Applications, Examples and Libraries

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I just wanted to remind everyone that this quarter's Möbius App Challenge closes Sept. 30.  This quarter's prize is an iPad Prize Pack, which looks very cool but sadly, I'm not allowed to enter.

To enter the contest, all you need to do is:

1) Create an interactive App in Maple

2) While in Maple, log-in to the MapleCloud through the MapleCloud palette.

3) Click on the Send Document to the Cloud button

Prior to the Finance package being updated to include holidays there was no easy way to have Maple generate when holidays occurred.  Hence for newer Maple users there would be no need for such a thing but I had an interest to create one for earlier versions.  The idea is quite simple enough and this is one solution I came up with.

I ran into trouble mathematically calculating easter (the first Sunday after the full moon after March 21st) I...

 

Hi, 
A new Physics:-Library:-SortProducts command got added to the Library, addressing the need for reordering operands in noncommutative products (Physics:-`*` and Physics:-`.`) in different ways (optional arguments of SortProducts). Note: SortProducts returns an expression mathematically...

My system: Windows 8 x64, Maple 17.01 x64.

After launching Maple we have a process maple.exe (C:\Program Files\Maple 17\jre\bin\maple.exe) that consumes approximately 80MB.

We run the following piece of code:

>restart;
>for i to 1000 do
>factorial(300);
>end do;

After running for the first time of this code the process maple.exe consumes 100.5MB
After second running of this code the process maple.exe consumes 111.6MB
third running --- 122.4MB

I have a rather complicated expressions involving several parameters. The parameters are calibrated to some baseline. I'm interested in having a quick look at how changing each parameter changes the value of the expression. This is very standard. I wrote a procedure to create a list of values to the left and to the right of the base value for a given parameter. I then use that to look at my expression, to plot lists of expressions, and so on.

I thought I'd share this...

I'm sharing this in the hope it might help someone (my future self being the most likely). Since my suggestions are not perfect and a little messy, feel free to suggest better ways.

I spend a great deal of time tweaking my plots. Oftentimes I want to add labels to the curves right onto the plot. Most of the time it's easy to do. Occasionally I struggle. Sometimes I succeed, sometimes I give up.

Below is an example of the kind of plot I sometimes create. It's not perfect.

I made 3 years ago a SOKOBAN game using Maple for my Math/Programming class.

Here is a video of the application:

http://www.youtube.com/watch?v=l00l82_LK2Y

Have a nice day!

(Presentation in Spain a month ago focusing on educational and research use)

ODEs and PDEs

 

"Computer algebra systems have evolved into powerful environments for studying and solving differential equations."

 

Some polemical questions:

 

Can a Computer Algebra system compute numerical ODE solutions as fast as for instance C or FORTRAN code ?

   

Can a computer really be more useful than a good book for finding exact ODE and PDE solutions ?

   

Aren't these computer algebra environments more like a black-box approach to the problem ?

   

Can we really study  the "differential equations" behind a problem using Computer Algebra as we would do by hand?

   

Is there something fundamentally relevant regarding ODEs and PDEs that we can only do with a computer?

   

___________________________________________________________________________

 

Special Functions

 

"Special functions, their inter-relation and representations become alive within a computer"

Conversions between mathematical functions

   

The FunctionAdvisor project

   

Differential Polynomial Form for non-polynomial expressions

   

___________________________________________________________________________

Conclusion

 

"Research and education are two things highly inter-related"

 

  

-  Constructive learning processes are mostly based on the building of logic structures by testing conjectures and analyzing the results. The proportion between success (the conjecture solves the problem) and frustration plays an important role as an emotional (+/-) accelerating factor for the whole "learning & discovery" process.

-  The simultaneous analysis of a greater number of results turns apparent the underlying logic structures more rapidly, and can strengthen the intuition unexpectedly.

  

- Genuine learning processes only happen when the individual who is learning participates actively.

  

- Inspiration is a function of intuition, excitement and fun, transformed into results through heavy exploration.

Symbolic computation can be used with these purposes, perhaps as the most important educational and research tool available at present.

___________________________________________________________________________

 

 

Santander_talk.pdf   Download Santander_talk.mw

 

Edgardo S. Cheb-Terrab
Physics, Maplesoft

Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.

In the Algebra/Precalculus section, examples of an

(Presentation in Spain a month ago with a full description of the project and its current status)

A computational environment for Physicists

 

 

"Algebraic manipulations in Physics and related numerical exploration and visualization come together within computer algebra systems"

Project background

   

Three reasons for the underuse of Computer Algebra Systems in Physics

   

The Physics project goals

   

Status of things in Maple 17

   

Examples

   

 

 

Download PhysicsProjectDescri.mw

 


Edgardo S. Cheb-Terrab
Physics, Maplesoft

Greetings to all.

A recent post at math.stackexchange.com asked for good approximations to pi using the nine nonzero digits, the four arithmetic operations and exponentiation. The problem definition definitely suggests a computational solution, which is actually non-trivial because the search space of all legal mathematical expressions over the nine digits and with the aforementioned operations is so huge that it cannot possibly be searched exhaustively.

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

Voting is open for the first individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive a MacBook Air! 

Here are the finalist Apps:

In this article I want to discuss the right way to store and build Maple code.

As mentioned in the Introducing the Maple IDE post, over 90 percent of the algorithms built into Maple are implemented using Maple language. The code of the algorithms is stored as Maple Libraries (.mla files).

As

One of the most basic decisions a baseball manager has to make is how to arrange the batting order.  There are many heuristics and models for estimating the productivity of a given order.  My personal favourite is the use of simulation, but by far the most elegant solution from a mathematical perspective uses probability matrices and Markov chains.  An excellent treatment of this topic can be found in Dr. Joel S. Sokol's article,

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