Maple (software)


Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.
Maple's capacity for symbolic computing include those of a general-purpose computer algebra system. For instance, it can manipulate mathematical expressions and find symbolic solutions to
certain problems, such as those arising from ordinary and partial differential equations.
Maple is developed commercially by the Canadian software company Maplesoft. The name 'Maple' is a reference to the software's Canadian heritage.

Overview

Core functionality

Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and visualization. Examples of symbolic computations are given below.
Maple incorporates a dynamically typed imperative-style programming language, which permits variables of lexical scope. There are also interfaces to other languages, as well as to Microsoft Excel.
Maple supports MathML 2.0, which is a W3C format for representing and interpreting mathematical expressions, including their display in web pages. There is also functionality for converting expressions from traditional mathematical notation to markup suitable for the typesetting system LaTeX.

Architecture

Maple is based on a small kernel, written in C, which provides the Maple language. Most functionality is provided by libraries, which come from a variety of sources. Most of the libraries are written in the Maple language; these have viewable source code. Many numerical computations are performed by the NAG Numerical Libraries, ATLAS libraries, or GMP libraries.
Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory as directed acyclic graphs. The standard interface and calculator interface are written in Java.

History

The first concept of Maple arose from a meeting in late 1980 at the University of Waterloo. Researchers at the university wished to purchase a computer powerful enough to run the Lisp-based computer algebra system Macsyma. Instead, they opted to develop their own computer algebra system, named Maple, that would run on lower cost computers. Aiming for portability, they began writing Maple in programming languages from the BCPL family. A first limited version appeared after three weeks, and fuller versions entered mainstream use beginning in 1982. By the end of 1983, over 50 universities had copies of Maple installed on their machines.
In 1984, the research group arranged with Watcom Products Inc to license and distribute the first commercially available version, Maple 3.3. In 1988 Waterloo Maple Inc. was founded. The company’s original goal was to manage the distribution of the software, but eventually it grew to have its own R&D department, where most of Maple's development takes place today.
In 1989, the first graphical user interface for Maple was developed and included with version 4.3 for the Macintosh. X11 and Windows versions of the new interface followed in 1990 with Maple V. In 1992, Maple V Release 2 introduced the Maple "worksheet" that combined text, graphics, and input and typeset output. In 1994 a special issue of a newsletter created by Maple developers called MapleTech was published.
In 1999, with the release of Maple 6, Maple included some of the NAG Numerical Libraries. In 2003, the current "standard" interface was introduced with Maple 9. This interface is primarily written in Java. The Java interface was criticized for being slow; improvements have been made in later versions, although the Maple 11 documentation recommends the previous interface for users with less than 500 MB of physical memory.
Between 1995 and 2005 Maple lost significant market share to competitors due to a weaker user interface. With Maple 10 in 2005, Maple introduced a new "document mode" interface, which has since been further developed across several releases.
In September 2009 Maple and Maplesoft were acquired by the Japanese software retailer Cybernet Systems.

Version history

Features of Maple include:
The following code, which computes the factorial of a nonnegative integer, is an example of an imperative programming construct within Maple:

myfac := proc
local out, i;
out := 1;
for i from 2 to n do
out := out * i
end do;
out
end proc;

Simple functions can also be defined using the "maps to" arrow notation:

myfac := n -> product;

Integration

Find

int;

Output:

Determinant

Compute the determinant of a matrix.

M := Matrix; # example Matrix

LinearAlgebra:-Determinant;

Series expansion


series

Solve equations numerically

The following code numerically calculates the roots of a high-order polynomial:

f := x^53-88*x^5-3*x-5 = 0
fsolve
-1.097486315, -.5226535640, 1.099074017

The same command can also solve systems of equations:

f := ^2 + exp*y+cot+cosh = 0:
g := x^5 - 8*y = 2:
h := x+3*y-77*z=55;

fsolve;

Plotting of function of single variable

Plot with ranging from -10 to 10:

plot;

Plotting of function of two variables

Plot with and ranging from -1 to 1:

plot3d;

Animation of functions


plots:-animate;


plots:-animate3d*sin;


M := Matrix:
plot3d;

Laplace transform


f := *exp;


inttrans:-laplace;


inttrans:-invlaplace;

Fourier transform


inttrans:-fourier

Integral equations

Find functions that satisfy the integral equation

eqn:= f-3*Int*f = h:
intsolve;

Use of the Maple engine

The Maple engine is used within several other products from Maplesoft:
Listed below are third-party commercial products that no longer use the Maple engine: