Maple (software)

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Maple

Maple 10 interface
Developer:	Waterloo Maple Inc. (Maplesoft)
Latest release:	11 / February 21, 2007
OS:	Cross-platform
Use:	Computer algebra system
License:	Proprietary
Website:	www.maplesoft.com/products/maple/

Maple is a general-purpose commercial mathematics software package. It was first developed in 1981 by the Symbolic Computation Group at the University of Waterloo in Waterloo, Ontario, Canada.

Since 1988, it has been developed and sold commercially by Waterloo Maple Inc. (also known as Maplesoft), a Canadian company also based in Waterloo, Ontario. The current version is Maple 11 which was released in February 2007.

1 Introduction
2 History
3 Origin of the Name
4 Example Maple code
5 Past releases
6 Use of the Maple Engine
7 Versions available
8 See also
9 References
10 External links

[edit] Introduction

Maple combines a programming language with an interface that allows users to enter mathematics in traditional mathematical notation. Most of the mathematical functionality of Maple is written in the Maple language, which is interpreted by the Maple kernel. The Maple kernel is written in C.

The Maple programming language is an interpreted, dynamically typed programming language. As is usual with computer algebra systems, symbolic expressions are stored in memory as directed acyclic graphs. Since Maple 6 the language has permitted variables of lexical scope.

[edit] History

The first concept of Maple arose from a meeting in November 1980 at the University of Waterloo. Researchers at the university wished to purchase a computer powerful enough to run Macsyma. Instead, it was decided that they would develop their own computer algebra system that would be able to run on more reasonably priced computers. Thus, the project began with the goal of creating a symbolic algebra system accessible to researchers and students.

The initial development of Maple proceeded very quickly, with the first limited version appearing in December 1980. Researchers tried and discarded many different ideas creating a continually evolving system. Maple was demonstrated first at conferences beginning in 1982.

By the end of 1983, over 50 universities had copies of Maple installed on their machines. Due to the large number of support and licensing requests, in 1984, the research group arranged with WATCOM Products Inc to license and distribute Maple.

In 1988, due to the increasing requests for support, Waterloo Maple Inc. was founded. The company’s original goal was to manage the distribution of the software. Eventually, the company evolved to have an R&D department where most of Maple’s development is done today. Development of Maple continues at university research labs including: the Symbolic Computation Laboratory at the University of Waterloo; the Ontario Research Centre for Computer Algebra at the University of Western Ontario; and labs at other universities worldwide.

In 1989 the first graphical user interface for Maple was developed and included with version 4.3 for the Macintosh. Prior versions of Maple included only a command line interface with two dimensional output. X11 and Windows versions of the new interface followed in 1990 with Maple V.

In 2003 the current "standard" interface was introduced with Maple 9. This interface is primarily written in Java, however portions, such as the rules for typesetting mathematical formulae, are written in the Maple language. The new interface was widely derided for being slow, and for this reason Maplesoft continued to include the previous "classic" interface while working to improve the performance and features of the new interface.

In 2005 Maple 10 introduced a new "document mode", as part of the standard interface. The main feature of this mode is that math is entered using two dimensional input, appearing similar to a formula in a book.

[edit] Origin of the Name

There is a common belief that the name, Maple, is an acronym. In fact, the name is a reference to Maple’s Canadian heritage.

[edit] Example Maple code

Find $\int\cos\left(\frac{x}{a}\right)dx$ .

int(cos(x/a), x);

Answer: $a \sin\left(\frac{x}{a}\right)$

Calculate the root of the equation $e x = x 2 + 2$ starting at the point $x = - 1$ .

evalf(RootOf(exp(x)=x^2+2,x,-1));

Answer: $1.319073677$

Compute an exact solution to the linear ordinary differential equation $\frac{d^2y}{dx^2}(x) - 3 y(x) = x$ subject to initial conditions $y(0) = 0 ,\quad \left. \frac{dy}{dx} \right|_{y=0} = 2$

dsolve( {diff(y(x),x,x) - 3*y(x) = x, y(0)=0, D(y)(0)=2}, y(x) );

Answer: $y(x)=\frac{7}{18}e^{\sqrt{3}x}\sqrt{3}-\frac{7}{18}e^{-\sqrt{3}x}\sqrt{3}-\frac{1}{3}x$

Plot $x 2 + y 2$ width $x$ and $y$ ranging from -1 to 1

plot3d(x^2+y^2,x=-1..1,y=-1..1);

[edit] Past releases

Maple 11: February 21, 2007
Maple 10: May 10, 2005
Maple 9.5: April 15, 2004
Maple 9: June 30, 2003
Maple 8: April 16, 2002
Maple 7: July 1, 2001
Maple 6: December 6, 1999
Maple V R5: November 1, 1997
Maple V R4: January, 1996
Maple V R3: March 15, 1994
Maple V R2: November 1992
Maple V: August, 1990
Maple 4.3: March, 1989
Maple 4.2: December, 1987
Maple 4.1: May, 1987
Maple 4.0: April, 1986
Maple 3.3: March, 1985 (first publicly available version)
Maple 3.2: April, 1984
Maple 3.1: October, 1983
Maple 3.0: May, 1983
Maple 2.2: December, 1982
Maple 2.15: August, 1982
Maple 2.1: June, 1982
Maple 2.0: May, 1982
Maple 1.1: January, 1982
Maple 1.0: January, 1982

[edit] Use of the Maple Engine

Maple T.A., Maplesoft’s online testing suite uses Maple to algorithmically generate questions and grade student responses.
MapleNet allows users to create JSP pages and Java Applets. MapleNet 10 also allows users to upload and work with Maple worksheets containing interactive components.
Versions of MathCad released between 1994 and 2006 included a Maple-derived algebra engine (MKM, aka Mathsoft Kernel Maple).
The Matlab Symbolic Toolbox contains a portion of the Maple 8 engine.
The mathematical editor Scientific Notebook can use Maple and MuPAD to perform algebraic operations.

[edit] Versions available

Maplesoft sells both student and professional editions of Maple, with a substantial difference in price (US$139 compared to US$1,995.00, respectively).

Recent student editions (from version 6 onwards) have not placed computational limitations but rather come with less printed documentation. This is similar to the difference between Mathematica's student and professional editions.

In releases prior to version 6, the student edition has had the following computational limitations:

A maximum of 100 floating point digits for computations and display.
A maximum size of 8000 (in machine words or objects contained) for any algebraic object.
A maximum of 3 dimensions for arrays.