View source for Maple (software)

{{Short description|Mathematical computing environment}}
{{Other uses|Maple (disambiguation)}}
{{Infobox software
| name = Maple
| logo = Maple 2015 logo.svg
| logo size = 250px
| caption = Maple interface
| developer = [[Waterloo Maple]] (Maplesoft)
| released = 1982
| latest release version = {{Latest stable software release/Maple}}
| programming language = [[C (programming language)|C]], [[Java (programming language)|Java]], Maple
| genre = [[Computer algebra system]], [[Numeric computation]]
| license = [[Proprietary software|Proprietary]] [[commercial software]]
| platform = [[Microsoft Windows|Windows]] (7, 8 and 10), [[macOS]], [[Linux]]
| language = [[English language|English]], [[Japanese language|Japanese]], and limited support in additional languages<ref>{{cite web|url=https://www.maplesoft.com/products/languages/|title=International Language Support in Maple|publisher=[[Maplesoft]]|access-date=2 June 2016}}</ref>
| website = {{url|https://www.maplesoft.com/products/Maple/}}
}}

'''Maple''' is a [[Symbolic computation|symbolic]] and [[Numerical analysis|numeric]] computing environment as well as a [[Programming paradigm#Multi-paradigm|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 [[Flag of Canada|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 [[Type system#Dynamic typing|dynamically typed]] imperative-style [[programming language]] (resembling [[Pascal (programming language)|Pascal]]), which permits variables of lexical [[scope (programming)|scope]].<ref>[http://www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html Power of two] {{Webarchive|url=https://web.archive.org/web/20100706181735/http://www.bitwisemag.com/copy/reviews/software/maths/maple10_mathematica52.html |date=2010-07-06 }} Bitwise Magazine</ref> There are also interfaces to other languages ([[C (programming language)|C]], [[C Sharp (programming language)|C#]], [[Fortran]], [[Java (programming language)|Java]], [[MATLAB]], and [[Visual Basic]]), 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.<ref>{{Cite web|url=http://www.maplesoft.com/standards/MathML/info.html|title=Welcome to the Maplesoft MathML Home Page|website=www.maplesoft.com}}</ref> 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 (operating system)|kernel]], written in [[C (programming language)|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]], [[Automatically Tuned Linear Algebra Software|ATLAS]] libraries, or [[GNU Multi-Precision Library|GMP]] libraries.

Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory as [[directed acyclic graph]]s. The standard interface and calculator interface are written in [[Java (programming language)|Java]].

==History==
The first concept of Maple arose from a meeting in late 1980 at the [[University of Waterloo]].<ref name="MacCallum2018">{{cite journal|last1=MacCallum|first1=Malcolm A. H.|title=Computer algebra in gravity research|journal=Living Reviews in Relativity|volume=21|issue=1|year=2018|page=6|issn=2367-3613|doi=10.1007/s41114-018-0015-6|pmid=30174551|pmc=6105178|bibcode=2018LRR....21....6M |doi-access=free}}</ref> Researchers at the university wished to purchase a computer powerful enough to run the [[Lisp (programming language)|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 (initially using a subset of [[B (programming language)|B]] and [[C (programming language)|C]], and later on only C).<ref name="MacCallum2018"/> A first limited version appeared after three weeks, and fuller versions entered mainstream use beginning in 1982.<ref name="Walz1998">{{cite web|url=http://zakuski.math.utsa.edu/~gokhman/ftp/mirrors/maple/mplhist.htm|title=History of Maple|date=1998-12-15|access-date=2020-04-06}}</ref> By the end of 1983, over 50 universities had copies of Maple installed on their machines.{{Citation needed|date=April 2020}}

In 1984, the research group arranged with [[Watcom|Watcom Products Inc]] to license and distribute the first commercially available version, Maple 3.3.<ref name="Walz1998"/> In 1988 [[Waterloo 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<ref>Two such university labs are the [https://www.scg.uwaterloo.ca/ Symbolic Computation Group] at the [[University of Waterloo]] and the [http://www.orcca.on.ca/ Ontario Research Centre for Computer Algebra] at the [[University of Western Ontario]]</ref>).

<!-- Deleted image removed: [[Image:Maple morphos.png|thumb|300px|Maple V Release 3 for [[Amiga]] (1995), running under [[MorphOS]] ]] -->
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.<ref>[http://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/v52 Maple V Release 2 Notes] Maplesoft</ref> In 1994 a special issue of a newsletter created by Maple developers called ''MapleTech'' was published.<ref>{{Cite web|url=http://web.mit.edu/maple/www/plibrary/mtn/mtn-si94.html|title=MTN Special Issue 1994|website=web.mit.edu}}</ref>

In 1999, with the release of Maple 6, Maple included some of the [[NAG Numerical Libraries]].<ref>[http://www.macworld.com/article/1870/2001/02/21reviewsmaple.html Maple 6.0] {{Webarchive|url=https://web.archive.org/web/20080618032934/http://www.macworld.com/article/1870/2001/02/21reviewsmaple.html |date=2008-06-18 }} Macworld, Feb 2001</ref>  In 2003, the current "standard" interface was introduced with Maple 9. This interface is primarily written in [[Java (programming language)|Java]] (although portions, such as the rules for typesetting mathematical formulae, are written in the Maple language). The Java interface was criticized for being slow;<ref>[http://www.scientific-computing.com/scwoctnov05review.html Capturing knowledge with pure maths], Scientific Computing World.</ref> improvements have been made in later versions, although the Maple&nbsp;11 documentation<ref>[http://www.maplesoft.com/documentation_center/maple11/Install.html Maple 11 Installation Guide] Maplesoft</ref> recommends the previous ("classic") interface for users with less than 500&nbsp;MB of physical memory.

Between 1995 and 2005 Maple lost significant market share to competitors due to a weaker user interface.<ref>[http://history.siam.org/oralhistories/gonnet.htm Interview with Gaston Gonnet, co-creator of Maple] {{webarchive|url=https://web.archive.org/web/20071229044836/http://history.siam.org/oralhistories/gonnet.htm |date=2007-12-29 }}, SIAM History of Numerical Analysis and Computing, 16 March 2005</ref> 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]].<ref>{{Cite web|url=https://www.maplesoft.com/company/news/releases/2009/2009-07-30-cybernet-systems-co-ltd-to-acquire-maple.aspx|title=Maplesoft Media Releases|website=www.maplesoft.com}}</ref>

==Version history==
{{Div col|colwidth=20em}}
*    Maple 1.0: January, 1982
*    Maple 1.1: January, 1982
*    Maple 2.0: May, 1982
*    Maple 2.1: June, 1982
*    Maple 2.15: August, 1982
*    Maple 2.2: December, 1982
*    Maple 3.0: May, 1983
*    Maple 3.1: October, 1983
*    Maple 3.2: April, 1984
*    Maple 3.3: March, 1985 (first public available version)
*    Maple 4.0: April, 1986
*    Maple 4.1: May, 1987
*    Maple 4.2: December, 1987
*    Maple 4.3: March, 1989
*    Maple V: August, 1990
*    Maple V R2: November 1992
*    Maple V R3: March 15, 1994
*    Maple V R4: January, 1996
*    Maple V R5: November 1, 1997
*    Maple 6: December 6, 1999
*    Maple 7: July 1, 2001
*    Maple 8: April 16, 2002
*    Maple 9: June 30, 2003
*    Maple 9.5: April 15, 2004
*    Maple 10: May 10, 2005
*    Maple 11: February 21, 2007
*    Maple 11.01: July, 2007
*    Maple 11.02: November, 2007
*    Maple 12: May, 2008
*    Maple 12.01: October, 2008
*    Maple 12.02: December, 2008
*    Maple 13: April 28, 2009<ref>{{cite web|url=https://www.mapleprimes.com/posts/37445-Maple-13-And-MapleSim-2-Now-Available|title=MaplePrimes Blog - Maple 13 and MapleSim 2 now available|access-date=28 Apr 2009}}</ref>
*    Maple 13.01: July, 2009
*    Maple 13.02: October, 2009
*    Maple 14: April 29, 2010<ref>{{cite web|url=https://www.mapleprimes.com/posts/80867-Announcing-Maple-14-And-MapleSim-4-|title=MaplePrimes Blog - Announcing Maple 14 and MapleSim 4|access-date=29 Apr 2010}}</ref>
*    Maple 14.01: October 28, 2010
*    Maple 15: April 13, 2011<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/103907-Introducing-Maple-15|title=MaplePrimes Blog - Introducing Maple 15|access-date=11 Apr 2011}}</ref>
*    Maple 15.01: June 21, 2011
*    Maple 16: March 28, 2012<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/132249-Maple-16-Is-Here|title=MaplePrimes Blog - Maple 16 is here|access-date=28 Mar 2012}}</ref>
*    Maple 16.01: May 16, 2012
*    Maple 17: March 13, 2013<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/144580-Introducing-Maple-17|title=MaplePrimes Blog - Introducing Maple 17|access-date=13 Mar 2013}}</ref>
*    Maple 17.01: July, 2013
*    Maple 18: Mar 5, 2014<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/200200-Announcing-Maple-18|title=MaplePrimes Blog - Announcing Maple 18|access-date=5 Mar 2014}}</ref>
*    Maple 18.01: May, 2014
*    Maple 18.01a: July, 2014
*    Maple 18.02: Nov, 2014
*    Maple 2015.0: Mar 4, 2015<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/200713-Maple-2015-Is-Now-Available|title=MaplePrimes Blog - Maple 2015 is now available!|access-date=4 Mar 2015}}</ref>
*    Maple 2015.1: Nov, 2015
*    Maple 2016.0: March 2, 2016<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/202794-Announcing-Maple-2016|title=MaplePrimes Blog - Announcing Maple 2016|access-date=2 Mar 2016}}</ref>
*    Maple 2016.1: April 20, 2016
*    Maple 2016.1a: April 27, 2016
*    Maple 2017.0: May 25, 2017<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/208276-Announcing-Maple-2017|title=MaplePrimes Blog - Announcing Maple 2017|access-date=25 May 2017}}</ref>
*    Maple 2017.1: June 28, 2017
*    Maple 2017.2: August 2, 2017
*    Maple 2017.3: October 3, 2017
*    Maple 2018.0: March 21, 2018<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/209095-Maple-2018-Is-Here-|title=MaplePrimes Blog - Maple 2018 is here!|access-date=21 Mar 2018}}</ref>
*    Maple 2019.0: March 14, 2019<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/210286-Announcing-Maple-2019|title=MaplePrimes Blog - Announcing Maple 2019|access-date=14 Mar 2019}}</ref>
*    Maple 2020.0: March 12, 2020<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/212086-Maple-2020-Has-Launched
|title=MaplePrimes Blog - Maple 2020 has launched!|access-date=20 Mar 2020}}</ref>
*    Maple 2021.0: March 10, 2021<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/214351-Unveiling-Maple-2021|title=MaplePrimes Blog - Unveiling Maple 2021|access-date= 2 Mar 2024}}</ref>
*    Maple 2022.0: March 15, 2022<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/217039-Unboxing-Maple-2022|title=MaplePrimes Blog - Unboxing Maple 2022|access-date= 2 Mar 2024}}</ref>
*    Maple 2023.0: March 9, 2023<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/220225-Maple-2023-Is-Here|title=MaplePrimes Blog - Maple 2023 is here!|access-date= 2 Mar 2024}}</ref>
{{div col end}}

==Features==
Features of Maple include:<ref>{{Cite web|url=https://www.maplesoft.com/products/Maple/features/|title=What is Maple: Product Features - Math & Engineering Software - Maplesoft|website=www.maplesoft.com}}</ref>
* Support for symbolic and numeric computation with [[Arbitrary-precision arithmetic|arbitrary precision]]
* [[Elementary function|Elementary]] and [[Special functions|special mathematical function]] libraries
* [[Complex number]]s and interval arithmetic
* Arithmetic, [[greatest common divisor]]s and [[factorization]] for [[multivariate polynomial]]s over the rationals, [[finite field]]s, [[algebraic number field]]s, and [[algebraic function field]]s
* Limits, series and [[asymptotic expansion]]s
* [[Gröbner basis]]
* Differential Algebra
* [[Matrix operation#Basic operations|Matrix manipulation]] tools including support for [[sparse array]]s
* Mathematical [[function graphing]] and animation tools
* Solvers for [[systems of equations]], [[diophantine equation]]s, [[Ordinary differential equation|ODEs]], [[Partial differential equation|PDEs]], [[Differential algebraic equation|DAEs]], [[Delay differential equation|DDEs]] and [[recurrence relation]]s 
* Numeric and symbolic tools for discrete and continuous [[calculus]] including definite and [[indefinite integration]], definite and [[indefinite sum]]mation, automatic differentiation and continuous and discrete [[integral transform]]s
* Constrained and unconstrained local and global [[Mathematical optimization|optimization]]
* [[Statistics]] including model fitting, [[hypothesis testing]], and [[probability distribution]]s
* Tools for data manipulation, visualization and analysis
* Tools for probability and [[combinatoric]] problems
* Support for time-series and unit based data
* Connection to online collection of financial and economic data
* Tools for financial calculations including bonds, annuities, derivatives, options etc.
* Calculations and simulations on random processes
* Tools for [[text mining]] including [[regular expressions]]
* Tools for [[signal processing]] and linear and non-linear [[control system]]s
* [[Discrete math]] tools including [[number theory]]
* Tools for visualizing and analysing directed and undirected [[graph (discrete mathematics)|graphs]]
* Group theory including permutation and finitely presented groups
* Symbolic tensor functions
* Import and export filters for data, image, sound, [[computer-aided design|CAD]], and document formats
* Technical word processing including [[formula editor|formula editing]] 
* Programming language supporting [[Procedural programming|procedural]], [[Functional programming|functional]] and [[Object-oriented programming|object-oriented]] constructs
* Tools for adding [[user interface]]s to calculations and applications
* Tools for connecting to [[SQL]], [[Java (software platform)|Java]], [[.NET Framework|.NET]], [[C++]], [[Fortran]] and [[Hypertext Transfer Protocol|http]]
* Tools for generating code for [[C (programming language)|C]], [[C Sharp (programming language)|C#]], [[Fortran]], [[Java (programming language)|Java]], [[JavaScript]], [[Julia (programming language)|Julia]], [[Matlab]], [[Perl]], [[Python (programming language)|Python]], [[R (programming language)|R]], and [[Visual Basic]]
* Tools for [[parallel programming]]

==Examples of Maple code==
The following code, which computes the factorial of a nonnegative integer, is an example of an [[imperative programming]] construct within Maple:

<syntaxhighlight lang="maple">
myfac := proc(n::nonnegint)
   local out, i;
   out := 1;
   for i from 2 to n do
       out := out * i
   end do;
   out
end proc;
</syntaxhighlight>
Simple functions can also be defined using the "maps to" arrow notation:
<syntaxhighlight lang="maple">
 myfac := n -> product(i, i = 1..n);
</syntaxhighlight>

===Integration===
Find
:<math>\int\cos\left(\frac{x}{a}\right)dx</math>.
<syntaxhighlight lang="maple">
 int(cos(x/a), x);
</syntaxhighlight>
Output:
:<math>a \sin\left(\frac{x}{a}\right)</math>

===Determinant===
Compute the determinant of a matrix.
<syntaxhighlight lang="maple">
 M := Matrix([[1,2,3], [a,b,c], [x,y,z]]);  # example Matrix
</syntaxhighlight>
: <math>
  \begin{bmatrix}
    1 & 2 & 3 \\
    a & b & c \\
    x & y & z
  \end{bmatrix}
</math>
 LinearAlgebra:-Determinant(M);
: <math>bz-cy+3ay-2az+2xc-3xb</math>

===Series expansion===
<syntaxhighlight lang="maple">
series(tanh(x), x = 0, 15)
</syntaxhighlight>
:<math>x-\frac{1}{3}\,x^3+\frac{2}{15}\,x^5-\frac{17}{315}\,x^7</math>
:<math>{}+\frac{62}{2835}\,x^9-\frac{1382}{155925}\,x^{11}+\frac{21844}{6081075}\,x^{13}+\mathcal{O}\left(x^{15}\right)</math>

===Solve equations numerically===
The following code numerically calculates the roots of a high-order polynomial:
<syntaxhighlight lang="maple">
 f := x^53-88*x^5-3*x-5 = 0

 fsolve(f)

 -1.097486315, -.5226535640, 1.099074017
</syntaxhighlight>

The same command can also solve systems of equations:
<syntaxhighlight lang="maple">
 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}
</syntaxhighlight>

===Plotting of function of single variable===
Plot <math>x \sin(x)</math> with {{mvar|x}} ranging from -10 to 10:
<syntaxhighlight lang="maple">
 plot(x*sin(x), x = -10..10);
</syntaxhighlight>
[[Image:Maple1DPlot.PNG|thumb|center|300px]]

===Plotting of function of two variables===
Plot <math>x^2+y^2</math> with {{mvar|x}} and {{mvar|y}} ranging from -1 to 1:
<syntaxhighlight lang="maple">
plot3d(x^2+y^2, x = -1..1, y = -1..1);
</syntaxhighlight>
[[Image:Maple163DPlot.jpg|thumb|center|300px]]

===Animation of functions===
* Animation of function of two variables
:<math>f := \frac{2k^2}{\cosh^2\left(x k - 4 k^3 t\right)}</math>
<syntaxhighlight lang="maple">
plots:-animate(subs(k = 0.5, f), x=-30..30, t=-10..10, numpoints=200, frames=50, color=red, thickness=3);
</syntaxhighlight>
[[File:Bellsoliton2.gif|thumb|center|300px|2D bell solution]]

* Animation of functions of three variables
<syntaxhighlight lang="maple">
plots:-animate3d(cos(t*x)*sin(3*t*y), x=-Pi..Pi, y=-Pi..Pi, t=1..2);
</syntaxhighlight>
[[File:3dsincos animation.gif|thumb|center|300px|3D animation of function]]

* Fly-through animation of 3-D plots.<ref>[http://www.maplesoft.com/applications/view.aspx?SID=33073&view=html Using the New Fly-through Feature in Maple 13] Maplesoft</ref>
<syntaxhighlight lang="maple">
 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]);
</syntaxhighlight>
[[File:Maple plot3D flythrough.gif|thumb|center|300px|Maple plot3D fly-through]]

===Laplace transform===
* [[Laplace transform]]
<syntaxhighlight lang="maple">
f := (1+A*t+B*t^2)*exp(c*t);
</syntaxhighlight>
:<math> \left(1 + A \, t + B \, t^2\right) e^{c t}</math>
<syntaxhighlight lang="maple">
 inttrans:-laplace(f, t, s);
</syntaxhighlight>
:<math>\frac{1}{s-c}+\frac{A}{(s-c)^2}+\frac{2B}{(s-c)^3}</math>

* inverse Laplace transform
<syntaxhighlight lang="maple">
inttrans:-invlaplace(1/(s-a), s, x);
</syntaxhighlight>
: <math>e^{ax}</math>

===Fourier transform===
* [[Fourier transform]]
<syntaxhighlight lang="maple">
 inttrans:-fourier(sin(x), x, w)
</syntaxhighlight>
:<math>\mathrm{I}\pi\,(\mathrm{Dirac}(w+1)-\mathrm{Dirac}(w-1))</math>

===Integral equations===
Find functions {{mvar|f}} that satisfy the [[integral equation]]
:<math>f(x)-3\int_{-1}^1(xy+x^2y^2)f(y)dy = h(x)</math>.
<syntaxhighlight lang="maple">
eqn:= f(x)-3*Int((x*y+x^2*y^2)*f(y), y=-1..1) = h(x):
intsolve(eqn,f(x));
</syntaxhighlight>
:<math>f \left( x \right) =\int _{-1}^{1}\! \left( -15\,{x}^{2}{y}^{2}-3\,xy \right) h \left( y \right) {dy}+h \left( x \right)
</math>

==Use of the Maple engine==
The Maple engine is used within several other products from [[Maplesoft]]:
* MapleNet allows users to create [[JavaServer Pages|JSP]] pages and [[Java (programming language)|Java]] [[Applets]]. MapleNet 12 and above also allow users to upload and work with [[Notebook interface|Maple worksheets]] containing interactive components.
* [[MapleSim]], an engineering simulation tool.<ref>{{cite journal|last1=Mahmud|first1=Khizir|last2=Town|first2=Graham E.|title=A review of computer tools for modeling electric vehicle energy requirements and their impact on power distribution networks|journal=Applied Energy|date=June 2016|volume=172|pages=337–359|doi=10.1016/j.apenergy.2016.03.100|bibcode=2016ApEn..172..337M }}</ref>
* Maple Quantum Chemistry Package from RDMChem computes and visualizes the electronic energies and properties of molecules.<ref>{{cite web|url=https://www.mapleprimes.com/maplesoftblog/210517-Introducing-The-Maple-Quantum-Chemistry-Toolbox|title=MaplePrimes Blog - Introducing the Maple Quantum Chemistry Toolbox|access-date=6 May 2019}}</ref>

Listed below are third-party commercial products that no longer use the Maple engine:
* Versions of [[Mathcad]] released between 1994 and 2006 included a Maple-derived algebra engine (MKM, aka [[Mathsoft]] Kernel Maple), though subsequent versions use [[MuPAD]].
* Symbolic Math Toolbox in [[MATLAB]] contained a portion of the Maple 10 engine, but now uses [[MuPAD]] (starting with MATLAB R2007b+ release).<ref>{{cite web|title=Release Notes for Symbolic Math Toolbox|url=http://www.mathworks.com/help/symbolic/release-notes.html#brqy3xk|publisher=MathWorks|access-date=10 July 2014}}</ref>
* Older versions of the mathematical editor [[Scientific Workplace]] included Maple as a computational engine, though current versions include [[MuPAD]].

==See also==
{{div col|colwidth=30em}}
* [[Comparison of computer algebra systems]]
* [[Comparison of numerical-analysis software]]
* [[Comparison of programming languages]]
* [[Comparison of statistical packages]]
* [[List of computer algebra systems]]
* [[List of computer simulation software]]
* [[List of graphing software]]
* [[List of numerical-analysis software]]
* [[Mathematical software]]
* [[SageMath|SageMath (an open source algebra program)]]
{{div col end}}

==References==
{{Reflist|30em}}

==External links==
{{Commons category}}
{{Wikibooks|Maple}}
* [https://www.maplesoft.com Maplesoft, division of Waterloo Maple, Inc.] – official website

{{Computer algebra systems}}
{{Numerical analysis software}}
{{Statistical software}}
{{Deep_Learning_Software}}
{{Fractal software}}
{{Graph Analysis Software}}
{{Authority control}}

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