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Preface


Technical computation forms the heart of problem solving in mathematics, engineering, and science. To help you, Maple™ offers a vast repository of mathematical algorithms covering a wide range of applications.
At the core of Maple, the symbolic computation engine is second to none in terms of scalability and performance. Indeed, symbolics was the core focus when Maple was first conceived at the University of Waterloo in 1980 and to this day Maple continues to be the benchmark software for symbolic computing.
Together with a large repository of numeric functionality, including industrystandard libraries such as the Intel® Math Kernel Library (MKL), Automatically Tuned Linear Algebra Software (ATLAS), and the C Linear Algebra PACKage (CLAPACK), as well as a broad selection of routines from the Numerical Algorithms Group (NAG® ) libraries, you can rely on Maple to support you a across many domains and applications. Using its unique hybrid technology, Maple integrates the symbolic and numeric worlds to solve diverse problems more efficiently and with higher accuracy.
The Maple user interface allows you to harness all this computational power by using contextsensitive menus, task templates, and interactive assistants. The first steps are intuitively easy to use and quickly lead you into the captivating, creative, and dynamic world of Maple.
As you get more proficient, you will want to explore more deeply and directly access all of the computational power available to you. You can accomplish this through the Maple programming language. Combining elements from procedural languages (such as Pascal), functional languages (such as Lisp) and objectoriented languages (such as Java™ ), Maple provides you with an exceptionally simple yet powerful language to write your own programs. Highlevel constructs such as map allow you to express in a single statement what would take ten lines of code in a language like C.
Maple allows you to quickly focus and reliably solve problems with easy access to over 5000 algorithms and functions developed over 30 years of cuttingedge research and development.
Maple's user community is now over two million people. Together we have built large collections of Maple worksheets and Maple programs, much of which is freely available on the web for you to reuse or learn from. The majority of the mathematical algorithms you find in Maple today are written in the Maple Programming Language. As a Maple user, you write programs using the same basic tools that the Maple developers themselves use. Moreover you can easily view most of the code in the Maple library and you can even extend the Maple system, tying your programs in with existing functionality.
This guide will lead you from your first steps in Maple programming to writing sophisticated routines and packages, allowing you to tackle problems in mathematics, engineering, and science effectively and efficiently. You will quickly progress towards proficiency in Maple programming, allowing you to harness the full power of Maple.
Have fun!

Audience


This guide provides information for users who are new to Maple programming, as well as experienced Maple programmers. Before reading this guide, you should be familiar with the following.
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How to use Maple interactively



Maple User Interfaces


You can access Maple functionality through several user interfaces. Maple interfaces accept user input, communicate with the Maple computational engine, and display solutions to mathematical problems.

The Standard Interface


The standard interface facilitates the performance of computations and lets you manipulate mathematical expressions. It also provides layout and document processing features that you can use to annotate your problemsolving process. The standard interface will be the focus of this guide.
To display the standard interface, doubleclick your Maple desktop icon (Windows® and Macintosh®) or run the xmaple command (UNIX®).


Other Maple Interfaces


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MapleNet™ lets you publish your interactive Maple documents on the web. Users with an Internet connection can then view and manipulate your published documents in a web browser. MapleNet also provides a web service interface that allows connected applications to pass data to Maple, run a program, and retrieve results. It also lets you create custom JavaServer™ Pages (JSP) applications and Java applets. For more information about MapleNet, see MapleNet.

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OpenMaple™ is the Maple application programming interface (API) that lets you build custom user interfaces or embed Maple in an existing application. OpenMaple can be used with a variety of languages including C, C++, Java, Fortran, Visual Basic®, and C#. For more information about OpenMaple, see OpenMaple.

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The Maple commandline interface is a consolebased application that can be used for batch processing Maple command files. For more information, see The Maple Commandline Interface.

For more information about the Maple user interfaces, refer to the Maple User Manual or the versions help page.



Programming in the Standard Interface


Most of the time, you will enter Maple code directly in a worksheet or document. The standard interface also provides other functionality for entering Maple code. For example, you can enter your code in a startup code region if you want to run certain commands or procedures automatically when a Maple document is opened. You can also enter your code in a code edit region if you want to keep a set of Maple commands or procedures in a confined region within your document. For more information, refer to the worksheet,documenting,startupcode and CodeEditRegion help pages.
You can also include your code in an external text file to be read by a worksheet or document, or batch processed. For more information, refer to the file help page.

Document Mode and Worksheet Mode


Two modes of interactive operation are available in the standard interface: document mode and worksheet mode.
In document mode, you enter mathematical expressions within document blocks; no Maple input prompt (>) or execution group boundaries are displayed in the document. You can use this mode to create professional reports that combine text and typeset math with plots, images, and other interactive components.
In worksheet mode, you enter mathematical expressions at input prompts, which are displayed at the start of each input line in a Maple document. When you type an expression and press Enter, the expression is evaluated and a new input prompt is displayed in the next line. In both modes, the default format for entering mathematical text is 2D math notation.
Both modes are equally suitable for creating and running programs in Maple. Select the mode that suits your preferences and tasks. For more information about both modes, refer to the worksheet,help,documentsvsworksheets help page.


1D and 2D Math Notation


When programming in Maple, you must also consider whether to use 2D math notation or 1D math notation. In 2D math notation, typeset mathematical text is displayed in black italicized characters.
$\∫\mathrm{sin}\left(x\right)\phantom{\rule[0.0ex]{0.3em}{0.0ex}}\ⅆx$
In 1D math notation (or Maple input), mathematical text is displayed in a red fixedwidth font that is not typeset.
1D math notation can be used in external text files to write Maple code that can be read by a worksheet or batch processed. You can enter individual statements in 1D math notation or configure Maple to display mathematical input in 1D math by default in all future Maple sessions.
Note: While 2D math is the recommended format for mathematical text and equations and can be used for short command sequences and procedures, it is generally not recommended for long programs and package definitions.
Most input in this guide is shown in 1D math notation. To clearly distinguish commands and input, this guide uses a leading prompt character (>) and all input is entered in worksheet mode.
For more information on starting Maple, toggling between 1D and 2D math notation, and managing your files, refer to the Maple User Manual or enter ?managing at the Maple prompt.



Web Resources


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Maplesoft Application Center: The Application Center provides thousands of complete applications that you can download and use in Maple. For more information, visit http://www.maplesoft.com/applications.

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MaplePrimes™: MaplePrimes is an online forum where you can search for tips and techniques, read blogs, and discuss your work in Maple with an active community. For more information, visit http://www.mapleprimes.com.

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Maplesoft Online Help: Documentation included with Maple is also posted online. The web version offers the latest updates, Google™based searching, and an easy way to provide feedback on help documentation. For more information, visit, http://www.maplesoft.com/support/help.

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Teacher Resource Center: The Teacher Resource Center provides course content, lecture notes, demonstrations, and other resources to help teachers incorporate Maple in their classrooms. For more information, visit http://www.maplesoft.com/TeacherResource.

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Student Resource Center: The Student Resource Center provides online forums, training videos, and other resources to help students with their work in Maple. For more information, visit http://www.maplesoft.com/studentcenter.

For additional resources, visit http://www.maplesoft.com.


Conventions


This guide uses the following typographical conventions.
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bold font  Maple command, package name, option name, dialog box, menu, or text field

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italics  new or important concept

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Note  additional information that is relevant to a concept or section

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Important  information that must be read and followed



Customer Feedback


Maplesoft welcomes your feedback. For suggestions and comments related to this and other manuals, contact doc@maplesoft.com.


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