| Maple | |
|---|---|
 | |
| Developer | Waterloo Maple (Maplesoft) |
| Initial release | 1982 |
| Stable release | |
| Written in | C,Java, Maple |
| Platform | Windows (10, 11) (64-bit),macOS (13 on Intel or Apple Silicon; 14, 15),Linux[2] |
| Available in | English,Japanese, and limited support in additional languages[3] |
| Type | Computer algebra system,Numeric computation |
| License | Proprietarycommercial software |
| Website | www |
Maple is asymbolic andnumeric computing environment as well as amulti-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-purposecomputer algebra system. For instance, it can manipulate mathematical expressions and find symbolic solutions tocertain problems, such as those arising from ordinary and partialdifferential equations.
Maple is developed commercially by the Canadian software companyMaplesoft. The name 'Maple' is a reference to the software'sCanadian heritage.
Users can enter mathematics in traditionalmathematical 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 adynamically typed imperative-styleprogramming language (resemblingPascal), which permits variables of lexicalscope.[4] There are also interfaces to other languages (C,C#,Fortran,Java,MATLAB, andVisual Basic), as well as toMicrosoft Excel.
Maple supportsMathML 2.0, which is aW3C format for representing and interpreting mathematical expressions, including their display in web pages.[5] There is also functionality for converting expressions from traditional mathematical notation to markup suitable for the typesetting systemLaTeX.
Maple is based on a smallkernel, written inC, 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 theNAG Numerical Libraries,ATLAS libraries, orGMP libraries.
Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory asdirected acyclic graphs. The standard interface and calculator interface are written inJava.
The first concept of Maple arose from a meeting in late 1980 at theUniversity of Waterloo.[6] Researchers at the university wished to purchase a computer powerful enough to run theLisp-based computer algebra systemMacsyma. 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 theBCPL family (initially using a subset ofB andC, and later on only C).[6] A first limited version appeared after three weeks, and fuller versions entered mainstream use beginning in 1982.[7] By the end of 1983, over 50 universities had copies of Maple installed on their machines.[citation needed]
In 1984, the research group arranged withWatcom Products Inc to license and distribute the first commercially available version, Maple 3.3.[7] In 1988Waterloo Maple Inc. (Maplesoft) 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 (the remainder being done at various university laboratories[8]).
In 1989, the first graphical user interface for Maple was developed and included with version 4.3 for theMacintosh. 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.[9] In 1994 a special issue of a newsletter created by Maple developers calledMapleTech was published.[10]
In 1999, with the release of Maple 6, Maple included some of theNAG Numerical Libraries.[11] In 2003, the current "standard" interface was introduced with Maple 9. This interface is primarily written inJava (although portions, such as the rules for typesetting mathematical formulae, are written in the Maple language). The Java interface was criticized for being slow;[12] improvements have been made in later versions, although the Maple 11 documentation[13] recommends the previous ("classic") 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.[14] 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 retailerCybernet Systems.[15]
Features of Maple include:[31]
The following code, which computes the factorial of a nonnegative integer, is an example of animperative programming construct within Maple:
myfac:=proc(n::nonnegint)localout,i;out:=1;forifrom2tondoout:=out*ienddo;outendproc;
Simple functions can also be defined using the "maps to" arrow notation:
myfac:=n->product(i,i=1..n);
Find
int(cos(x/a),x);
Output:
Compute the determinant of a matrix.
M:=Matrix([[1,2,3],[a,b,c],[x,y,z]]);# example Matrix
LinearAlgebra:-Determinant(M);
series(tanh(x),x=0,15)
The following code numerically calculates the roots of a high-order polynomial:
f:=x^53-88*x^5-3*x-5=0fsolve(f)-1.097486315,-.5226535640,1.099074017
The same command can also solve systems of equations:
f:=(cos(x+y))^2+exp(x)*y+cot(x-y)+cosh(z+x)=0:g:=x^5-8*y=2:h:=x+3*y-77*z=55;fsolve({f,g,h});{x=-2.080507182,y=-5.122547821,z=-0.9408850733}
Plot withx ranging from -10 to 10:
plot(x*sin(x),x=-10..10);
Plot withx andy ranging from -1 to 1:
plot3d(x^2+y^2,x=-1..1,y=-1..1);
plots:-animate(subs(k=0.5,f),x=-30..30,t=-10..10,numpoints=200,frames=50,color=red,thickness=3);
plots:-animate3d(cos(t*x)*sin(3*t*y),x=-Pi..Pi,y=-Pi..Pi,t=1..2);
M:=Matrix([[400,400,200],[100,100,-400],[1,1,1]],datatype=float[8]):plot3d(1,x=0..2*Pi,y=0..Pi,axes=none,coords=spherical,viewpoint=[path=M]);
f:=(1+A*t+B*t^2)*exp(c*t);
inttrans:-laplace(f,t,s);
inttrans:-invlaplace(1/(s-a),s,x);
inttrans:-fourier(sin(x),x,w)
Find functionsf that satisfy theintegral equation
eqn:=f(x)-3*Int((x*y+x^2*y^2)*f(y),y=-1..1)=h(x):intsolve(eqn,f(x));
The Maple engine is used within several other products fromMaplesoft:
Listed below are third-party commercial products that no longer use the Maple engine:
| Open-source | |
|---|---|
| Proprietary | |
| Discontinued | |
| Open source | |
|---|---|
| Proprietary |
|
| International | |
|---|---|
| National | |
