MuPAD is a computer algebra project of the MathPAD group at the University of Paderborn. MuPAD was designed as a parallel system. The design and implemen tation of MuPAD grew out of the desire to efficiently handle large data generated by algorithms used to investigate the group theoretical structure of nonlinear sys tems. Nevertheless, MuPAD outgrew this original goal and was developed as a general purpose system and should be used as such. MuPAD had two major design goals. As already mentioned, firstly we wanted to prm·ide a tool for fast and efficient handling of large data. This goal was motivated by the special problems which came up in our research on nonlinear systems, where data of several GB are not unusual. As a consequence of this MuPAD is a parallel computer algebra system working on the basis of a shared memor)" machine. Special interfaces, simulating ~hared memory, will be provided for machines with a different architecture. A sequential version of MuPAD is available which, nevertheless, in its high-end language provides parallel constructs for programming. In this sequential version parallEl blocks are executed at random, thus allowing for logical tests of parallel programs on sequential machines. The sequential MuPAD version is the topic of this refErence manual. The second major design goal was to make sure that future versions of MuPAD could be the basis for a system capable of learning during interactive use.

Inhaltsangabe1 Preface.- 2 A sample session.- 2.1 Simple arithmetic.- 2.2 Number theory.- 2.3 Roots and transcendental numbers.- 2.4 Expressions and Identifiers.- 2.5 Polynomials.- 2.6 The sequence operator $.- 2.7 Data types.- 2.8 Domains.- 2.9 Data Structures.- 2.10 Evaluation.- 2.11 Programming.- 2.12 Input, Output, Files and Text.- 2.13 Graphics.- 2.14 Errors and Debugger.- 2.15 The Profiler.- 2.16 Underline Functions.- 2.17 Functional Environments.- 2.18 Program Manipulation.- 3 Programs.- 3.1 Some Tips and Tricks.- 3.1.1 A non commutative Product.- 3.1.2 Evalassign and FUNC.- 3.2 More sample Programs.- 3.2.1 A user defined differential Procedure.- 3.2.2 Polynomials.- 3.2.2.1 Heuristic GCD.- 3.2.2.2 Orthogonal Polynomials.- 3.2.3 Combinatorics: Permutations.- 3.2.4 Sorting.- 3.2.5 Graphs.- 3.2.5.1 Shortest Paths.- 3.2.5.2 Matching.- 3.2.6 Domains.- 3.2.6.1 Domain Generator.- 3.2.6.2 Extension of the real numbers by ? and -?.- 3.2.7 Data Manipulation Flattening.- 3.2.8 Fast Fourier Transformation.- 4 MuPAD - A Summary.- 4.1 The MuPAD language in brief.- 4.2 Evaluation in MuPAD.- 4.2.1 MuPAD expressions.- 4.2.2 Evaluation of expressions.- 4.2.3 Execution of MuPAD-Procedures.- 4.2.4 Execution of System Functions.- 4.2.5 The Substitution Depth.- 4.2.6 Control of the Substitution Depth.- 4.2.7 Fine Control of Evaluation.- 5 Tools and User Interfaces.- 5.1 Graphical User Interfaces under X-Windows.- 5.1.1 XMuPAD.- 5.1.2 HyTEX.- 5.1.2.1 HyTEX-Window.- 5.1.2.2 Help-Pages.- 5.1.3 Debugging in MuPAD - mdx.- 5.1.4 VCam - The interactive MuPAD graphics.- 6 List of functionality items provided by the system.