MuPAD
Encyclopedia
MuPAD is a computer algebra system
(CAS). Originally developed by the MuPAD research group at the University of Paderborn
, Germany
, development was taken over by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities starting in 1997.
Until autumn 2005, the version "MuPAD Light" was offered for free for research and education, but as a result of the closure of the home institute of the MuPAD research group, only the version "MuPAD Pro" became available for purchase.
The MuPAD kernel is bundled with Scientific Notebook and Scientific Workplace
. Former versions of MuPAD Pro were bundled with SciLab
. Its version 14 release was adopted as the CAS engine for the MathCAD
software package.
In September 2008, SciFace was purchased by MathWorks and the MuPAD code was included in the Symbolic Math Toolbox add-on for MATLAB
. On 28 September 2008, MuPAD was withdrawn from the market as a software product in its own right. However, it is still available in the Symbolic Math Toolbox in MATLAB and can also be used as a stand-alone program.
Often used commands are accessible via menus. MuPAD offers a notebook concept similar to word processing systems that allows the formulation of mathematical problems as well as graphics visualization and explanations in formatted text.
It is possible to extend MuPAD with C++
routines to accelerate calculations. Java
code can also be embedded.
MuPAD's syntax was modeled on Pascal, and is similar to the one used in the Maple computer algebra system. An important difference between the two is that MuPAD provides support for object-oriented programming
. This means that each object "carries with itself" the methods allowed to use on it. For example, after defining
all of the following are valid expressions and give the expected result:
where A.A is the concatenated 2×4 matrix, while all others, including the last two, are again 2×2 matrices.
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
(CAS). Originally developed by the MuPAD research group at the University of Paderborn
University of Paderborn
The University of Paderborn in Paderborn, North Rhine-Westphalia, Germany was founded in 1972. 15,228 students were enrolled at the university as of December 2010....
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, development was taken over by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities starting in 1997.
Until autumn 2005, the version "MuPAD Light" was offered for free for research and education, but as a result of the closure of the home institute of the MuPAD research group, only the version "MuPAD Pro" became available for purchase.
The MuPAD kernel is bundled with Scientific Notebook and Scientific Workplace
Scientific WorkPlace
Scientific WorkPlace is a software package for scientific word processing on Microsoft Windows. It is shipped as a WYSIWYG LaTeX-based word processor, together with the LaTeX document preparation system and an optional computer algebra system.Scientific WorkPlace allows one to edit and typeset...
. Former versions of MuPAD Pro were bundled with SciLab
Scilab
Scilab is an open source, cross-platform numerical computational package and a high-level, numerically oriented programming language. Itcan be used for signal processing, statistical analysis, image enhancement, fluid dynamics simulations, numerical optimization, and modeling and simulation of...
. Its version 14 release was adopted as the CAS engine for the MathCAD
MathCad
Mathcad is computer software primarily intended for the verification, validation, documentation and re-use of engineering calculations. First introduced in 1986 on DOS, it was the first to introduce live editing of typeset mathematical notation, combined with its automatic computations...
software package.
In September 2008, SciFace was purchased by MathWorks and the MuPAD code was included in the Symbolic Math Toolbox add-on for MATLAB
MATLAB
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
. On 28 September 2008, MuPAD was withdrawn from the market as a software product in its own right. However, it is still available in the Symbolic Math Toolbox in MATLAB and can also be used as a stand-alone program.
Functionality
MuPAD offers:- a computer algebra systemComputer algebra systemA computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
to manipulate formulas symbolically - classic and verified numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
in discretionary accuracy - program packages for linear algebraLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
, differential equations, number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, and functional programmingFunctional programmingIn computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state... - an interactive graphic system that supports animations and transparent areas in 3D
- a programming languageProgramming languageA programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
that supports object-oriented programmingObject-oriented programmingObject-oriented programming is a programming paradigm using "objects" – data structures consisting of data fields and methods together with their interactions – to design applications and computer programs. Programming techniques may include features such as data abstraction,...
and functional programming
Often used commands are accessible via menus. MuPAD offers a notebook concept similar to word processing systems that allows the formulation of mathematical problems as well as graphics visualization and explanations in formatted text.
It is possible to extend MuPAD with C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
routines to accelerate calculations. Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
code can also be embedded.
MuPAD's syntax was modeled on Pascal, and is similar to the one used in the Maple computer algebra system. An important difference between the two is that MuPAD provides support for object-oriented programming
Object-oriented programming
Object-oriented programming is a programming paradigm using "objects" – data structures consisting of data fields and methods together with their interactions – to design applications and computer programs. Programming techniques may include features such as data abstraction,...
. This means that each object "carries with itself" the methods allowed to use on it. For example, after defining
A := matrix( 1,2],[3,4 )
all of the following are valid expressions and give the expected result:
A+A, -A, 2*A, A*A, A^-1, exp( A ), A.A, A^0, 0*A
where A.A is the concatenated 2×4 matrix, while all others, including the last two, are again 2×2 matrices.