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Another feature added to Maple 15 partially in response to the MaplePrimes forums is the new/improved ?HTTP package.  It provides one-step commands for fetching data from the web: much simpler than using the ?Sockets package directly. In most cases, the command ?HTTP,Get is what you would use:

 (s, page, h) := HTTP:-Get(""):

The above fetches the HTML source of a page from Wikipedia and stores it as a string 'page'. The other two outputs are 's', and integer HTTP status code and 'h' a table of the headers returned in the HTTP response from the server.  Compare this to the amount of code needed to fetch data in my Baby Names application for Maple 12, for example.

In part due to a large number of requests on MaplePrimes, the command ?plottools,getdata was added to Maple 15. This new command gives programmers a better way to access the internals of plots and do things with the data they contain.

I was trying to come up with something really fun to do with this command, and another recent obsession came to mind: the game Minecraft.  Minecraft is nice, since like Maple it is written in Java and runs on lots of platforms!  For the uninitiated, Minecraft is a a sort of mostly unstructured "sandbox" game. The player starts in alone in a procedurally generated landscape consisting of blocks. They player can collect blocks with their hands or with tools and they use them to build new things. The wide array of things that people create in Minecraft is staggering.

So, I thought I would write some commands to export 3D plots in Maple to block structures in Minecraft.

Classic Triangle Peg Board GameIn high school I was briefly fascinated by a triangular "jump all but one" game, commonly found at Cracker Barrel restaurants.  The basic premise is that any peg can "jump" over an adjacent peg to occupy the empty hole next to the jumped peg.  The jumped peg is then removed.  The goal is to continue jumping pegs until there is only one left.  

The instructions on the face of the Cracker Barrel version of this game say, "LEAVE ONLY ONE -- YOU'RE A GENIUS".  Wanting to claim the right to call myself a genius, unlike ordinary kids, who might just play the game a few times, I sat down on my Turbo-XT and started writing BASIC code.  The algorithm I came up with ran a bit slow, so I directed output to my printer and let it run over night.  In the morning the program was still chugging along.  I advanced the paper feed on the dot-matrix lineprinter -- the kind that used continuous feed paper with perforated edges and holes on each side.   Into view came 3 solutions represented by a string of numbers.   A quick check verified that I was now a genius.  

Now that Maple 15 is out, I thought I should share this little application I made: It is an application partially inspired by the BMI tracker in Nintendo's WiiFit application; you could easily use it to track a weight loss goal. But it could also be used to track other quantifiable goals. I am posting it here mostly because it takes advantage of two new features in Maple 15.

Introducing Maple 15...

April 07 2011 laurent 680 Maple

I am pleased to announce that Maple 15 will be available on April 13. We are very proud of this new release of Maple, which has been twelve months in the making, and I...

Each of my two previous two blog posts (Maple Gems, More Maple Gems) contained five "gems" from my Little Red Book of Maple Magic, a red ring-binder in which I record...

Back when I was working at the University of Waterloo, I found several copies of a VHS tape sitting on a dusty bookshelf full of old Maple boxes and manuals. The tape's cover had a line drawing of Issac Newton on it and the title "Maple V: The Future of Mathematics".

There was...

I had originally planned for a light-hearted post on a recent customer visit that I recently made in Europe but in light of the events in Japan these past few days, it somehow seemed terribly inappropriate. Around the world, people are coming to grips with this recent series of disasters, but for us at Maplesoft, being part of the global Cybernet corporate team, there are very personal dimensions.

The good news is that all of our colleagues at Cybernet Systems, headquartered...

In a recent blog post, I discussed five "gems" in my Little Red Book of Maple Magic, a notebook I use to keep track of the Maple wisdom I glean from interactions with the Maple programmers in the building. Here are five more such "gems" that appeared in a Tips & Techniques column in a recent issue of the ...


Update - April 4, 2011: I corrected a typo in Table 2, first column, bottom row.  What was sqrt(6) has been changed to sqrt(5).


Since coming to Maplesoft in 2003, I've kept a notebook of "gems" I've gleaned from consulting with the programmers in the building. I call it my "Little Red Book of Maple Magic." It really is red. The first spiral-bound notebook was little, and it was red. When it overflowed, I moved the notes to a red ring-binder. But it's not so little any more.

This post will explain how to configure the compiler and other tools that will be necessary for you to build the External Calling examples that will come in later posts.  This is an advanced topic and so this post is fairly complex.

First, I am going to be using the compilers via the command line, so you will need to familarize yourself with the terminal program on your particular OS.  You'll have to do this for yourself, but here are a few starting points:



I am going to assume that Linux and Solaris users are familar with using the terminal.

For Linux, Apple and Solaris, I am going to use gcc as the compiler.  For Linux you should use your distribution's package management system to get it, for Apple you need to install Xcode and for Solaris, well, gcc is probably already installed or you'll want to talk to you sys admin to have it installed (or if you are your own sys admin, you probably know how to install gcc for yourself).  For Windows, you need to install the Windows Software Development Kit.  If you already have a copy of Visual Studio C++ (Express or Professional) installed, then you already have these tools.

I am also going to use the "make" program to manage the building of the examples, thus you will need to install a version of make as well (you won't need to learn how make works unless you want to modify the examples).  I will be using gnu make, which should be easy to install on Linux and Solaris (similar to how you installed gcc) and it is included in Xcode for Apple.  For Windows, use this:

Installing 32 bit make on 64 bit windows is fine.

Now you'll need to launch a terminal.  For Linux, Apple and Solaris this should be easy, on Windows go to the Windows SDK folder (or Windows Visual Studio folder) on the Start menu, there should be an icon for Windows SDK Command Prompt.  Click that to launch the terminal.  This version of the terminal has the environment configured to run the compiler.

On Windows you'll also have to add the location you installed make to your path, which can be done on 32 bit windows like this:

path=%PATH%;C:\Program Files\GnuWin32\bin

and on 64 bit Windows like this:

path=%PATH%;C:\Program Files (x86)\GnuWin32\bin

assuing you used the default install location for make.

You can test this by running "make" in the terminal.  If everything is set up correctly, make should run but not find a Makefile and it will raise an error.  If the path is not set properly, make won't be found you'll get a message saying that.

Path not set properly:

C:\Program Files\Microsoft SDKs\Windows\v7.1>make
'make' is not recognized as an internal or external command,
operable program or batch file.

Set the path:

C:\Program Files\Microsoft SDKs\Windows\v7.1>path=%PATH%;"C:\Program Files (x86)

Make is now found, but there is no makefile in the current directory

C:\Program Files\Microsoft SDKs\Windows\v7.1>make
make: *** No targets specified and no makefile found.  Stop.

As a final test, I've attached a small example ( that contains a Makefile and a simple source file.  If you extract the files to a new directory, go to that new directoy in the terminal and run make (with make added to the path as described above) it should build an executable (test or test.exe).  You can run the executable by executing "test" on the command line.

By default the Makefile is configured for Windows, so Windows users won't need to change it, however other users will need to comment out the


line in Makefile by changing it to


I know this is a little confusing, especially if you are not familar with the command line interface, therefore I encourage you post replies if you have problems.  Hopefully we will be able to answer your questions.  Once everyone has figured out how to get this simple example to compile and run on their system, the upcoming external calling examples will be (relatively) easy.

Good Luck!


A prospective customer recently asked if we had a MapleSim model of a double pipe heat exchanger. Heat exchangers are a critical unit operation in the process industries, and accurate models are needed for process control studies.  I couldn't find an appropriate model so I decided to derive the dynamic equations, and implement them using MapleSim's custom component interface.  I'll outline my modeling strategy in this blog post.

I've had a few request to provide some more information on External Calling, so I thought I would make a few posts about it. This first post will be a high level description of External Calling and how it works, with examples coming later. As External Calling is an advanced topic, I am going to assume you know how to compile a shared library and are generally familiar with the C language. Although this first post won't require any real programming knowledge.

What is External Calling?

External Calling is the name for Maple's ability to connect to and call functions from other programming languages. Maple uses this for various reasons. We have written our own libraries in C, C++ and Java to solve particular problems. We partner with various labs around the world who have developed code, often in languages like C or C++, so external calling is used to interface with their code. We also connect to high performance libraries like NAG and BLAS to provide those high performance routines in Maple. Of course, you can use External Calling to connect Maple to your code as well.

Although Maple can call various programming languages, the most common languages we connect to are C and C++, and those are the languages I am going to focus on.

How does it work?

In Maple, you call ?define_external or use the ?ExternalCalling package. Both these methods take a description of the function that you want to call and returns a Maple procedure. Normally you would assign the procedure to a name and then call the externally defined function just like any other Maple procedure.

There are a couple different ways to use define_external to connect to a shared library, the differences are mostly concerned with how the parameters given in Maple are converted to parameters used in the external function.

  • Wrapperless external calling. With wrapperless external calling, Maple calls a function implemented in the shared library by automatically converting the values given in Maple into valid types for the external function.
  • Generated wrappers: With generated wrappers, Maple automatically generates a small C library that handles conversions from Maple values to the values used in the external function. Using generated wrappers allows Maple to handle more data types, like call back procedures.
  • Custom wrappers: A custom wrapper is a C function that you write yourself. This function accepts arguments as Maple data structures and returns a Maple data structure. You are responsible for converting the Maple data structures into whatever forms you need and converting your computed value back into a Maple data structure. Maple provides the External Calling API to assist in working with Maple from the externally defined function.

The first two forms of external calling are the easiest to do, however they are also the most limited. Internally we exclusively (I think) use the third, custom wrapper, form of external calling. That is the form I am going to talk about.

Custom Wrapper

The name "custom wrapper" is a bit of a misnomer. The function that you write does not need to "wrap" anything, it can implement anything you want. As long as you can convert the result into a Maple data structure, you can pass it back into Maple. In fact Maple also supports returning generic data, via the ?MaplePointer routines, but that is a more complex topic for a later blog post.

Your external function is simply a C function with the following calling convention:

ALGEB CustomWrapper( MKernelVector kv, ALGEB args )

ALGEB is the C data type that represents a Maple data structure. The MKernelVector is a data structure that acts as an intermediary between your external calling routines and the Maple engine. You will need to pass this structure back into the External Calling API functions. Both of these types, plus the External Calling API functions are defined in a header, maplec.h, that needs to be included in your code. I will provide more details when I provide examples.

The External Calling API

The External Calling API is a set of functions that we make available for working with the Maple Engine from external code. Maple also allows third party applications to load the Maple engine as a shared library, we call this ?OpenMaple. The External Calling functions are also available in OpenMaple, so you will often see OpenMaple used in the Maple help pages. Most functions can be used in both OpenMaple and External Calling, except for a few that are OpenMaple specific and involve starting and stopping the Maple Engine.

Maple's help system documents all the External Calling functions so you can see what is available. There is an overview of the external calling functions on this page, ?ExternalCalling,C,API. Briefly, however there are functions for converting Maple types to C and back, creating and interacting with Maple data structures (list, set, rtable, table, string, etc), creating and interacting with Maple language elements (names, procedures, etc), printing to the Maple interface, memory allocation, evaluating Maple statements and raising exceptions. There is even a C interface to the Task Programming Model.

Next Time...

In my next post I will provide some examples of using the External Calling API to actually do stuff in an externally defined procedure.  However, I am going to spend some time trying to figure out the easiest way for you to get the tools you'll need to be able to develop externally defined functions yourself, so my next post might take a bit of time.


I have always preferred the notation  for the derivative of

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