MuPAD is a

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

(CAS). Originally developed by the MuPAD research group at the

University of Paderborn Paderborn University (german: Universität Paderborn) is one of the fourteen public research universities in the state of North Rhine-Westphalia in Germany. It was founded in 1972 and 20,308 students were enrolled at the university in the winter ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

, 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. MuPAD's graphics package was particularly successful, especially considering the era when it was developed. 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 Scientific WorkPlace (often abbreviated to SWP) is a software package for scientific word processing on Microsoft Windows and OS X. Although advertised as a WYSIWYG LaTeX-based word processor, it is actually a graphical user interface for editi ...

and

Scientific Workplace Scientific WorkPlace (often abbreviated to SWP) is a software package for scientific word processing on Microsoft Windows and OS X. Although advertised as a WYSIWYG LaTeX-based word processor, it is actually a graphical user interface for editin ...

. Former versions of ''MuPAD Pro'' were bundled with

SciLab Scilab is a free and open-source, cross-platform numerical computational package and a high-level, numerically oriented programming language. It can be used for signal processing, statistical analysis, image enhancement, fluid dynamics simulat ...

. In

MathCAD Mathcad is computer software for the verification, validation, documentation and re-use of mathematical calculations in engineering and science, notably mechanical, chemical, electrical, and civil engineering. Released in 1986 on DOS, it introduce ...

's version 14 release Mupad was adopted as the CAS engine. In September 2008, SciFace was purchased by

MathWorks MathWorks is an American privately held corporation that specializes in mathematical computing software. Its major products include MATLAB and Simulink, which support data analysis and simulation. History The company's key product, MATLAB, was ...

and the MuPAD code was included in the Symbolic Math Toolbox add-on for

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...

. 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 by the command mupad entered into the MATLAB terminal. The MuPAD notebook feature has been removed in

R2020a. However,

's Symbolic Math Toolbox still uses the MuPAD language as part of its underlying computational engine.

Live Editor is the recommended environment for performing, documenting, and sharing symbolic math computations.

Functionality

MuPAD offers: * a

to manipulate formulas symbolically * classic and verified

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

in discretionary accuracy * program packages for

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrices. ...

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, and

functional programming In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declar ...

* an interactive graphic system that supports animations and transparent areas in 3D * a

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

that supports

object-oriented programming Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of pr ...

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. MuPad does not follow the NIST 4.37 definition for

inverse hyperbolic cosine In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The s ...

. It is possible to extend MuPAD with

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

-routines to accelerate calculations.

Java Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's List ...

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 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 othe ...

. An important difference between the two is that MuPAD provides support for

. This means that each object "carries with itself" the methods allowed to be used on it. For example, after defining A := matrix( 1,2 ,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

concatenate In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenat ...

d 2×4 matrix, while all others, including the last two, are again 2×2 matrices.

References

{{Authority control 2008 disestablishments Computer algebra system software for Linux Computer algebra systems Discontinued software Products introduced in 1997 Proprietary commercial software for Linux