The REDUCE Computer Algebra System

Current Version: REDUCE 3.8

Information available from the current page (www.uni-koeln.de/REDUCE/) contains archival information on older versions of REDUCE, and is being offered to support those who may still be running older versions of REDUCE.

Previous Versions

There is also a Y2K compliance statement for REDUCE 3.7.

REDUCE 3.6 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. New Second Category Packages Documentation
9. Packages Available from Other Sources
10. REDUCE Demonstrations at other sites
11. REDUCE Network Library
12. Further Online Information Resources
13. Standard LISP and Symbolic Mode
14. Old Documentation
15. About the REDUCE Home Page

Introduction

• expansion and ordering of polynomials and rational functions;
• substitutions and pattern matching in a wide variety of forms;
• automatic and user controlled simplification of expressions;
• calculations with symbolic matrices;
• arbitrary precision integer and real arithmetic;
• facilities for defining new functions and extending program syntax;
• analytic differentiation and integration;
• factorization of polynomials;
• facilities for the solution of a variety of algebraic equations;
• facilities for the output of expressions in a variety of formats;
• facilities for generating optimized numerical programs from symbolic input;
• calculations with a wide variety of special functions;
• Dirac matrix calculations of interest to high energy physicists.

1. Code stability. Various versions of REDUCE have been in use for over twenty years. There has been a steady stream of improvements and refinements since then, with the source being subject to wide review by the user community. REDUCE has thus evolved into a powerful system whose critical components are highly reliable, stable and efficient.
2. Wide user base. A particular algebra system is often chosen for a given calculation because of its widespread use in a particular application area, with existing packages and templates being used to speed up problem solving. As evidenced by more than 800 reports listed in the current bibliography, REDUCE has a large and dedicated user community working in just about every branch of computational science and engineering. A large number of special purpose packages are available in support of this, with many contributed by users.
3. Full source code availability. From the beginning, it has been possible to obtain the complete REDUCE source code, including the ``kernel''. Consequently, REDUCE is a valuable educational resource and a good foundation for experiments in the discipline of computer algebra. Many users do in fact effectively modify the source code for their own purposes.
4. Flexible updating. One advantage of making all code accessible to the user is that it is relatively easy to incorporate patches to correct small problems or extend the applicability of existing code to new problem areas. An electronic mail service and World Wide Web servers allow users to get such updates and complete new packages as they become available, without having to wait for a formal system release.
5. State-of-the-art algorithms. Another advantage of an ``open'' system is that there is a shared development effort involving both distributors and users. As a result, it is easier to keep the code up-to-date, with the best current algorithms being used soon after their development. At the present time, we believe REDUCE has the best available code for solving nonlinear polynomial equations using Groebner bases, real and complex root finding to any precision, exterior calculus calculations and optimized numerical code generation among others. Its simplification strategy, using a combination of efficient polynomial manipulation and flexible pattern matching is focussed on giving users as natural a result as possible without excessive programming.
6. Algebraic focus. REDUCE aims at being part of a complete scientific environment rather than being the complete environment itself. As a result, users can take advantage of other state-of-the-art systems specializing in numerical and graphical calculations, rather than depend on just one system to provide everything. To this end, REDUCE provides facilities for writing results in a form compatible with common programming numerical languages (such as Fortran) or document processors such as TeX.
7. Portability. Careful design for portability means REDUCE is often available on new or uncommon machines soon after their release. This has led to significant user communities throughout the world. At the present time, REDUCE is readily available on essentially all workstations and high-end microprocessor-based machines in the market.
8. Uniformity. Even though REDUCE is supported with different Lisps on many different platforms, much attention has been paid to making all versions perform in the same manner regardless of implementation. As a result, users can have confidence that their calculations will not behave differently if they move them to a different machine.
9. Flexible Offerings. To support the differing needs of the user community, REDUCE is available in a number of different configurations:
   1. personal system, ready to run, available for a selection of common personal computers, shipped without source and hence with less easy updatability between major releases, but at lowest cost for a single user site;
   2. professional system, which comes with source, and is licensed for use on one CPU or fileserver and so can be especially attractive for laboratories or work-groups;
   3. site licenses, which extend the professional system to cover all similar machines at a single postal address.
10. Cost. The cost of a complete REDUCE to the end-user is moderate, and does not vary substantially from platform to platform. In addition, the personal systems and site licenses are offered on very generous terms. Moreover, since all systems are derived from the same source base, they are very compatible from platform to platform (from a PC to a Cray supercomputer). This makes it possible to have compatible versions at home and work.

REDUCE Demonstrations at Other Sites

1. The CATHODE 2 demonstrations of solutions of differential equations
2. SPDE (Symmetries of Partial Differential Equations)

Copyright

Please see the Copyright Notice for more information. 

General Information

A more detailed Introduction to REDUCE 3.5 is also available.

The REDUCE Bibliography lists several hundred books and papers citing REDUCE.

The central archive of the REDUCE mailing list, including recent mail, is available at http://ftp.rand.org/software_and_data/reduce/info.

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

Ordering Information

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)
Takustr. 7
D-14195 Berlin-Dahlem, GERMANY
E-Mail:

Melenk@zib.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

Demonstration Versions

Konrad-Zuse Zentrum Berlin (ZIB)

offers PSL based demo versions of REDUCE 3.6 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

REDUCE 3.6 Contributed Software Documentation

New Second Category Packages

Note that sometimes there are new releases of user packages that were already included in the REDUCE 3.6 distribution. The documentation for these packages is not listed as a new package, but rather as Contributed Software. 

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

Emacs Mode for REDUCE

A major GNU Emacs editing mode for REDUCE files and sessions
Author: Francis J.Wright

GRG 3.2

making calculation in differential geometry and field theory as simple and natural as possible
Author: Vadim V. Zhytnikov

REDLOG

REDuce LOGic system: symbolic algorithms on first-order formulas w.r.t. temporarily fixed first-order languages and theories (theories currently available are ordered fields and discretely valued fields).
Authors: Andreas Dolzmann, Thomas Sturm

REDTEN

Tensor manipulation package
Author: John Harper

SCOPE 1.5

Source Code Optimization
Author: Hans van Hulzen 

REDUCE Network Library

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

ZIB Berlin

Others

Standard LISP and Symbolic Mode

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. 

Old Documentation

About the REDUCE Home Page

maintained by
Andreas Strotmann
Regionales Rechenzentrum
Universität zu Köln