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MACSYMA - A SYMBOLIC MANIPULATION SYSTEM

IP.com Disclosure Number: IPCOM000149051D
Original Publication Date: 1975-Dec-31
Included in the Prior Art Database: 2007-Mar-30

Publishing Venue

Software Patent Institute

Related People

Wang, Paul S.: AUTHOR [+2]

Abstract

Proceedings of International Computer Sympadum 1975 (Vol. I) HACEfM A SYMEOLIC MANIPULATION SYSTEM PAUL S. WANG Abstract Coajpu.ter systems for symbolic ~aP,bensticsenable one t o manipulate symbols as ell as numbers on a computer for the solution of one's mathematiceel problems. Brief descrip- Lfons of current symbolic manipulation systems are given. MACSYMA is a large and h.9.ghI.y mathe- matically sophjisticated system being developed at M.I.T. Its designp organization and cap- abllStles are discussed and the usage of manyof its commands are illustrated. Current and possible future applications of such systems are indicated. I. INTRODUCTION Computer based software systems for the purpose of facilitating symbolic bathematical computation are generally known as symbol man- ipulation systems. Such systems enable one to use a computer in attempting to solve his mathe- matical problems symbolfcally. This usually means that the user of such a system w i l l be able Lo avoid numerical approximations as much as possible. In m y cases he w i l l be able t o obtain exact solutions without loss of' preci- sion, In other cases he may be able t o use series approximations Instead of numerical pro- cesses. MCSYMA Ls the name of one such

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Proceedings of International Computer Sympadum 1975 (Vol. I)

HACEfM - A SYMEOLIC MANIPULATION SYSTEM
PAUL S. WANG

    Abstract - Coajpu.ter systems for symbolic ~aP,benstics
enable one t o manipulate symbols as
ell as numbers on a computer for the solution of one's mathematiceel problems. Brief descrip- Lfons of current symbolic manipulation systems are given. MACSYMA is a large and h.9.ghI.y mathe- matically sophjisticated system being developed at M.I.T. Its designp organization and cap- abllStles are discussed and the usage of many
of its commands are illustrated. Current and possible future applications of such systems are indicated.

I. INTRODUCTION

   Computer based software systems for the purpose of facilitating symbolic bathematical computation are generally known as symbol man- ipulation systems. Such systems enable one to use a computer in attempting to solve his mathe- matical problems symbolfcally. This usually means that the user of such a system w i l l be able Lo avoid numerical approximations as much as possible. In m y
cases he w i l l be able t o obtain exact solutions without loss of' preci- sion, In other cases he may be able t o use series approximations Instead of numerical pro- cesses. MCSYMA Ls the name of one such

computer system st Project ffit~ of the Massa- chusetts Institute of Technology.

    A brief introduction to current syntbolic manfpulatfon syotems w i l l be given f Srst. Then
the design and facilities of MCSYVA w i l l be discuesed in detail. MACSYMA conslsts of n

number of modules or packages of program w r l t - ten fn the LISP 1181 programming language. These modules serve different functions that are essential to such a system. They include two dfsmeasional display of mathematical ex- pressions, simplification, ratfonal function package, dilferentiation, solving equations, l i m i t , polmr series, definite and indef inite Pntegration, etc

.

    A num1)er of new algorlthlrls for certain basic math6matic:al computation that have been davel- oped as a result of butding these symbolic manipulati.on systems on comptlter w i l l be des- cribed. f'olynomial greatest common divisor
and multivariate polynomial Pactorleation are among the notable examples. Brief descriptions will also be gfwn to applications of symbolic systems l n science, engineering and educatbon.

XI. SYXWLIC MJD ALGEBRAIC

~ P ~ T I O N

              msmm
Current computer systems for symbolfc mathe- matlcs fall into two broad categories. The systems m m N [5], FORMAC, REDUCE2 [la], for Paul S. Wang is with Project MAC and Depart-
ment of Mathematics, Ha.ssachusetts Institute of IBM 360/75, SAC-1, SCHOONSGHIP and sYMBAL are Technology, Cambridge, Maes., USA. for batch ,;recessing. While the systems

   Work reported herein 7m.8 supported irr part
by Project UC, an M.I,T. interdepartmental ANALXTIK, ~ : M L , IAM, MBCSWp REDUCE2 for leboratory spons...