Anthony C. Hearn

REDUCE 2: A system and language for algebraic manipulation

A description of a new version of the algebraic manipulation system REDUCE is presented. In its latest form, REDUCE provides a complete language for interactive symbol manipulation by computer in addition to increased facilities for the simplification of algebraic expressions.

A portable lisp compiler

The programming language LISP is usually implemented via an interpreter, and a compiler is added later as a LISP program. However, all such production compilers known to the authors produce explicit instructions for the given computer being used. This paper describes the development of a portable LISP compiler in the sense that only Standard LISP functions are used in its definition and the output is a sequence of abstract machine codes, easily mapped to instruction sequences on current computers. The resulting code is quite efficient, demonstrating once again the maxim that most compiler optimization is largely machine independent.

Standard LISP report

Although the programming language LISP was first formulated in 1960 [6], a widely accepted standard has never appeared. As a result, various dialects of LISP have been produced [4-12], in some cases several on the same machine! Consequently, a user often faces considerable difficulty in moving programs from one system to another. In addition, it is difficult to write and use programs which depend on the structure of the source code such as translators, editors and cross-reference programs.

Analytic computation of some integrals in fourth order quantum electrodynamics

Abstract A program for the analytic evaluation of some parametric integrals which occur in fourth order QED calculations is described.

A mode analyzing algebraic manipulation program

A new version of the REDUCE program for algebraic manipulation which performs a complete mode analysis of each command as a separate extension of the parse is presented. As a result, programs become more efficient and are easier to write and debug because the semantic error checking is more complete.

A new REDUCE model for algebraic simplification

This paper shows how the general concepts of mode analysis can play a useful role in the design and implementation of programs for algebraic simplification. We utilize these ideas in presenting a new model for simplification which will be incorporated into REDUCE in the near future.

Standard LISP (reprint)

When it was first formulated in 1960, (1) the programming language LISP was a truly machine independent language. However, even the earliest computer implementation encountered problems in input-output control and the handling of free variables which were not considered in the original paper. Successive implementations of LISP on more sophisticated machines have solved such problems by independent methods and introduced extensions of the language peculiar to those machines. Consequently, a LISP user now faces considerable difficulty in moving a program from one machine to another and is often involved in weeks of debugging in the process. As a possible solution to this problem, this paper is an attempt to provide a uniform subset of LISP 1.5 and its variants as it exists today. The version of LISP described, which we call Standard LISP, is sufficiently restricted in form so that programs written in it can run under any LISP system upwardly compatible with LISP 1.5 as described in the LISP 1.5 Programmers Manual (2). As function names vary from system to system and input-output control is different, some modification of the code is of course necessary before function definitions can be successfully compiled in any given system. However, this modification is performed automatically by a preprocessor, whloh is custom built for a particular system. This preprocessor is a LISP program which is loaded before any Standard LISP programs are run, and could be built automatically into a system if only Standard LISP programs are run. Parts of this preprocessor are similar for all systems, but some of it is peculiar to a given implementation. Standard LISP preprocessors have been written for SHARE LISP for the IBM 7090 series machines, Stanford LISP/360 for IBM System 360 machines, Stanford AI LISP 1.6 for the PDP-6 and PDP-10, BBN-LISP for the SDS 940 and Texas LISP for the CDC 6600. For convenience in exposition we shall refer to the first four systems as SHARE LISP, LISP/360, PDP LIST and BBN-LISP respectively.

SCIENTIFIC APPLICATIONS OF SYMBOLIC COMPUTATION

This paper reviews the use of symbolic computation systems for problem solving in scientific research. The nature of the field is described, and particular examples are considered from celestial mechanics, quantum electrodynamics and general relativity. Symbolic integration and some more recent applications of algebra systems are also discussed.

An improved non-modular polynomial GCD algorithm

An improved non-modular algorithm for the calculation of the greatest common divisor of two multivariate polynomials is presented.

Applications of symbol manipulation in theoretical physics

This paper surveys the applications of symbolic computation techniques to problems in theoretical physics. Particular emphasis is placed on applications in quantum electrodynamics where the most activity has occurred.