MuPAD - FACTSHEET

# ... FACTSHEET

## MuPAD - the Multi Processing Algebra Data Tool

Because of the attention MuPAD has received on the net, here are some basic facts about it:

- MuPAD is a system for symbolic and numeric computation, parallel mathematical programming and mathematical visualization. It is intended to be a 'general purpose' computer algebra system.

- MuPAD has easy-to-use language constructs for parallel programming. A prerelease Version for parallel programming exists for Sequent and Sun multiprocessor machines. Programming in MuPAD's own programming language is supported by a comfortable source code debugger. Window-based user interfaces for MuPAD exist for the X-Window-System and the Apple Macintosh.

- The 400+ page user manual (in German) and the 200 page tutorial (in English) for MuPAD are published by Birkhaeuser, Basel. On-line Hypertext versions of the manual/tutorial and a demo are distributed with the system. The English reference manual will follow in autumn 1995. There also is sufficient on-line documentation, both in English and German. (Reference manual and helppages in German; tutorial, sample session and a demo in English)

- MuPAD is distributed for free, but not in the public domain; a registration is required. MuPAD is available via anonymous ftp for several systems: Sun, Silicon Graphics, DEC, PC with Linux or FreeBSD, IBM workstations, Apple Macintosh. Prereleased versions exist for Sequent and HP.

- For the development of libraries MuPAD counts on its user community. Anyone who wants to make contributions to the libraries is invited to contact the MuPAD group. We will be eager to support you and to solve any problems you might have with the system.

## FACT SHEET

MuPAD is a system for symbolic and numeric computation, parallel mathematical programming and mathematical visualization.

##### OVERVIEW

The program consists of a small kernel written in C and Libraries written in the MuPAD programming language. All features described may be used interactively or via the programming language. Control structures for programming are also available at the interactive level. Kernel and library are machine independant. In addition to the terminal-based user interface window-based interfaces exist for the X-Window-System and the Apple Macintosh.

The MuPAD programming language has various built-in constructs for parallel programming, accessible at any level of programming experience. First parallel implementations exist. MuPAD is devoted to the scientific community and freely distributed for non-commercial use.

##### SYMBOLIC AND NUMERIC COMPUTATION

##### Data Types

Integers and rational numbers of any length, floating point and complex numbers of arbitray precision, multivariate sparse polynomials, strings, Booleans, variable identifiers, dynamic lists, sets and tables, arrays of any dimension, user defined types (domains) and objects, a rich set of expressions, procedures and statements, which are first class data objects.

##### Constants

E, PI, I, FALSE, TRUE, various system constants.

##### Data Manipulation

Operand extraction, counting and substitution, object type testing, indeterminate extraction, concatenation of strings and lists, set manipulation, extraction, sorting and substitution of list, set, table and array elements, mapping operands to functions, string searching, pattern matching, parsing, conversion of strings and polynomials to expressions and vice versa, run-time generation and manipulation of procedures.

##### Operators

Arithmetic (+, -, *, /, ^, mod, div), relational (<, >, <=, >=, =, <>), Boolean (and, or, not), set operations (union, intersect, minus), concatenation (.,#), range (..), sequencing (, and $), domain attribute access (::), assignment (:=), last output (%), user defined operators. System functions and operators may be overloaded by user defined types.

##### Arithmetic

Absolute value, exponential, logarithm, square root, sign, trigonometric and hyperbolic functions and inverses, rounding, ceil and floor, truncation, modular computation, factorial, maximum and minimum, numeric evaluation, extraction of numerator and denumerator, fractional part, real and imaginary part, set union, intersection and difference, set membership, differentiation and expansion of expressions, taylor series and order terms, differential operator.

##### Polynomials

Coefficient mapping and extraction, degree, leading coefficient, term and monomial (lexical and degree order), trailing coefficient, number of terms, nth coefficient, division and pseudo-division, evaluation, integer content, norm, factorisation.

##### Domains

User defined types and data structures, operator overloading, object oriented programming, generic algorithms. As experimental library: parametric domains, domain constructors, categories, category constructors, axiomes.

##### Number Theory (standard)

Integer factorisation, integer GCD and LCM, extended Euclidean algorithm, prime number test, prime number generation, Eulers phi function, random number generation.

##### Library packages

- Linear Algebra
  About 40 functions. A short selection of functions provided by linalg: gaussian elimination, Gauss-Jordan elimination, solving systems of linear equations, inverting matrices, computing the norm, the rank and the determinant of a matrix, computing the Sylvester matrix, computing a basis for a vector space, QR factorization of regular matrices and many operations on matrices.
- Polynomial Factorisation
  Factorization of a multivariate polynomial with integer or rational coefficients and factorization of a univariate polynomial over a finite field.
- Integration
- Number Theory
  About 30 functions. A short selection of functions provided by this package: chinese remainder; hensel lifting; computing the Carmichael and Fibonacci numbers, the Jacobi and Legendre symbol; solving linear congruences; computing roots.
- Typechecking
  Very comfortable possibility to check the type of an expression.
- Share
  Indefinite summation of rational functions, finding integer roots of a polynomial over Q[x], Lindenmayer-Systems and 2D-Turtle graphics.

Also refer to the MuPAD Demo and read about the new features of the next release of MuPAD.

##### USER INTERFACES

##### General

Selection of printing and error level, line width, formatted or non-formatted output, verbose printing during procedure execution, recalling of earlier results. Line editor for raw terminal interface.

##### X-Windows Version

Look and feel of OpenLook, editing and recall of input and output, scroll back, two and also three dimensional plotting with mouse-controlled interface , on-line manual and tutorial with hypertext functionality, pasting of examples from these documents into the input window, mouse controlled interface for source code debugger.

##### Macintosh Version

Mac-like interface with notebook functionality, structured session documents, editing of text documents, graphics, debugger and hypertext system as in the X-Windows version.

##### GRAPHICS

##### General

Any property of a plot may be set interactively in VCam or defined in a plot-command. VCam Graphics front-end for 2- and 3-dimensional plotting, running under X-Windows and MacOS; thightly coupled with the MuPAD kernel. Defining functions may be entered and manipulated directly in VCam, objects can be added or deleted by mouse-click.

##### 2D-Plotting Facilities

Two-dimensional scenes, graphs, curves, list of points/lines/polygons; multiple objects per scene; object style may be points, lines or impulses; options for titling, labeling, colour selection, smooth colouring by height, colouring by user defined functions, axes scaling and style, automatic viewing box, grid and smoothness.

##### 3D-Plotting Facilities

Three-dimensional scenes, graphs, surfaces, space curves, list of points/ lines/polygons; multiple objects per scene; object style may be points, lines, impulses, wire frame, mesh, x-line, y-line, hidden line, colour patches, transparent; options for titling, labeling, colour selection, smooth colouring by height, colouring by user defined functions, axes scaling and style, automatic viewing box, camera point and focal point, grid and smoothness.

Plots can be directly saved in different formats: ASCII, Binary, Raster-, Gif- and Postscript-Files.

##### PROGRAMMING FACILITIES

##### General

Functional programming language with procedural extensions and Pascal-like syntax. Procedures and statements are ordinary data objects and may be manipulated at run-time. Any language construct is available as system function. Any system function may be overwritten by user-defined procedures. Unnamed functions. Formatted output of procedures.

##### Language Constructs

Assignment, expression, statement sequence, if then elif else end_if, for from to step do end_for, while do end_while, repeat until end_repeat, case of do otherwise end_case, proc() begin end_proc, break, next, error, return, parameter lists of varying length.

##### Evaluation

The programmer can control any aspect of expression evaluation and variable substitution: holding evaluation, evaluation in an outer context, defining substitution level, additional evaluation, retrieving values directly. Procedures may remember calculations to speed up execution. Results are stored in a history table which may be accessed by procedures.

##### Input and Output

Reading and writing of text and binary (M-Code) files, opening and closing of files, reading and writing of MuPAD data and raw text, printing output to file, writing a session protocol to file. Entering expressions or text interactively.

##### Debugging

Execution tracing, verbose procedure execution, different printing and error levels, error trapping. A source code debugger allows to step through procedures, print and observe values of variables, alter values of variables, execute instructions, display the procedure stack. The debugger is integrated into the kernel and may be used via command language or a comfortable window-based user interface (available under the X-Window-System).

##### PARALLEL PROGRAMMING

##### General

There are two levels of parallelism in MuPAD : micro-parallelism on a processor cluster with high speed communication facilities (a multi-processor machine for example) and macro-parallel ism on a network of clusters with medium- to low-speed communication.

##### Micro-Parallelism

Automatic task creation and distribution by the system. Easy-to-use language constructs: parallel for-loop, parallel and sequential blocks, private and global variables, task abortion.

##### Macro-Parallelism

Blocking and non-blocking message queues and pipes, global network-wide variables, topology informations.

##### DYNAMIC MODULES

Beside the conventional concept of libraries written in the language of the CA system, MuPAD offers another library concept, called dynamic modules. Users can implement algorithms in the C programming language (in the near future moreover in C++) to extend the MuPAD system by new functions. The advantages are:

- Spead. Functions written in the MuPAD programming language are executed by MuPAD's interpreter, whereas moduls are compiled into machine code.
- Users can use the flexibily of C (C++) and have access to all internal functions and data structures of the MuPAD kernel.

Dynamic modules forces no interprocess communication, they are directly linked to the MuPAD kernel on demand at run time. It is also possible to unload modules at run time. This is why we speak of dynamic modules. The method used is called dynamic linking. Because the operating system must support dynamic linking, modules are available only for the following platforms:

- Sun SPARC - SunOS 4.1.1 or later, SunOS 5.x (Solaris)
- Silicon Graphics - Irix 5.1 or later
- IBM RS/6000 - AIX 3.1 or later
- PC/AT - FreeBSD 1.1.5.1 or later

##### AVAILABILITY

MuPAD Version 1.2.1a is now available for Sun SPARCstation (under SunOS and Solaris), IBM RS6000, Silicon Graphics, DECstations (under Ultrix), PC (under Linux and FreeBSD) and Apple Macintosh.

Prereleased versions exist for the Sequent Symmetry and HP 9000. A version for SUN Multiprocessor systems is in preparation. Please call for others.

##### DOCUMENTATION

##### in German:

       Birkhaeuser Verlag Basel, 1993
       MuPAD: Multi Processing Algebra Data Tool;
       Benutzerhandbuch; MuPAD Version 1.1
       ISBN 3-7643-2872-X

##### in English:

       Birkhaeuser Verlag Basel, 1993
       MuPAD: Multi Processing Algebra Data Tool;
       Tutorial
       ISBN 3-7643-5017-2

The English reference manual of MuPAD will follow in summer 1995. But there also is sufficient on-line documentation, both in English and German (Reference manual and helppages in German; tutorial, sample session and a demo in English).

Furthermore you will find information on different aspects of MuPAD in the following issues of MathPAD Vol. 3. Heft 2, 9/93 (in German) and Vol. 4. Heft 1, 3/94 (in English), both issues are to be found on our server. There you also will find additional information on MuPAD.

##### FURTHER INFORMATIONS

##### Internet Services

    E-mail: MuPAD-distribution@uni-paderborn.de     (further email addresses)
    WWW   : http://math-www.uni-paderborn.de/~cube/
    FTP   : ftp.uni-paderborn.de:/local/MuPAD/      (further ftp sites)

##### Mail Address

    MuPAD-Distribution
    Fachbereich 17
    University of Paderborn
    Warburger Str. 100
    D-33095 Paderborn
    Germany