SYMSAC86

A specific model depicting the nature of research and development work in symbolic mathematical computation is presented. The model provides the organization for this introduction and overview. Basic concepts and issues are adumbrated from the user's ...

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.

During the past decade efficient algorithms for many basic group theoretic constructions have been developed. These include centralizers, normalizers, conjugacy classes, subgroup lattices and character tables. In order to effectively utilize such ...

The purpose of this paper is to provide an introduction to some computational techniques which have proved useful in the study of large permutation groups. In particular they have been used to study the Suzuki simple group of degree 1782 and order 448,...

MATHLAB 68 is an on-line system providing machine aid for the mechanical symbolic processes encountered in analysis. It is capable of performing, automatically and symbolically, such common procedures as differentiation, polynomial factorization, ...

The SCRATCHPAD/1 system is designed to provide an interactive symbolic computational facility for the mathematician user. The system features a user language designed to capture the style and succinctness of mathematical notation, together with a ...

MACSYMA is a system for symbolic manipulation of algebraic expressions which is being developed at Project MAC, M.I.T. This paper discusses its philosophy, goals, and current achievements.

MACSYMA makes extensive use of the power of its rational ...

In 1936, J.A. Todd and H.S.M. Coxeter published a paper in which they described a technique for enumerating the cosets of a finite group given only the defining relations for the group and the generators of the subgroup written in terms of the ...

Both special purpose programs and more general systems have been implemented for the study of groups. The special programs were in most cases designed for calculations occurring in the investigation of very big finite groups, such as some of the newly ...

Studying mathematics is, in part, a language problem. Naturally, mathematicians are more likely to resist using a computer as a tool in their work if the tedious task of learning a new language for mathematics is part of the bargain. Furthermore, until ...

This paper is devoted to the display system of a system named Aladin which is very similar to Martin's Symbolic Mathematical Laboratory. Therefore, it is not something basically new; nevertheless, we want to show the way we have followed to implement a ...

The conference paper “Computer Input/Output of Mathematical Expressions” by Professor Martin is an excellent summary of the characteristics of 2D math expressions and of algorithms for their recognition and display. Professor Martin argues that for ...

Notational devices are invented to aid the visualization and mental manipulation of abstract representations or models of real or imagined problems. The notations of mathematics are a prime example, but we must not forget those of logic, chemistry, or ...

A survey of some computational techniques available to the finite group theorist and a description of several outstanding problems in which the computer may prove helpful.

The PL/I-FORMAC Interpreter is a Type III IBM Programming System designed to add the capabilities of a formula manipulation language to the capabilities of PL/I. The program and/or documentation may be obtained by ordering program number 360D-03.3.004 ...

The principal features of IAM, a system for interactive algebraic manipulation, are described. The primary goal of IAM is to make algebraic manipulation by computer available to a non-programming person. IAM has a JOSS-like command language, emphasizing ...

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 ...

This paper discusses the design of the CAMbridge ALgebra system and describes some of the techniques that are used in its implementation. These techniques enable that system to provide reasonably general algebraic manipulation in an efficient way. The ...

SAC-1 is a program system for performing operations on multivariate polynomials and rational functions with infinite-precision coefficients. It is programmed, with the exception of a few simple primitives, in ASA Fortran. As a result the system is ...

ALTRAN is a complete system for writing programs for the formal manipulation of rational functions in several variables with integer coefficients. This paper gives a brief description of the language, run-time data structures, and implementation.

In programming a software package for group theoretic calculations one is faced with a number of problems including:

1 the size of the package,

2 the size of the problems to be run in terms of execution time and storage requirements,

3 the need for ...

There is a close correspondence between the set of subgroups of a finite group G and the set of inequivalent transitive permutation representations of G. For many purposes the latter is as useful as the former and more easily calculated. The present ...

This article is a report of some computations that were done recently with the hope of understanding an apparently simple, though as yet unanswered, question in linear algebra.

In the present survey an outline is given of certain recent as well as earlier developments in the use of electronic high-speed computers in algebraic number theory.

A method is given for reduction of representations by finite matrices of finite and infinite groups, using the matrices of the generators for the representations provided these are finite in number. It does not necessitate construction of every element ...

We describe here two applications of the Coxeter-Todd coset enumeration algorithm. One is the computation of part of the Schur multiplier of a small finite Lie group, in this case PSU(3, 4), directly from the presentation used to define the Steinbrg ...

The paradigm of algorithm analysis has achieved major pre-eminence in the field of symbolic and algebraic manipulation in the last few years. A major factor in its success has been the use of modular arithmetic. Application of this technique has proved ...

This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The phenomenon of coefficient growth is described, and the history of successful efforts first to control it and then to ...

An efficient algorithm is presented for the exact calculation of resultants of multivariate polynomials with integer coefficients. The algorithm applies modular homomorphisms and the Chinese remainder theorem, evaluation homomorphisms and interpolation, ...

This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GF(p ^m) to the problem of finding ...