Some time ago, @marc005 asked how he could send an email from the Maple command line.

Why would you want to do this? Using Maple's functionality, you could programatically construct an email - perhaps with the results of a computation - and email it yourself or someone else.

I originally posted a solution that involved communicating with a locally-installed SMTP server using the Sockets package. But of course, you need to set up an SMTP server and ensure the appropriate ports are open.

I recently found a better solution. Mailgun (http://mailgun.com) is a free email delivery service with an web-based API. You can communicate with this API via the URL package; simply send Mailgun a URL:-Post() message that contains account-specific information, and the text of your email.

The general steps and Maple commands are given below, and you can download the worksheet here.

Note: Maplesoft have no affiliation with Mailgun.

Step 1:
Sign up for a free Mailgun account.

Step 2:
In your Mailgun account, go to the Domains section - it should look like the screengrab below (account-specific information has been blanked).

Note down the API Base URL and the API key.

• the API Base URL looks like https://api.mailgun.net/v3/sandboxXXXXXXXXXXXXXXXXXXXXXXXXXXX.mailgun.org.  
• •the API Key looks like key-XXXXXXXXXXXXXXXXXXXXXXXXXX

Step 3:

In Maple, define strings containing your own API Base URL and API Key. Also, define the recipient's email address, the email you want the recipient to reply to, the email subject and email body.

>restart:

>APIBaseURL := "https://api.mailgun.net/v3/sandboxXXXXXXXXXXXXXXXXXXXXXXXX.mailgun.org":

>APIKey:="key-XXXXXXXXXXXXXXXXXXXXXXXX":

>toEmail := "xxxxx@xxxxxx.com":

>fromEmail:="First Last <FirstLast@Domain.com>":

>subject:= "Email Subject Goes Here":

>emailBody := "I'd rather have a bottle in front of me than a frontal lobotomy":

Step 4:
Run the following code

> URL:-Post(cat(APIBaseURL,"/messages"),[

"from"=fromEmail,"to"=toEmail,

"subject"=subject,

"text"= emailBody],

user="api",password=APIKey);

If you've successfully sent the email, you should see something like this (account-specific information is blanked out)

You can also send HTML emails by replacing the "text" line with "html" = str, where str is a string with your HTML code.

For those who are running Maple and/or MapleSim on the Mac, and who may have missed an earlier question on this site, we wanted to let you know that there are some problems with running Maple and MapleSim on the new Mac OS, Mac OS X 10.11 (El Capitan). We’re working on a solution, which we expect will be ready in a few weeks. We’ll keep you posted, but in the meantime, please delay updating your Mac OS for now to avoid problems.

eithne

Earlier today, we published some changes to MaplePrimes in order to add some new features that have been requested by our users.

Delete as Spam

Users with a reputation score above 500 have always had the ability to remove inappropriate or spam posts using the Delete function. As of this update, a Delete as Spam feature has been added that provides some additional capabilities targeted directly at the spam messages that are posted on MaplePrimes. When this feature is used, the following occurs:

• The message is deleted
• The author's account is marked as a spam account and blocked
• All other messages from the author are removed

Since this is a powerful feature, there are also some safeguards in place to prevent accidents from occurring:

• Only users with a reputation less than 10 can be removed in this way
• In the event that content is ever inadvertently removed, MaplePrimes administrators have the ability to restore content removed in this way.

Hopefully, these features make it much more difficult for spam accounts to get traction on MaplePrimes, and also reduce the time involved in policing the spam that is posted.

Draft Messages

You now have the ability to save a message as a draft so that you can come back to it later. All draft messages are saved in your profile and can be managed by clicking the account option at the top of every page. 

Advanced Search

Some powerful searching capabilities have been added to MaplePrimes with the addition of a new Advanced Search feature. Using this search allows you to quickly find questions or posts within a particular date range, by author and/or by tag.

Save page as PDF

We know that some of our members maintain personal archives of MaplePrimes content, and to make this easier, we have added a feature that generates a PDF copy of a page. This option is available in the More area that appears under every post and question.

View your Replies

Your MaplePrimes user profile page has always included archives of your posts, questions and answers. With today's update, replies are also available.

In addition to these, some other minor changes & fixes were made.

As always, thank you very much for your dedication to MaplePrimes and for your suggestions. We hope that you find these features useful and look forward to other ideas that you have!

Like most companies today, Maplesoft monitors its website traffic, including the traffic coming to MaplePrimes. This allows us to view statistical data such as how many total visits MaplePrimes gets, how many unique visitors it gets, what countries these visitors come from, how many questions are asked and answered, how many people read but never respond to posts, etc. 

Recently one of our regular MaplePrimes users made the comment that MaplePrimes does not reach new Maple users. We found this comment interesting because our data and traffic numbers show a different trend. MaplePrimes gets unique visitors in the hundreds of thousands each year, and since its inception, it has welcomed unique visitors in the many millions. Based on these unique visitor numbers and the thousands of common searches specifically about Maple that people are doing, we can see that many of these unique visitors are in fact new Maple users looking for resources and support as they begin using Maple. Other visitors to MaplePrimes include people who use Google (or other search engines) to find an answer to a particular mathematics or engineering question, regardless of what mathematics software they choose to use, and Google points them to MaplePrimes. There are some popular posts that were written months, even years ago, that are still getting high visitor views today, showing the longevity of the information on MaplePrimes. 

MaplePrimes gets the majority of its visible activity from a small number of extremely active members. In public user forums around the world, these types of members are given many names – power users, friendlies, evangelists. Every active public user forum has them. On MaplePrimes, it’s this small number of active members that are highly visible. But, what our traffic data reveals is the silent majority. These people, many of them repeat visitors, are quietly reviewing the questions and answers that our evangelists are posting. The silent majority of MaplePrimes visitors are the readers; they are the quiet consumers of information. For every person that writes, comments on, or likes a post, there are thousands more that read it. 

Here are a few more MaplePrimes traffic data points for your reference:

• MaplePrimes is very international and draws people from all around the world. Here are the top 10 countries where the most MaplePrimes visitors come from:

1. USA
2. India
3. Canada
4. Germany
5. China
6. United Kingdom
7. Brazil
8. Australia
9. France
10. Denmark

• Here are the top 5 keywords people are using in their searches on MaplePrimes:

1. Data from plot
2. Physics
3. Sprintf
4. Size of plot
5. Fractal

• MaplePrimes is growing at a very fast rate: Traffic (visitors to the site) and membership size is growing at nearly double the pace it was last year. The total number of posts and questions this year is also much higher compared to the same timeframe last year. 

• This question has been viewed nearly 50,000 times since it was posted in June 2009: http://www.mapleprimes.com/questions/37261-Sinnpi2

• Our top 5 MaplePrimes members have each visited MaplePrimes more than 1200 times and viewed a combined total of more than 10,000 pages (that is total page views, not unique page views). Our top 25 MaplePrimes members have visited at least 250 times each (many of them nearly 1000 times each) and our top 50 MaplePrimes members have visited a combined total of over 23,000 times, visiting nearly 200,000 pages. Thank you! We’re glad you like it. :-)

Why hasn't mapleprimes yet been able to solve the spam problem.  There was never this long a problem with Mapleprimes 1, every morning I find spam for the last few weeks. 

Also the timing still has yet to be fixed.  After 1 hour the times for when a post was made goes back to 0 minutes ago.

Mathematica 10.3.0 was announced yesterday. This is the 6th release of Mathematica 10 during 16 months. I wonder its  MathematicaFunctionData and   FindFormula . At first sight, the former is an analog of FunctionAdvisor of Maple, but the latter isn't any analog. Also compare the outputs of

Residue[Binomial[n,k],{n,-j}]

(-1)^j/(j!*k!*(-j-k)!)

 and

>`assuming`([residue(binomial(n, k), n = -j)], [integer, j > 0]);

                residue(binomial(n, k), n = -j)
Let us wait for Maple 2016.

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!

This October 21st, Maplesoft will be hosting a full-production, live streaming webinar featuring Dr. Robert Lopez, Emeritus Professor and Maple Fellow. You might have caught Dr. Lopez's Clickable Calculus webinar series before, but this webinar is your chance to meet the man behind the voice and watch him use Clickable Math techniques live!

In this webinar, Dr. Lopez will present examples of what "resequencing concepts and skills" looks like when implemented with Maple's point-and-click syntax-free paradigm. He will demonstrate how Maple can not only be used to elucidate the concept, but also, how it can be used to illustrate and implement the manipulations that ultimately the student must master.

Click here for more information and registration.

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: Rearranging the expression of equations

SY G wanted to be able to re-write an equation in terms of different variables.  SY G presented this example: 

I have the following two equations:

x1 = a-y1-d*y2;
x2 = a-y2-d*y1;

I wish to express the first equation in terms of y1 and x2, so that

x1 = c - b*y1+d*x2;

where c=a-a*d and b=1-d^2. How can I get Maple to rearrange the original equation x1 in term of y1, x2, c and b?

This question was answered by nm who provided code with a systematic approach:

restart;
eq1:=x1=a-y1-d*y2:
eq2:=x2=a-y2-d*y1:
z:=expand(subs(y2=solve(eq2,y2),eq1)):
z:=algsubs((a-a*d)=c,z):
algsubs((1-d^2)=b,z);

On the other hand, Carl Love answered this enquiry using a more direct and simple code:

simplify(x1=a-y1-d*y2, {a-y2-d*y1= x2, 1-d^2= b, a-a*d= c});

Let’s talk more about the expand, algsubs, subs, and simplify commands

First let’s take a look at the method nm used to solve the problem using the commands expand, subs, solve and algsubs.

The expand command, expand(expr, expr1, expr2, ..., exprn), distributes products over sums. This is done for all polynomials. For quotients of polynomials, only sums in the numerator are expanded; products and powers are left alone.

The solve command, solve(equations, variables), solves one or more equations or inequalities for their unknowns.

The subs command, subs(x=a,expr), substitutes a for x in the expression expr.

The function algsubs, algsubs(a = b, f),performs an algebraic substitution, replacing occurrences of a with b in the expression f.  It is a generalization of the subs command, which only handles syntactic substitution.

Let’s tackle the Maple code written by nm step by step:

1) restart;
The restart command is used to clear Maple’s internal memory

2)  eq1:=x1=a-y1-d*y2:
      eq2:=x2=a-y2-d*y1:
The names eq1 and eq2 were assigned to the equations SY G provided.

3) z:=expand(subs(y2=solve(eq2,y2),eq1)):
A new variable, z, was created, which will end up being x1 written in the terms SY G wanted.

• solve(eq2,y2)
  • the solve command was used to solve the expression eq2 for the variable y2.
    
    
• subs(y2=solve(eq2,y2),eq1)
  • The subs command was used to replace in expression eq1, y2 as determined by the solve step. 
    
    
• expand(subs(y2=solve(eq2,y2),eq1))
• The expand command was used to distribute products over sums. Note: this step served to ensure that the final output looked exactly how SY G wanted.

4) z:=algsubs((a-a*d)=c,z):
First, nm equated a-a*d to c, so later the algsubs command could be applied to substitute the new variable c into the expression z.

5) algsubs((1-d^2)=b,z);
Again, nm equated 1-d^2 to b, so later the algsubs command could be applied to substitute the new variable b into the expression z.

An alternate approach

Now let us check out Carl Love’s approach. Carl Love uses the simplify command in conjunction with side relations.

The simplify command has many calling sequences and one of them is the simplify(expr,eqns), that is known as simplify/siderels. A simplification of expr with respect to the side relations eqns is performed. The result is an expression which is mathematically equivalent toexpr but which is in normal form with respect to the specified side relations. Basically you are telling Maple to simplify the expression (expr) using the parameters (eqns) you gave to it.

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. 

 Obtain the tri-stimulus XYZ values from the CIE Color matching functions.

 Show the gamut of maximum chroma for the standard observer model with a D65 Illuminant.

 Approximate the white point of a Planckian source and compare to D65.

 Translate the maximum chroma gamut in xy to Lab (CIE L*a*b*) for perceived gamut (Violet and Magenta come together)

 Map the RGB color cube of fully saturated color into Lab and compare to perceivable colors.

10/6/15  Initial Document

•12/28/15 Improve RGB gamut with more data points: Procedures added for RGB to Lab: Wavlength Colors now based on CIEDE2000 model for Lab.                   

 Here is the latest version of this document, the MSL_data must be in a directory set in the mw file;

MSL_data.xlsx    Vision_RGB_Gamut.mw

In this paper we will demonstrate the many differences of implementation in the modeling of mechanical systems using embedded components through Maplesoft. The mechanical systems are used for different tasks and therefore have different structure in its design; as to the nature of the used functional elements placed on them, they vary greatly. This diversity is reflected in approaches and practices in modeling.

The following cases focus on mechanical components of the units manufacturing and processing machines. We can generate graphs for analysis using different dynamic pair ametros; all in real-time considerations in its manufacturing costs from the equations of conservation of energy.
Therefore modeling with Maplesoft ensures the smooth optimum performance in mechanical systems, highlighting the sustainability criteria for other areas of engineering.

XXXIII_Coloquio_SMP_2015.pdf

XXXIII_Coloquio_UNASAM_2015.mw

(in spanish)

L.AraujoC.

Apparently inconsistent behaviour of the BesselJ() function.

Examples: BesselJ(-3, 0)  ... gives 0 (correct)

but BesselJ(-3.0, 0), BesselJ(-3, 0.0)  and BesselJ(-3, 0.0) all give Float(infinity) (wrong! - should be 0.0)

The problem seems to occur for all negative integer values of the first argument (the order) when the second argument is 0 or 0.0.

Download Physics[Factor].mw

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

We have a new video about plotting with procedures, specifically on how to avoid an error related to evaluation that many people make. 

The worksheet I used in the video is available here:  PlottingWithProcedures.mw

By the way, this mistake doesn't occur just in the context of plotting. Users of Optimization commands (and other commands that allow functions to be expressed as either an expression in a variable or as a procedure) frequently run into this problem too.