REDUCE Information Package

REDUCE is an interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers. Its capabilities include:

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

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. In support of this goal, REDUCE has the following characteristics:

  1. Code stability. Various versions of REDUCE have been in use for over forty 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 approximately 1000 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. 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.

The most recent release of REDUCE is available for most common computing systems, in some cases in more than one version for the same machine. REDUCE is based on a dialect of Lisp called "Standard Lisp", and the differences between versions are the result of different implementations of this Lisp; in each case the source code for REDUCE itself remains the same. The complete source code for REDUCE is available. On-line versions of the manual and other support documents and tutorials are also normally included with the distribution.

In order to help users choose the best version of REDUCE for their purposes, we describe the general characteristics of the available Lisps, followed by a table of the particular versions supported on each machine, and finally the full names and addresses of the REDUCE distributors.

The distributed versions of REDUCE are based on two easily available Lisps, namely:

  1. Portable Standard Lisp (PSL). This is currently the Lisp used most widely for running REDUCE. It evolved from the original Standard Lisp definition, but now contains many more facilities. It is quite efficient in its use of both space and time, and has been optimized for algebraic computation. All PSL versions of REDUCE are distributed with sufficient PSL support to run on the given computing system. PSL is supported on many architectures and is an ideal system for those wanting to run REDUCE as a standalone system. The current principal developer of PSL is the Konrad Zuse Center, Berlin (ZIB).
  2. Codemist Standard Lisp (CSL). This is a Lisp system written completely in ANSI C, which makes it very easy to port to a new machine. Like PSL, it is a faithful implementation of Standard Lisp and has been optimized for running REDUCE. It requires a very small memory partition for its Lisp support. Furthermore, most of the REDUCE facilities are supported as machine independent pseudocode, which is quite compact. In the worst case, the performance of this system is about a factor of two slower than PSL, though in many cases it matches PSL performance. However, the memory use is smaller. All CSL versions are distributed with sufficient CSL support to run on the given computing system. This is an ideal system for those wishing to embed algebraic calculations in a C-based programming environment. The developer of CSL is Codemist Ltd.

Versions Available

Various versions of REDUCE are available free of charge from SourceForge. Please contact this site for further information.

Obtaining Further Information about REDUCE

You can obtain a current copy of this information form at any time from the REDUCE home page. In addition to general information about REDUCE, this server has pointers to the network library, the demonstration versions, examples of REDUCE programming, a set of manuals, and the REDUCE online help system.