Mathematica_V5_Book.pdf

STEPHEN WOLFRAM

THE

Published by Wolfram Media

Library of Congress Cataloging--in--Publication Data

Comments on this book will be welcomed at:

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Wolfram, Stephen, 1959 –

Mathematica book / Stephen Wolfram. — 5th ed.

p. cm.

Includes index.

ISBN 1–57955–022–3 (hardbound).

1. Mathematica (Computer ﬁle) 2. Mathematics—Data processing.

I. Title.

QA76.95.W65 2003

510'.285'5369—dc21

In publications that refer to the Mathematica

system, please cite this book as:

Stephen Wolfram, The Mathematica Book , 5th ed.

(Wolfram Media, 2003)

03–53794

CIP

First and second editions published by Addison--Wesley Publishing Company

under the title Mathematica: A System for Doing Mathematics by Computer.

Third and fourth editions co--published by Wolfram Media

and Cambridge University Press.

Published by Wolfram Media, Inc.

photocopying, recording or otherwise, without the prior written permission of the copyright holder.

Wolfram Research is the holder of the copyright to the Mathematica software system described in this book, including without limitation such aspects of

the system as its code, structure, sequence, organization, “look and feel”, programming language and compilation of command names. Use of the system

unless pursuant to the terms of a license granted by Wolfram Research or as otherwise authorized by law is an infringement of the copyright.

The author, Wolfram Research, Inc. and Wolfram Media, Inc. make no representations, express or implied, with respect to this documentation

or the software it describes, including without limitations, any implied warranties of merchantability, interoperability or ﬁtness for a particular

purpose, all of which are expressly disclaimed. Users should be aware that included in the terms and conditions under which Wolfram

Research is willing to license Mathematica is a provision that the author, Wolfram Research, Wolfram Media, and their distribution licensees,

distributors and dealers shall in no event be liable for any indirect, incidental or consequential damages, and that liability for direct damages

shall be limited to the amount of the purchase price paid for Mathematica .

In addition to the foregoing, users should recognize that all complex software systems and their documentation contain errors and omissions.

The author, Wolfram Research and Wolfram Media shall not be responsible under any circumstances for providing information on or

corrections to errors and omissions discovered at any time in this book or the software it describes, whether or not they are aware of the

errors or omissions. The author, Wolfram Research and Wolfram Media do not recommend the use of the software described in this book for

applications in which errors or omissions could threaten life, injury or signiﬁcant loss.

Mathematica , MathLink and MathSource are registered trademarks of Wolfram Research. J/Link , MathLM , MathReader , .NET/Link , Notebooks and

web Mathematica are trademarks of Wolfram Research. All other trademarks used are the property of their respective owners. Mathematica is not associated

with Mathematica Policy Research, Inc. or MathTech, Inc.

Printed in the United States of America. • Acid--free paper.

15 14 13 12 11 10 9 8 7 6 5 4 3 2

Author’s website:

www.stephenwolfram.com

Other books by Stephen Wolfram:

· Cellular Automata and Complexity: Collected Papers (1993)

· A New Kind of Science (2002)

Author’s address:

email: s.wolfram@wolfram.com

mail: c/o Wolfram Research, Inc.

100 Trade Center Drive

Champaign, IL 61820, USA

www.wolfram.com

vii

About the Author

Stephen Wolfram is the creator of Mathematica ,andawell-

known scientist. He is widely regarded as the most important

innovator in technical computing today, as well as one of the

world’s most original research scientists.

Following his scientiﬁc work on complex systems research,

Wolfram in 1986 founded the ﬁrst research center and ﬁrst

journal in the ﬁeld. Then, afterahghly successful career in

academia—ﬁrst at Caltech, then at the Institute for Advanced

Study in Princeton, and ﬁnally as Professor of Physics, Math-

ematics and Computer Science at the University of Illinois—

Wolfram launched Wolfram Research, Inc.

Born in London in 1959, he was educated at Eton, Oxford and

Caltech. He published his ﬁrst scientiﬁc paper at the age of ﬁfteen,

and had received his PhD in theoretical physics from Caltech by

the age of twenty. Wolfram’s early scientiﬁc work was mainly

in high--energy physics, quantum ﬁeld theory and cosmology,

and included several now--classic results. Having started to use

computers in 1973, Wolfram rapidly became a leader in the

emerging ﬁeld of scientiﬁc computing, and in 1979 he began

the construction of SMP—the ﬁrst modern computer algebra

system—which he released commercially in 1981.

Wolfram began the development of Mathematica in late 1986.

The ﬁrst version of Mathematica was released on June 23,

1988, and was immediately hailed as a major advance in com-

puting. In the years that followed, the popularity of Mathe-

matica grew rapidly, and Wolfram Research became established

as a world leader in the software industry, widely recognized

for excellence in both technology and business. Wolfram has

been president and CEO of Wolfram Research since its incep-

tion, and continues to be personally responsible for the overall

design of its core technology.

In recognition of his early work in physics and computing,

Wolfram became in 1981 the youngest recipient of a Mac-

Arthur Prize Fellowship. Late in 1981, Wolfram then set out

on an ambitious new direction in science: to develop a gen-

eral theory of complexity in nature. Wolfram’s key idea was

to use computer experiments to study the behavior of simple

computer programs known as cellular automata. And in 1982

he made the ﬁrst in a series of startling discoveries about the

origins of complexity. The publication of Wolfram’s papers on

cellular automata led to a major shift in scientiﬁc thinking, and

laid the groundwork for a new ﬁeld of science that Wolfram

named “complex systems research”.

Following the release of Mathematica Version 2 in 1991,

Wolfram began to divide his time between Mathematica

development and scientiﬁc research. Building on his work

from the mid--1980s, and now with Mathematica as a tool,

Wolfram made a rapid succession of major new discoveries. By

the mid--1990s his discoveries ledhim to develop a fundamentally

new conceptual framework, which he then spent the remainder

of the 1990s applying not only to new kinds of questions, but

also to many existing foundational problems in physics, biology,

computer science, mathematics and several other ﬁelds.

Through the mid--1980s, Wolfram continued his work on

complexity, discovering a number of fundamental connections

between computation and nature, and inventing such con-

cepts as computational irreducibility. Wolfram’s work led to a

wide range of applications—and provided the main scientiﬁc

foundations for the popular movements known as complexity

theory and artiﬁcial life. Wolfram himself used his ideas to

develop a new randomness generation system and a new

approach to computational ﬂuid dynamics—both of which are

now in widespread use.

After more than ten years ofhghly concentrated work,

Wolfram ﬁnally described his achievements in his 1200--page

book ANewKind of Science .Released on May 14, 2002, the

book was widely acclaimed and immediately became a best-

seller. Its publication has been seen as initiating a paradigm

shift of historic importance in science.

In addition to leading WolframResearch to break new ground

with innovative technology, Wolfram is now developing a

series of research and educational initiatives in the science he

has created.

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