.

Solving DAEs in Maple

As I had mentioned in many posts, Maple cannot solve nonlinear DAEs. As of today (Maple 2015), given a system of index 1 DAE dy/dt = f(y,z); 0 = g(y,z), Maple “extends” g(y,z) to get dz/dt = g1(y,z). So, any given index 1 DAE is converted to a system of ODEs dy/dt = f, dz/dt = g1 with the constraint g = 0, before it solves. This is true for all the solvers in Maple despite the wrong claims in the help files. It is also true for MEBDFI, the FORTRAN implementation of which actually solves index 2 DAEs directly. In addition, the initial condition for the algebraic variable has to be consistent. The problem with using fsolve is that one cannot specify tolerance. Often times one has to solve DAEs at lower tolerances (1e-3 or 1e-4), not 1e-15. In addition, one cannot use compile =true for high efficiency.

The approach in Maple fails for many DAEs of practical interest. In addition, this can give wrong answers. For example, dy/dt = z, y^2+z^2-1=0, with y(0)=0 and z(0)=1 has a meaningful solution only from 0 to Pi/2, Maple’s dsolve/numeric will convert this to dy/dt = z and dz/dt = -y and integrate in time for ever. This is wrong as at t = Pi/2, the system becomes index 2 DAE and there is more than 1 acceptable solution.

We just recently got our paper accepted that helps Maple's dsolve and many ODE solvers in other languages handle DAEs directly. The approach is rather simple, the index 1 DAE is perturbed as dy/dt = f.S ; -mu.diff(g,t) = g. The switch function is a tanh function which is zero till t = tinit (initialization time). Mu is chosen to be a small number. In addition, lhs of the perturbed equation is simplified using approximate initial guesses as Maple cannot handle non-constant Mass matrix. The paper linked below gives below more details.

http://depts.washington.edu/maple/pubs/U_Apprach_FULL_DRAFT.pdf  

Next, I discuss different examples (code attached).

Example 1: Simple DAE (one ODE and one AE), the proposed approach helps solve this system efficiently without knowing the exact initial condition.

Hint: The code is given with a semicolon at the end of the most of the statements for educational purposes for new users. Using semicolon after dsolve numeric in classic worksheet crashes the code (Maplesoft folks couldn’t fix this despite my request).

Example 2:

This is a nickel battery model (one ODE and one AE). This fails with many solvers unless exact IC is given. The proposed approach works well. In particular, stiff=true, implicit=true option is found to be very efficient. The code given in example 1 can be used to solve example 2 or any other DAEs by just entering ODEs, AEs, ICs in proper places.

Example 3:

This is a nonlinear implicit ODE (posted in Mapleprimes earlier by joha, (http://www.mapleprimes.com/questions/203096-Solving-Nonlinear-ODE#answer211682 ). This can be converted to index 1 DAE and solved using the proposed approach.

Example 4:

This example was posted earlier by me in Mapleprimes (http://www.mapleprimes.com/posts/149877-ODEs-PDEs-And-Special-Functions) . Don’t try to solve this in Maple using its dsolve numeric solver for N greater than 5 directly. The proposed approach can handle this well. Tuning the perturbation parameters and using compile =true will help in solving this system more efficiently.

Finally example 1 is solved for different perturbation parameters to show how one can arrive at convergence. Perhaps more sophisticated users and Maplesoft folks can enable this as automatically tuned parameters in dsolve/numeric.

Note:

This post should not be viewed as just being critical on Maple. I have wasted a lot of time assuming that Maple does what it claims in its help file. This post is to bring awareness about the difficulty in dealing with DAEs. It is perfectly fine to not have a DAE solver, but when literature or standard methods are cited/claimed, they should be implemented in proper form. I will forever remain a loyal Maple user as it has enabled me to learn different topics efficiently. Note that Maplesim can solve DAEs, but it is a pain to create a Maplesim model/project just for solving a DAE. Also, events is a pain with Maplesim. The reference to Mapleprimes links are missing in the article, but will be added before the final printing stage. The ability of Maple to find analytical Jacobian helps in developing many robust ODE and DAE solvers and I hope to post my own approaches that will solve more complicated systems.

I strongly encourage testing of the proposed approach and implementation for various educational/research purposes by various users. The proposed approach enables solving lithium-ion and other battery/electrochemical storage models accurately in a robust manner. A disclosure has been filed with the University of Washington to apply for a provisional patent for battery models and Battery Management System for transportation, storage and other applications because of the current commercial interest in this topic (for batteries). In particular, use of this single step avoids intialization issues/(no need to initialize separately) for parameter estimation, state estimation or optimal control of battery models.

Download SolvingDAEsinMaple.mws

It looks like the Online Help has now been updated for Maple 2015.

Here's the What's New in Maple 2015 Overview, which is similar to the product pages currently available here.

But we can now also link to and view the online versions of full help pages of new or enhanced commands or example worksheets. For example, dataplot.

acer

Here are some tips and tricks that will help you get the most out of Maple 2015, covering from short cuts to how to use the newest features.

1. Whenever you are asking yourself “..but how do I do it?”, just type ?Portal+Enter, and you will access the Maple Portal, which will give you a complete guide on how to do things.
   
   
2. If you want to implement 1 of the 300 tasks that Maple offers in a syntax-free way, like Completing the Square, just follow this path: Tools≻Tasks≻Browse.
   
   
3. Type Ctrl+F2 or Command+F2 and the Quick Reference window with shortcut keys and other information about working with the Maple interface will pop up.
   
   
4. If you need quick help with a specific mathematical function, click or highlight the function + F2 and a Help box that contains a summary of the basic characteristics of the function will pop up.
   
   
5. If you have installed the Excel Add-in and you want to perform some Maple commands within Excel, make sure to enable the Maple add in by following this path: Excel’s Tool Menu>Add-Ins>Select Maple Excel Add-in Box> OK
   
   
6. Export Maple’s data into Excel by right clicking and choosing ‘Export As’>Excel.
   
   
7. Instead of having to copy-paste your Maple information into a Power Point Presentation, just turn the slideshow mode on by pressing F11. This way you will have an interactive presentation that holds all the live plots and embedded components that Maple offers.
   
   
8. Whenever you want to create interactive mini-applications that can be used to explore the parameters of any arbitrary Maple expression, such as a plot, mathematical equation, or command use the Exploration Assistant. Do this by either right-clicking +Explore from the context-sensitive menus, or by calling the Explore command.
   
   
9. Save time while computing mathematical expressions by calling the equation label instead of having to re-type the equation. Do this by pressing CTRL+L and then input the number that identifies the equation.
   
   
10. Reference mathematical equations or expressions from other documents. First, determine which label is associated with the equation you want. In the main document, select "Insert" > "Reference". From the file dialog, select the file containing the expression. Then select the equation reference number of your equation from the list that appears.
    
    
11. In Maple, the letter "e" entered using the keyboard does not represent the exponential function. The exponential function can be entered using command completion (Ctrl+Space or ESC) or the "exp(a)" item in the Expression Palette (Standard interface only). The exponential can also be entered as:          

    > exp(x)
    
    

12. With Maple 2015 you can now access data sets from various built-in and online data sources. This package is able to access time series data from the data aggregator Quandl, as well as locally installed data from countries and cities. To learn more, click here.
    
    
13. Whenever you assign plots to a variable name, p:=[plot(sin(x)), plot(cos(x))] a thumbnail of the plot will appear instead of the code.
    
    
14. Save time when inputting existing or personalized units. Just click CTRL+SHIFT+U and type the desired units you want.
    
    
15. With Maple 2015 you can now zoom in or out just by pressing CTRL+SCROLL or CTRL+ place two fingers on the pad and move them up to zoom in or down to zoom out.
    
    
16. Convert a Maple Worksheet into Microsoft Word: This can be done using the Export to HTML feature.
    
    1. Prepare your worksheet as you would like it to appear in the document.
    2. From the "File" menu in Maple, select "Export As ..." > "HTML".
    3. Give the HTML file a name, "output.html" for example.
    4. When the export has completed, start Word, and open the HTML file. If you used "output.html" as the name to save the file as, open the file called "output1.html" into Word.
    5. From the "File" menu in Word, select "Save as Word Document" to save the file. You now have a Word document which contains the content of your Maple worksheet.
       
       Note: this procedure will work with any Word Processing program that can open an HTML document.
       
       
17. Change Maple’s default input from 2D to 1D:
    1. Open the Tools > Options... menu (Maple > Preferences on a MACINTOSH machine).
    2. Select the Display tab
    3. From "Input Display" menu select Maple Notation
    4. Press the Apply to Session button to make the change take effect for the current Maple session.
    5. Press Apply Globally to have the change take effect permanently. Maple will need to be restarted if you choose Apply Globally for the changes to take effect.
       
       You may download a set of instruction on how to change your 2D interface to the “Classic” Style here: ftp://public.maplesoft.com/miscellaneous/ChangeToClassicInterface.pdf

We hope that you find this list helpful. Please feel free to add any of your tips or techniques to this post, or to create your own new topic.

You are teaching linear algebra, or perhaps a differential equations course that contains a unit on first-order linear systems. You need to get across the notion of the eigenpair of a matrix, that is, eigenvalues and eigenvectors, what they mean, how are they found, for what are they useful.

Of course, Maple's Context Menu can, with a click or two of the mouse, return both eigenvalues and eigenvectors. But that does not satisfy the needs of the student: an answer has been given but nothing has been learned. So, of what use is Maple in this pedagogical task? How can Maple enhance the lessons devoted to finding and using eigenpairs of a matrix?

In this webinar I am going to demonstrate how Maple can be used to get across the concept of the eigenpair, to show its meaning, to relate this concept to the by-hand algorithms taught in textbooks.

Ah, but it's not enough just to do the calculations - they also have to be easy to implement so that the implementation does not cloud the pedagogic goal. So, an essential element of this webinar will be its Clickable format, free of the encumbrance of commands and their related syntax. I'll use a syntax-free paradigm to keep the technology as simple as possible while achieving the didactic goal.

Notes added on July 7, 2015:

• This live webinar has already been presented and you can view the recording here: http://www.maplesoft.com/webinars/recorded/featured.aspx?id=922
  
  
• For one reaction to a point made in the webinar, see this post.

The question of colorbars for plots comes up now and then.

One particular theme involves creating an associated 2D plot as the colorbar, using the data within the given 3D plot. But the issue arises of how to easily display the pair together. I'll mention that Maple 2015.1 (the point-release update) provides quite a simple way to accomplish the display of a 3D plot and an associated 2D colorbar side-by-side.

I'm just going to use the example of the latest Question on this topic. There are two parts to here. The first part involves creating a suitable colorbar as a 2D plot, based on the data in the given 3D plot. The second part involves displaying both together.

Here's the 3D plot used for motivating example, for which in this initial experiment I'll apply shading by using the z-value for hue shading. There are a few ways to do that, and a more complete treatment of the first part below would be to detect the shading scheme and compute the colorbar appropriately.

Some of the code below requires update release Maple 2015.1 in order to work. The colors look much better in the actual Maple Standard GUI than they do in this mapleprimes post (rendered by MapleNet).

f := 1.7+1.3*r^2-7.9*r^4+16*r^6:

P := plot3d([r, theta, f],
            r=0..1, theta=0..2*Pi, coords=cylindrical,
            color=[f,1,1,colortype=HSV]):

P;

Now for the first part. I'll construct two variants, one for a vertical colorbar and one for a horizontal colorbar.

I'll use the minimal and maximal z-values in the data of 3D plot P. This is one of several aspects that needs to be handled according to what's actually inside the 3D plot's data structure.

zmin,zmax := [min,max](op([1,1],P)[..,..,3])[]:

verthuebar := plots:-densityplot(z, dummy=0..1, z=zmin..zmax, grid=[2,49],
                                 size=[90,260], colorstyle=HUE,
                                 style=surface, axes=frame, labels=[``,``],
                                 axis[1]=[tickmarks=[]]):

horizhuebar := plots:-densityplot(z, z=zmin..zmax, dummy=0..1, grid=[49,2],
                                  size=[300,90], colorstyle=HUE,
                                  style=surface, axes=frame, labels=[``,``],
                                  axis[2]=[tickmarks=[]]):

Now we can approach the second part, to display the 3D plot and its colorbar together.

An idea which is quite old is to use a GUI Table for this. Before Maple 2015 that could be done by calling plots:-display on an Array containing the plots. But that involves manual interation to fix it up to look nice: the Table occupies the full width of the worksheet's window and must be resized with the mouse cursor, the relative widths of the columns are not right and must be manually adjusted, the Table borders are all visible and (if unwanted) must be hidden using context-menu changes on the Table, etc. And also the rendering of 2D plots in the display of the generated _PLOTARRAY doesn't respect the size option if applied when creating 2D plots.

I initially thought that I'd have to use several of the commands for programmatic content generation (new in Maple 2015) to build the GUI Table. But in the point-release Maple 2015.1 the size option on 2D plots is respected when using the DocumentTools:-Tabulate command (also new to Maple 2015). So the insertion and display is now possible with that single command.

DocumentTools:-Tabulate([P,verthuebar],
                        exterior=none, interior=none,
                        weights=[100,25], widthmode=pixels, width=420);

DocumentTools:-Tabulate([[P],[horizhuebar]],
                        exterior=none, interior=none);

We may also with to restrict the view, vertically, and have the colorbar match the shades that are displayed.

DocumentTools:-Tabulate([plots:-display(P,view=2..5),
                         plots:-display(verthuebar,view=2..5)],
                        exterior=none, interior=none,
                        weights=[100,25], widthmode=pixels, width=420);

DocumentTools:-Tabulate([[plots:-display(P,view=2..5)],
                         [plots:-display(horizhuebar,view=[2..5,default])]],
                        exterior=none, interior=none);

I'd like to wrap both parts into either one or two procedures, and hopefully I'd find time to do that and post here as a followup comment.

Apart from considerations such as handling various kinds of 3D plot data (GRID vs MESH, etc, in the data structure) there are also the matters of detecting a view (VIEW) if specified when creating the 3D plot, handling custom shading schemes, and so on. And then there's the matter of what to do when multiple 3D surfaces (plots) have been merged together.

It's also possible that the construction of the 2D plot colorbar is the only part which requires decent programming as a procedure with special options. The Tabulate command already offers options to specify the placement, column weighting, Table borders, etc. Perhaps it's not necessary to roll both parts into a single command.

3dhuecolorbarA.mw

acer

In case anyone is interested, we recently posted a new application on the Application Center,

Time Series Analysis: Forecasting Average Global Temperatures

While interesting in itself (well, I think so, anyway), this application also provides tips and techniques for analyzing time series data in Maple, and shows how to access online data sets through the new data sets functionality in Maple 2015.

eithne

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Case Study: Transforming a University's Placement Testing Process

This webinar will feature the story of how the University of the Virgin Islands moved their placing testing process from paper and pen to using the Mathematical Association of America’s (MAA) placement tests offered through the Maple T.A. testing environment. Instructors at the university now handpick questions to create their own placement tests that best fit the course they are teaching. From there, they are able to analyze the data and craft lessons based on student performance. The end result is that students are more satisfied with the education they are receiving and instructors have made enormous gains with regards to efficiency and flexibility.

To join us for the live presentation with Dr. Celil Ekici from the University of the Virgin Islands, please click here to register.

Getting Started with Maple

This webinar is designed for the user who comes to Maple for the first time. It will demonstrate “how to get started” by clarifying the user interface and the ways math can be entered into Maple, and then “processed.” Coverage includes

• Entering mathematical expressions and interacting with them in a syntax-free way.
• The difference between input in mathematical notation and “linear” or text form.
• The role of the Context Sensitive Menu system for interacting with mathematical objects.
• Graphing and interacting with various types of graphs, including animations, surfaces, and implicit plots.
• Use of built-in tools such as Assistants, Tutors, and Task Templates.
• The Maple help system and the Maple Portal.
• Introduction to differential equations and matrix manipulations.

To join us for the live presentation, please click here to register.