A Computer Algebra System (CAS) is a software package designed for the symbolic manipulation of mathematical expressions. A CAS should be able to:
perform numerical arithmetic with precision bounded only by the computer's hardware
perform basic calculus: partial and complete differentiation; symbolic and numerical integration
solve differential equations (partial and total)
manipulate power series
simplify algebraic expressions
understand standard functions: exponential, trigonometric, hyperbolic; in particular their derivatives and anti-derivatives, and their power series expansions
have a knowledge of some other functions: hypergeometric, Bessel
manipulate matrices and vectors; basic arithmetic, eigensystems, determinants, matrix decomposition
create two- and three-dimensional graphs
produce output in various forms: TeX/LaTeX, Fortran, C, HTML, PostScript
interact with other software; the CAS should be able to incorporate programs written in other languages
be extended: the CAS should have some programming language built in so that a user can add further functionality
number theoretical functions: primality testing, modular arithmetic, primitive root finding
orthogonal functions: Legendre, Chebyshev, Laguerre
animation of sequences of graphs
recurrence relation solving
MuPAD is a CAS developed at the University of Paderborn by a team headed by Benno Fuchssteiner. Although it may not have quite the range and pizazz of its better known rivals Maple and Mathematica, it is equal to them in depth, and in some ways even surpasses them. Its name is short for “MultiProcessing Algebra Data Tool”, and as we shall see, is a fairly good descriptor of it.
In contrast to the major commercial CASs, MuPAD is designed to be an open system—anybody can extend and add to it. The current version is 1.4, and was released in March 1998.
Let us suppose that you have installed MuPAD on your system. (I will discuss installation later.) What now?
You can start MuPAD in two ways: in a console, using the command
or, if you are running X, the command
xmupadwill provide a graphical interface. If you have installed MuPAD correctly, both of these commands are, in fact, shell scripts which define certain environment variables and then call the actual executables.
Let us suppose you have chosen the latter. You will obtain a window something like that shown in Figure 1.
Notice the OpenWindows look and feel. As yet the MuPAD team has not released a Linux binary using Athena or Motif widgets, although one is in preparation. MuPAD was designed to work with the OpenWindows widget set, and as such behaves best if you use an OpenLook window manager. Many of its subsidiary windows do not have their own close or exit button, but rely on the window manager for this. For all the figures and screenshots in this article I have used olvwm: the Open Look Virtual Window Manager.
You will also notice that the menus are rather sparse; there is, in fact, not a great deal more functionality offered by the graphical interface than in an intelligent console. Don't be put off—there's more here than meets the eye!
To save displaying too many screenshots, we shall go back to console mode. All MuPAD expressions are terminated with a colon or semi-colon (the colon suppresses display of the output), and the syntax is similar to that of Maple.
When MuPAD is started, a kernel (written in C++) is loaded; this defines a number of basic commands, functions, and constants. Other commands are available in specialized libraries, written in MuPAD's own language. These commands have to be loaded explicitly: either individually, or with the entire library.