The REDUCE Computer Algebra System

Table of Contents

  1. Introduction
  2. Copyright Information
  3. General Information
  4. Ordering Information
  5. Demonstration Versions
  6. Main System Documentation and Online Help
  7. Contributed Software Documentation
  8. Second Category User Packages Documentation
  9. New Second Category Packages Documentation
  10. Packages Available from Other Sources
  11. REDUCE Network Library
  12. Further Online Information Resources
  13. Standard LISP and Symbolic Mode
  14. About these REDUCE HTML Documents
This is an experimental service to the REDUCE community. We would like to receive feedback from users that would allow us to improve the service.

Introduction

REDUCE is an interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers. Its capabilities include: It is often used as an algebraic calculator for problems that are possible to do by hand. However, the main aim of REDUCE is to support calculations that are not feasible by hand. Many such calculations take a significant time to set up and can run for minutes, hours or even days on the most powerful computers.

The most recent release of REDUCE (Version 3.5) is dated 15 October 1993.

Copyright

All information available through this service is
Copyright (c) RAND 1994. All rights reserved.

Please see the Copyright Notice for more information.

General Information

The REDUCE 3.5 Announcement includes a short overview of the capabilities of the REDUCE 3.5 computer algebra system.

A more detailed Introduction to REDUCE 3.5 is also available.

The REDUCE Bibliography lists several hundred books and papers citing REDUCE. Due to its size, this document has been split into several parts: A - E, F - H, I - O, and P - Z.

An archive of the REDUCE mailing list is available for the years 1988, 1989, 1990, 1991, 1992, 1993, and 1994. The archive is not up-to-date; recent messages to the forum are available from the central archive.

See also the section on "Further Online Information Sources" below for references to other sources of general information about REDUCE.

Ordering Information

The REDUCE computer algebra system is not in the public domain, but it is available at a very low price (cost recovery for improving, porting, supporting, and distributing it). In addition, there is a very generous site license policy in effect.

The most important distributors for REDUCE are the following:

ZIB
offer a PSL based version for a wide range of computers. Online REDUCE ordering information is available from ZIB. Their address is:
Herbert Melenk
Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
Heilbronner Str. 10
D 10711 Berlin, GERMANY
E-Mail:
Melenk@sc.zib-berlin.de
Codemist
offer a C based version of REDUCE using their own CSL written in C. Online REDUCE ordering information is available from Codemist. Their address is:
Codemist Ltd.
"Alta", Horsecombe Vale
Combe Down
Bath BA2 5QR, UNITED KINGDOM
E-Mail:
jpff@maths.bath.ac.uk
Cologne
(the Computer Center of the University of Cologne, Germany) offer a generic Common LISP version of REDUCE. Their address is:
Universität zu Köln
Regionales Rechenzentrum
A. Strotmann
Robert-Koch-Str. 10
D 50931 Köln
E-Mail:
Strotmann@RRz.Uni-Koeln.DE

The Information Package (also available as a single ASCII file) lists all the machines and operating systems REDUCE 3.5 is available for, and more information on the various distributors of the software. See also the section on "Further Online Information Sources" below for references to other sources of ordering information about REDUCE.

Demonstration Versions

Demonstration versions of REDUCE 3.5 are available from two sites:
Konrad-Zuse Zentrum Berlin (ZIB)
offers PSL based demo versions of REDUCE 3.5 for IBM-compatible PCs running MS/DOS, Windows 3.1, or Linux.
Codemist Ltd.
offers CSL based demonstration versions for PCs running MS/DOS (file demored.zip) and for the Apple Macintosh (file demored.hqx).

Main System Documentation

 For REDUCE users, both the REDUCE 3.5 User's Manual and the REDUCE 3.5 Online Help system are available on this server, the latter containing a searchable and browsable index to the help pages. Hardcopies of the REDUCE 3.5 User's Manual and other REDUCE documentation may be ordered from Codemist (cf. the corresponding ordering information).

REDUCE 3.5 Contributed Software Documentation

The documentation for almost all of the REDUCE 3.5 Contributed Software Packages is available online. Hardcopies of some of these documents may also be ordered.

ARNUM:
An Algebraic Number Package
AVECTOR:
A Vector Algebra and Calculus Package
COMPACT:
A Package for Compacting Expressions
EXCALC:
A Differential Geometry Package
GENTRAN:
A Code Generation Package
GROEBNER:
A Gröbner Basis Package
LIMITS:
A Package for Finding Limits
NUMERIC:
Solving Numerical Problems using Rounded Mode
ODESOLVE:
Ordinary Differential Equations Solver
ORTHOVEC:
A Package for the Manipulation of Scalars and Vectors
ROOTS:
A REDUCE Root Finding Package
SCOPE:
REDUCE Source Code Optimization Package
SPDE:
A Package for finding Symmetry groups of PDE's
SPECFN, SPECFN2:
A Package for Special Functions
SUM:
A Package for Series Summation
TAYLOR:
A Package for the Manipulation of Taylor Series
TPS:
A Truncated Power Series Package

Second Category User Packages

Packages in the second category must normally be individually compiled and loaded by the installer or user. Except for some very simple packages, most come with separate documentation and a test file in the ``lib'' directory. These items should be studied for details on the use of any particular package.

The user must load all packages in this category with the LOAD_PACKAGE command. Such packages included in the REDUCE 3.5 release are:

ASSIST:
Useful utilities for various applications
Author: Hubert Caprasse
CALI:
A Package for computational commutative algebra
Author: Hans-Gert Graebe
CAMAL:
Calculations in celestial mechanics
Author: John P. Fitch
CHANGVAR:
Change of Independent Variable(s) in DEs
Author: G. Üçoluk
CRACK:
A package for solving overdetermined systems of PDEs or ODEs
Authors: Andreas Brand, Thomas Wolf
CVIT:
Fast Calculation of Dirac Gamma matrices traces
Authors: V.Ilyin, A.Kryukov, A.Rodionov, A.Taranov
DESIR:
Differential linear homogeneous Equation Solutions in the neighborhood of Irregular and Regular singular points
Documentation for this package is in plain text.
Authors: C. Dicrescenzo, F. Richard-Jung, E. Tournier
FIDE:
Finite difference method for partial differential equations
Documentation for this package is in plain text.
Author: Richard Liska
IDEALS:
Arithmetic for polynomial ideals
Author: Herbert Melenk
LAPLACE:
Laplace and inverse Laplace transform
Documentation for this package is in plain text.
Author: C. Kazasov, M. Spiridonova, V. Tomov
LIE:
Functions for the classification of real n-dimensional Lie algebras
Authors: Carsten and Franziska Schöbel
LININEQ:
Solving systems of linear inequalities
Author: Herbert Melenk
PHYSOP:
Package for Operator Calculus in Quantum Theory
Author: Mathias Warns
PM:
A REDUCE Pattern Matcher
Documentation for this package is in plain text.
Author: Kevin McIsaac
REACTEQN:
Support for chemical reaction equation systems
Documentation for this package is in plain text.
Author: Herbert Melenk
RLFI:
REDUCE LATEX Formula Interface
Author: Richard Liska
SYMMETRY:
Symmetry-adapted bases and block diagonal forms of symmetric matrices
Author: Karin Gatermann
TRI:
TeX REDUCE Interface
Author: Werner Antweiler
Available as DVI file (96 kilobytes) and in PostScript (258 kilobytes).
WU:
Wu Algorithm for polynomial systems
Author: Russell Bradford.

New Second Category Packages

 Since the release of REDUCE 3.5, a number of new packages have been contributed to the REDUCE Netlib, the on-line repository of software and information related to REDUCE. The documentation for some of these packages is available for on-line browsing:
BOOLEAN:
Computing with Boolean Expressions
DFPART:
A Package for Calculating with Derivatives of Generic Functions
DUMMY:
Finding Canonical Form of Expressions Involving Dummy Variables
FPS:
Algorithmic Calculation of Formal Power Series
GHYPER:
Simplification of Generalized Hypergeometric Functions
GROEBNER:
A Package for Calculating Groebner Bases (new version)
INVBASE:
A Package for Computing Involutive Bases
LINALG:
A Linear Algebra Package for REDUCE
MEIJERG:
Simplification of Meijer's G Function
NCPOLY:
Computation in non-commutative polynomial ideals
NORMFORM:
Computation of Several Matrix Normal Forms
RANDPOLY:
Random Polynomial Generator
RSOLVE:
Rational and integer zeros of a univariate polynomial using fast modular methods
SAVE:
Saving Interactive REDUCE Sessions
SETS:
Sets: A Basic Set Theory Package
XIDEAL:
Gröbner Bases for Exterior Algebra
ZEILBERG:
Zeilberg: A Package for the Indefinite and Definite Summation
Note that sometimes there are new releases of user packages that were already included in the REDUCE 3.5 distribution. The documentation for these packages is not listed as a new package, but rather as Contributed Software or as Second Category User Package.

Packages Available from Other Sources
CALI 2.2
A Package for computational commutative algebra
Author: Hans-Gert Graebe
DIMSYM
Symmetry determination and linear differential equation package
Author: James Sherring
REDTEN
Tensor manipulation package
Author: John Harper
SCOPE 1.5
Source Code Optimization
Author: Hans van Hulzen

REDUCE Network Library

 The most important and up-to-date source of REDUCE online information is the REDUCE Netlib which is now accessible using the Gopher protocol. The URL for this service is gopher://info.rand.org/11/software/reduce/, i.e. the Gopher server's Internet name is info.rand.org, and REDUCE information is available in a directory (Gopher type `1') with the path 1/software/reduce/.

The REDUCE Netlib can also be accessed via electronic mail. To do so, send a message containing the line

send index to reduce-netlib@rand.org, reduce-netlib@can.nl, or reduce-netlib@pi.cc.u-tokyo.ac.jp.

Further On-line Information Resources

The experimental REDUCE WWW-Server of the Symbolic Computation group of Konrad-Zuse-Zentrum, Berlin (ZIB), contains a lot of useful information on REDUCE, including a hypertext overview of REDUCE for newcomers, example files demonstrating the use of REDUCE and its contributed software, answers to frequently asked questions about REDUCE, patches to REDUCE, and ordering information for the PSL based implementation of REDUCE.

Standard LISP and Symbolic Mode

The Standard LISP Report is also available for online browsing. It defines the portable language that REDUCE and most of its packages are written in.

A REDUCE 3.5 Symbolic Mode Primer explains how Standard LISP is used to extend REDUCE.

There are also documents (in German) available as hypertext technical reports of the Computer Center of the University of Cologne describing in detail the port of PSL (Portable Standard LISP) to an exotic machine architecture. This includes a description of PSL internals.

About the REDUCE HTML Documents

Most of these documents have been converted from their respective LaTeX sources using successive versions of Nikos Drakos' LaTeX2HTML conversion tool. Special support was added for a few LaTeX commands that appear in REDUCE documents by writing a REDUCE-specific PERL script to augment LaTeX2HTML.

You will need a WWW browser that supports transparent inline GIF images to view these documents. NCSA Mosaic is a well-known browser with that capability that is available for a wide range of platforms.

Please note that some of the document pages are big! The reason is generally that certain types of graphics cannot be represented in HTML and are therefore inserted as binary images. Some of these images are very big, and a few document pages reference several such images.

Please also note that some problems still exist in the automatic conversion process. Due to the sheer number and size of the resulting set of files, we will certainly have overlooked some.

The World Wide Web version of the new REDUCE online help facility was generated from the REDUCE online help files co-authored by A. C. Hearn and H. Melenk using an adaptation of software from ZIB to HTML generation, and it was augmented by a simple CGI script to provide searching capability anologous to the search function available in the online help system distributed along with most REDUCE versions.

You can also take a look at the access statistics for the REDUCE online information available from this server.

see also: The World Wide Web Virtual Library: Mathematics

edited by
Andreas Strotmann
Regionales Rechenzentrum
Universität zu Köln

Strotmann@RRz.Uni-Koeln.DE
95-07-24