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The engineering design process involves numerous steps that allow the engineer to reach his/her final design objectives to the best of his/her ability. This process is akin to creating a fine sculpture or a great painting where different approaches are explored and tested, then either adopted or abandoned in favor of better or more developed and fine-tuned ones. Consider the x-ray of an oil painting. X-rays of the works of master artists reveal the thought and creative processes of their minds as they complete the work. I am sure that some colleagues may disagree with the comparison of our modern engineering designs to art masterpieces, but let me ask you to explore the innovations and their brilliant forms, and maybe you will agree with me even a little bit.

Design Process

Successful design engineers must have the very best craft, knowledge and experience to generate work that is truly worthy of being incorporated in products that sell in the tens, or even hundreds, of millions. This is presently achieved by having cross-functional teams of engineers work on a design, allowing cross checking and several rounds of reviews, followed by multiple prototypes and exhaustive preproduction testing until the team reaches a collective conclusion that “we have a design.” This is then followed by the final design review and release of the product. This necessary and vital approach is clearly a time consuming and costly process. Over the years I have asked myself several times, “Did I explore every single detail of the design fully”? “Am I sure that this is the very best I can do?” And more importantly, “Does every component have the most fine-tuned value to render the best performance possible?” And invariably I am left with a bit of doubt. That brings me to a tool that has helped me in this regard.

A Great New Tool

I have used Maple for over 25 years to dig deeply into my designs and understand the interplay between a given set of parameters and the performance of the particular circuit I am working on. This has always given me a complete view of the problem at hand and solidly pointed me in the direction of the best possible solutions.

In recent years, a new feature called “Explore” has been added to Maple. This amazing feature allows the engineer/researcher to peer very deeply into any formula and explore the interaction of EVERY variable in the formula. 

Take for example the losses in the control MOSFET in a synchronous buck converter. In order to minimize these losses and maximize the power conversion efficiency, the most suitable MOSFET must be selected. With thousands of these devices being available in the market, a dozen of them are considered very close to the best at any given time. The real question then is, which one is really the very best amongst all of them? 

There are two possible approaches - one, build an application prototype, test a random sample of each and choose the one that gives you the best efficiency.  Or, use an accurate mathematical model to calculate the losses of each and chose the best. The first approach lacks the variability of each parameter due to the six sigma statistical distribution where it is next to impossible to get a device laying on the outer limits of the distribution. That leaves the mathematical model approach. If you take this route, you can have built-in tolerances in the equations to accommodate all the variabilities and use a simplified equation for the control MOSFET losses (clearly you can use a very detailed model should you chose to) to explore these losses. Luckily you can explore the losses using the Explore function in Maple.

The figure below shows a three dimensional plot, plus five other variables in the formula that the user can change using sliders that cover the range of values of interest including Minima and Maxima, while observing in real time the effects of the change on the power loss.

This means that by changing the values of any set of variables, you can observe their effect on the function. To put it simply, this single feature helps you replace dozens of plots with just one, saving you precious time and cost in fine-tuning your design. In my opinion, this is equivalent to an eight-dimensional/axes plot.

I used this amazing feature in the last few weeks and I was delighted at how simple it is to use and how much it simplifies the study of my approach and my components selection, in record times!

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: Source Code of Math Apps

Eberch, a new Maple user, was interested in learning how to build his own Math Apps by looking at the source code of some of the already existing Math Apps that Maple offers.

Acer helpfully suggested that he look into the Startup Code of a Math App, in order to see definitions of procedures, modules, etc. He also recommended Eberch take a look at the “action code” that most of the Math Apps have which consist of function calls to procedures or modules defined in the Startup Code. The Startup Code can be accessed from the Edit menu. The function calls can be seen by right-clicking on the relevant component and selecting Edit Click Action.

Acer’s answer is correct and helpful. But for those just learning Maple, I wanted to provide some additional explanation.

Let’s talk more about building your own Math Apps

Building your own Math Apps can seem like something that involves complicated code and rare commands, but Daniel Skoog perfectly portrays an easy and straightforward method to do this in his latest webinar. He provides a clear definition of a Math App, a step-by-step approach to creating a Math App using the explore and quiz commands, and ways to share your applications with the Maple community. It is highly recommended that you watch the entire webinar if you would like to learn more about the core concepts of working with Maple, but you can find the Math App information starting at the 33:00 mark.

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. 

My code works in Maple (18.02), not Maple Player (2015.1). Much headache ensued.

I've isolated the problem in a toy form:

Defn := proc (scaleby)

Explore(Defn(p), parameters = [p = [1, 10, 100]]);

In Maple will return "integer" for any value of p selected in the combobox.

In Maple Player returns "string" for any value of p selected in the combobox

Is there something I'm missing here? Is Maple Player not backwards compatible to versions of Maple prior to 2015?

My understanding is that Maple Code should export without headache to Maple Player. Is this a solid understanding?

Thanks for helping out a newbie!




I would like to slightly modify the "Explore" command -- I find it extremely useful, but the layout often doesn't work well for me (my typical use case is say 12 plots with ~10 parameters that vary). The problem is that the default alignment the columns of the table that contains a matrix of plots is "Center" and my plots don't fit on the screen properly (no matter how I play with sizes, placement, etc) and I would like it to be "Left" aligned --- aligning things manually (via right click) after the explore command is executed is possible, but painful, given that I often change my code.

... bottom line is that I would like to be able to re-define the "Explore" command.

I tried doing so by first calling:

... then removing all the numbers, renaming the proc to sat MyExplore, declaring it (i.e. so maple understands it) and for now using that instead of the old Explore in my program (with no actual code changes for now). The problem is that I get the following error:

Error, (in DocumentTools:-Layout:-Table) number of Column arguments, 3, exceeds total column span, 1, computed from Rows' Cells

I think, somehow maybe showstat is not showing the full thing? or maybe it is part of a more complicated module? or maybe by removing the numbers the formatting got screwed up (i was careful here)?

So my question:

How would I define my own function "MyExplore" that (for now) contains exactly the same code and functionality as the built-in "Explore"?




I'm trying to create interactive plots by using Explore to help demonstrate the effects parameters have on functions. I created one successfully to illustrate shifts and stretches of a polynomial:


transform(A,B,X,H,P,K):=Explore(plot(a*(b*x+h)^(p)+k,x=X),parameters=[a=A, b= B,h=H,p=P,k=K],placement=right)


However when I try to do the same with a solved ODE it returns an error message:


Explore(plot(1/(-p*x+x+1)^(1/(p-1)), x = -5 .. 5), parameters = [p = -20 .. 20], placement = right);


Executing this gives the error message: 

Warning, expecting only range variable x in expression 1/((-p*x+x+1)^(1/(p-1))) to be plotted but found name p

VIEW(-5. .. 5., DEFAULT, _ATTRIBUTE("source" = "mathdefault"))),

parameters = [p = -20 .. 20], placement = right


I'm not sure why it is having difficulty dealing with "p" when it had no difficulty with the first. Any help would be appreciated!

Here in this work and used as the main topic a short description of electrostatics and electrodynamics using the Explore to model the fundamental laws command.

 Corriente_Elé   (in spanish)



L. Araujo C.


I have a question regarding maple reader.


It seems like in maple reader, one cannot interact with the output of the Explore function.... which mean I am forced to make my own component if I want to creat application for my co-worker to use..this is some what annoying.  Is there another way around?


please open the attached file in maple player and you will see the output created by Explore gives error message.




Hi everyone

I'd be pleased if you could give a hand with the exploration assistant.


1. I want the exploration assistant to appear on the same document I am working on, but everytime I use it (either by right-clicking or by the explore command) it automatically appears on a new document.


2. can I manipulate a piecewise function when using embedded components? i.e.: plot the function and varying the parameters using sliders.





I only recently started to work with Maple17 and tried to test the Explore command. In Classic worksheet I tried a very simple function with a parameter, but after setting the inteval of the parameter in the Java pop-up window I have no result. In return I take: "Error, (in Explore) invalid input: rtable_dims uses a 1st argument, A (of type rtable), which is missing"

Has anyone encounter the same issue before?


Hello,When I plot graphs I can simply add colors, gridlines, labels, etc., but when I want to do this with the command 'Explore' it doesn't work.The commad 'Explore' sees the words 'color', 'labeldirections' and other commands as extra variables.For exmaple is does recognize 'labels' and 'title', which I can fill in, but it doesn't some of the other commands I would like to insert.I have a formula for deriving the eigenfrequency of a concrete beam, where I want to add some things to (like the things mentioned above).Somebody knows what the difference is between 'normal' plotting and plotting with 'Explore'?Explore_-_Adding_Col.mwGreetingsFrank

Before doing an explore-plot command I had given constant or expression assignments to certain parameters in preliminary statements, e.g.

k = 4* 10-5 ;

mpgo = 45;

mpgave = mpgo - k*(md /2 );

mpgmave = mpgo - k*(m / 2);


Then I did an explore-plot :


Explore(plot(7.28*m*( (1/mpgmave) - (1/mpgave) ) ,


The Locator object is a nice piece of Mathematica's Manipulate command's functionality. Perhaps Maple's Explore command could do something as good.

Here below is a roughly laid out example, as a Worksheet. Of course, this is not...

Hi there

I'm a new user of Maple 15 and would really appreciate some tips on how to get started, this time more specifically on how to change the axis orientation. I'm a geotechnical engineer and in practice we always plot all the soil properties (strength, density, water content, etc) with depth, and so it should be positive downwards. 

I've seen a few posts where the issue was raised by some people years ago but was just curious to know if the new version...

Is it somehow possible to apply the Explore command to a procedure with numerical parameters?
It would be convenient in some cases. For example, let us consider  the following  procedure:
K := proc (alpha, theta1, theta2, sigma, n::posint)
uses Statistics;
t[alpha] := fsolve(CDF(RandomVariable(NormalDistribution(0, 1)), -t) = alpha, t);
 beta := evalf(CDF(RandomVariable(NormalDistribution(0, 1)),

The iPad is a very exciting device and it has been gaining broad adoption from our academic and professional customers alike. It was a logical step for us to bring Maple technology to this platform.
The Maple Player for iPad is now available in the Apple App Store. It comes bundled with ready-made interactive Maple documents, covering topics like integration, differentiation, computing...

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