Version 3.5 of REDUCE is now available for distribution. This is the first major update since the release of REDUCE 3.4.1 in July 1992. As is usual for a new release, a large number of bugs and awkward features reported by users have been corrected. Just about all the code in the system has been revised in one way or another in response to these reports and to general coding improvements. Taken together with the many new features that have been added, REDUCE 3.5 represents a significant enhancement over previous versions.

In addition to the capabilities of REDUCE 3.4.1, this new version has, among other improvements:

• Vastly Improved Arithmetic Support. Most of the code for floating point arithmetic has been completely rewritten, so that it is now far more rugged and also considerably faster. We have examples of code running from three to ten times faster than the previous version, especially for higher precision calculations. In addition, there is increased support for elementary function evaluation, plus support for a large number of special functions. A list of those special functions supported is given later.

• Improved Root Finding. Along with the increased efficiency possible with the improved arithmetic, the root finding package has been extended to handle much harder cases than were possible previously. For example, the close roots of the following polynomial could not be successfully separated with the previous version:

        ((10^12x^2-sqrt 2)^2+x^7)*((10^12x^2+sqrt 2)^2+x^7)

• Simplification Extensions. A large number of improvements in expression simplification appear with this release. These include:
  • Support for combining non-integer exponents. REDUCE, like most general purpose algebraic computation systems, is poor at surd simplification. However, the new version includes a switch combineexpt, that, when on, attempts to combine exponentials whenever possible. For example, with combineexpt on:

          3^(1/2)*3^(1/3)*3^(1/6);   ->   1.

  • Simplification of nested square roots. In the new system, the following sort of reduction occurs automatically:

          sqrt( 2*sqrt(5) + 6);   ->   sqrt(5) + 1.

  • Improved simplification of absolute value expressions. For example, we now have

          abs(e-pi)   -> - e + pi.

  • Improved support for the simplification of expressions involving elementary functions. Most of this support has been provided by rule lists. As a result, users can use the showrules operator, which has been integrated into the core REDUCE, to view such operator properties. For example, rules you will see with the command showrules atan include:

                sqrt(3) + 1       5*pi
          atan(-------------) => ------,
                sqrt(3) - 1        12
    
                ~x*i               ~x
          atan(------) => i*atanh(----) when impart(~y)=0,
                 ~y                ~y
    
                                  2
                            1 - ~x     sign(~x)
          atan(~x) => acos(---------)*----------
                                  2       2
                            1 + ~x

    This example also illustrates the use of a new operator sign.

• Vastly improved solve code. Many more cases can now be handled by solve, including a wider variety of non-linear equations, and classes of transcendental equations, e.g.,

                                                 sqrt(3) - 1
  solve(2*asin(x) + asin(2*x) - pi/2,x); ->  {x=-------------}
                                                     2

• Improved integration. The standard indefinite integrator now handles integrands with rational powers of the dependent variable, and can handle a larger number of square roots in the integrand. In particular, it can recognize some integrals involving arcsine functions.

• Improved determination of limits. Many more limits involving algebraic and transcendental functions can now be calculated, e.g.,

        limit((sqrt(x^(2/5) +1) - x^(1/3)-1)/x^(1/3),x,0);  ->  -1
  
        limit(log(x+1)^2/sqrt x,x,infinity);                ->  0

• Support for many special functions. These include Bernoulli numbers, Euler numbers, Stirling numbers, binomial coefficients, Pochhammer notation, the gamma function, the psi function and its derivatives, the Riemann zeta function, the Bessel functions J and Y of the first and second kind, the modified Bessel functions I and K, the Hankel functions H1 and H2, the Kummer hypergeometric functions M and U, the beta function, Struve, Lommel and Whittaker functions, the exponential integral, the sine and cosine integrals, the hyperbolic sine and cosine integrals, the Fresnel integrals, the error function, the dilog function, Hermite polynomials, Jacobi polynomials, Legendre polynomials, Laguerre polynomials, Chebyshev polynomials, Gegenbauer polynomials, Euler polynomials, Bernoulli polynomials, generalized hypergeometric functions and Meijer's G function.

  Both numerical and algebraic properties of these functions are supported.

• New packages. All the major packages in the REDUCE network library have been included in this release, including some that were not part of REDUCE 3.4.1, namely:
  • CALI: A Package for computational commutative algebra.

    Author: Hans-Gert Graebe

  • CRACK: A package for solving overdetermined systems of PDEs or ODEs.

    Authors: Andreas Brand, Thomas Wolf

  • LIE: Functions for the classification of real n-dimensional Lie algebras.

    Authors: Carsten and Franziska Schöbel

• Improved integration with other utilities. In selected versions of REDUCE 3.5, the following are also provided:
  • Improved support for the GNUPLOT package

  • On-line help information
• Support for Rlisp '88. This is a superset of the traditional Rlisp used to support REDUCE, fully documented in Marti, Jed B., ``RLISP '88: An Evolutionary Approach to Program Design and Reuse'', World Scientific, Singapore, 1993.

Updated documentation includes an improved and expanded User's Manual in format, and a bibliography listing over 750 references to REDUCE-related publications.

A complete information package is obtainable from:

REDUCE Secretary
RAND
1700 Main Street
P.O. Box 2138
Santa Monica CA 90407-2138 U.S.A.
Telephone: +1-310-393-0411 Ext. 7681
Facsimile: +1-310-393-4818
Electronic Mail: reduce@rand.org

If you have e-mail access to the Internet, you can also obtain current information by sending the message send info-package to reduce-netlib@rand.org, reduce-netlib@can.nl, redlib@elib.zib-berlin.de or reduce-netlib@pi.cc.u-tokyo.ac.jp. The single line message can either be the subject of the message or the body. This message is answered by an automated server for the REDUCE network library. The library will in time contain any packages made available since the release of REDUCE 3.5 and patches to correct any bugs that may be discovered. Further information on this library, as well as instructions on how to join the REDUCE electronic forum, can be obtained by including the word help on a separate line in the message.

You can also obtain the available information from an Internet gopher server with the address ``is.rand.org''. The network library files are in a ``REDUCE Library'' directory under the directory ``Publicly Available Software''.

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see also: REDUCE Home Page

Copyright (c) 1994, RAND. All Rights Reserved.