1、Library of Congress Cataloging-in-Publication DataWolfram, Stephen, 1959 Mathematica book / Stephen Wolfram. 5th ed.p. cm.Includes index.ISBN 1579550223 (hardbound).1. Mathematica (Computer file) 2. MathematicsData processing.I. Title.QA76.95.W65 2003510 .285 5369dc21 XXXXXXXCIPComments on this book
2、 will be welcomed at: In publications that refer to the Mathematicasystem, please cite this book as:Stephen Wolfram, The Mathematica Book, 5th ed.(Wolfram Media, 2003) First and second editions published by Addison-Wesley Publishing Companyunder the title Mathematica: A System for Doing Mathematics
3、by Computer.Third and fourth editions co-published by Wolfram Media and Cambridge University Press.Published by: ISBN 1579550223 Wolfram Media, Inc. web: ; email: phone:+12173989090; fax: +12173989095mail: 100 Trade Center Drive, Champaign, IL 61820, USA Copyright 1988, 1991, 1996, 1999, 2003 by Wo
4、lfram Research, Inc.All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, inany form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the priorwritten permission of the copyright holder. Printed from the Mathe
5、matica Help Browser 11988-2003 Wolfram Research, Inc. All rights reserved.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, “lookand feel”,
6、programming language and compilation of command names. Use of the system unless pursuantto the terms of a license granted by Wolfram Research or as otherwise authorized by law is an infringementof the copyright. The author, Wolfram Research, Inc. and Wolfram Media, Inc. make no representations, expr
7、ess orimplied, with respect to this documentation or the software it describes, including without limita-tions, any implied warranties of merchantability or fitness for a particular purpose, all of which areexpressly disclaimed. Users should be aware that included in the terms and conditions under w
8、hichWolfram Research is willing to license Mathematica is a provision that the author, WolframResearch, Wolfram Media, and their distribution licensees, distributors and dealers shall in no eventbe liable for any indirect, incidental or consequential damages, and that liability for direct damagessha
9、ll 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 theirdocumentation contain errors and omissions. The author, Wolfram Research and Wolfram Mediashall not be responsible under any circums
10、tances for providing information on or corrections toerrors and omissions discovered at any time in this book or the software it describes, whether or notthey are aware of the errors or omissions. The author, Wolfram Research and Wolfram Media do notrecommend the use of the software described in thi
11、s book for applications in which errors or omis-sions 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 webMathematica are trademarks of Wolfram Research. All othert
12、rademarks used are the property of their respective owners. Mathematica is not associated with Mathemat-ica 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 1 2 Printed from the Mathematica Help Browser1988-2003 Wo
13、lfram Research, Inc. All rights reserved.About the AuthorStephen Wolfram is the creator of Mathematica, and a well-known scientist. He is widely regarded as the most impor-tant innovator in technical computing today, as well as one of the worlds most original research scientists. Born in London in 1
14、959, he was educated at Eton, Oxford and Caltech. He published his first scientific paper at the ageof fifteen, and had received his PhD in theoretical physics from Caltech by the age of twenty. Wolframs early scientificwork was mainly in high-energy physics, quantum field theory and cosmology, and
15、included several now-classicresults. Having started to use computers in 1973, Wolfram rapidly became a leader in the emerging field of scientificcomputing, and in 1979 he began the construction of SMPthe first modern computer algebra systemwhich hereleased commercially in 1981. In recognition of his
16、 early work in physics and computing, Wolfram became in 1981 the youngest recipient of aMacArthur Prize Fellowship. Late in 1981, Wolfram then set out on an ambitious new direction in science: to developa general theory of complexity in nature. Wolframs key idea was to use computer experiments to st
17、udy the behavior ofsimple computer programs known as cellular automata. And in 1982 he made the first in a series of startling discover-ies about the origins of complexity. The publication of Wolframs papers on cellular automata led to a major shift inscientific thinking, and laid the groundwork for
18、 a new field of science that Wolfram named “complex systemsresearch”. Through the mid-1980s, Wolfram continued his work on complexity, discovering a number of fundamental connec-tions between computation and nature, and inventing such concepts as computational irreducibility. Wolframs workled to a w
19、ide range of applicationsand provided the main scientific foundations for the popular movements known ascomplexity theory and artificial life. Wolfram himself used his ideas to develop a new randomness generation systemand a new approach to computational fluid dynamicsboth of which are now in widesp
20、read use. Following his scientific work on complex systems research, Wolfram in 1986 founded the first research center and firstjournal in the field. Then, after a highly successful career in academiafirst at Caltech, then at the Institute forAdvanced Study in Princeton, and finally as Professor of
21、Physics, Mathematics and Computer Science at the Universityof IllinoisWolfram launched Wolfram Research, Inc. Wolfram began the development of Mathematica in late 1986. The first version of Mathematica was released on June23, 1988, and was immediately hailed as a major advance in computing. In the y
22、ears that followed, the popularity ofMathematica 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 WolframResearch since its inception, and continues
23、 to be personally responsible for the overall design of its core technology. Following the release of Mathematica Version 2 in 1991, Wolfram began to divide his time between Mathematicadevelopment and scientific research. Building on his work from the mid-1980s, and now with Mathematica as a tool,Wo
24、lfram made a rapid succession of major new discoveries. By the mid-1990s his discoveries led him to develop afundamentally new conceptual framework, which he then spent the remainder of the 1990s applying not only to newkinds of questions, but also to many existing foundational problems in physics,
25、biology, computer science, mathematicsand several other fields. After more than ten years of highly concentrated work, Wolfram finally described his achievements in his 1200-pagebook A New Kind of Science. Released on May 14, 2002, the book was widely acclaimed and immediately became abestseller. It
26、s publication has been seen as initiating a paradigm shift of historic importance in science. In addition to leading Wolfram Research to break new ground with innovative technology, Wolfram is now developinga series of research and educational initiatives in the science he has created. Other books b
27、y Stephen Wolfram: Cellular Automata and Complexity: Collected Papers (1993)Printed from the Mathematica Help Browser 11988-2003 Wolfram Research, Inc. All rights reserved. A New Kind of Science (2002)Authors website:Authors address:email: mail: c/o Wolfram Research, Inc.100 Trade Center DriveChampa
28、ign, IL 61820, USAFor comments on this book or Mathematicasend email to 2 Printed from the Mathematica Help Browser1988-2003 Wolfram Research, Inc. All rights reserved.About MathematicaMathematica is the worlds only fully integrated environment for technical computing. First released in 1988, it has
29、 hada profound effect on the way computers are used in many technical and other fields. It is often said that the release of Mathematica marked the beginning of modern technical computing. Ever since the1960s individual packages had existed for specific numerical, algebraic, graphical and other task
30、s. But the visionaryconcept of Mathematica was to create once and for all a single system that could handle all the various aspects oftechnical computing in a coherent and unified way. The key intellectual advance that made this possible was theinvention of a new kind of symbolic computer language t
31、hat could for the first time manipulate the very wide range ofobjects involved in technical computing using only a fairly small number of basic primitives. When Mathematica Version 1 was released, the New York Times wrote that “the importance of the program cannot beoverlooked”, and Business Week la
32、ter ranked Mathematica among the ten most important new products of the year.Mathematica was also hailed in the technical community as a major intellectual and practical revolution. At first, Mathematicas impact was felt mainly in the physical sciences, engineering and mathematics. But over theyears
33、, Mathematica has become important in a remarkably wide range of fields. Mathematica is used today throughoutthe sciencesphysical, biological, social and otherand counts many of the worlds foremost scientists among itsenthusiastic supporters. It has played a crucial role in many important discoverie
34、s, and has been the basis for thousandsof technical papers. In engineering, Mathematica has become a standard tool for both development and production, andby now many of the worlds important new products rely at one stage or another in their design on Mathematica. Incommerce, Mathematica has played
35、a significant role in the growth of sophisticated financial modeling, as well asbeing widely used in many kinds of general planning and analysis. Mathematica has also emerged as an important toolin computer science and software development: its language component is widely used as a research, protot
36、yping andinterface environment. The largest part of Mathematicas user community consists of technical professionals. But Mathematica is also heavilyused in education, and there are now many hundreds of coursesfrom high school to graduate schoolbased on it. Inaddition, with the availability of studen
37、t versions, Mathematica has become an important tool for both technical andnon-technical students around the world. The diversity of Mathematicas user base is striking. It spans all continents, ages from below ten up, and includes forexample artists, composers, linguists and lawyers. There are also
38、many hobbyists from all walks of life who useMathematica to further their interests in science, mathematics and computing. Ever since Mathematica was first released, its user base has grown steadily, and by now the total number of users isabove a million. Mathematica has become a standard in a great
39、 many organizations, and it is used today in all of theFortune 50 companies, all of the 15 major departments of the U.S. government, and all of the 50 largest universities inthe world. At a technical level, Mathematica is widely regarded as a major feat of software engineering. It is one of the larg
40、estsingle application programs ever developed, and it contains a vast array of novel algorithms and important technicalinnovations. Among its core innovations are its interconnected algorithm knowledgebase, and its concepts of symbolicprogramming and of document-centered interfaces. The development
41、of Mathematica has been carried out at Wolfram Research by a world-class team led by StephenWolfram. The success of Mathematica has fueled the continuing growth of Wolfram Research, and has allowed a largecommunity of independent Mathematica-related businesses to develop. There are today well over a
42、 hundred special-ized commercial packages available for Mathematica, as well as more than three hundred books devoted to the system. Printed from the Mathematica Help Browser 11988-2003 Wolfram Research, Inc. All rights reserved.New in Version 5Mathematica Version 5 introduces important extensions t
43、o the Mathematica system, especially in scope and scalabilityof numeric and symbolic computation. Building on the core language and extensive algorithm knowledgebase ofMathematica, Version 5 introduces a new generation of advanced algorithms for a wide range of numeric and symbolicoperations. Numeri
44、cal computation Major optimization of dense numerical linear algebra. New optimized sparse numerical linear algebra. Support for optimized arbitrary-precision linear algebra. Generalized eigenvalues and singular value decomposition. LinearSolveFunction for repeated linear-system solving. p norms for
45、 vectors and matrices. Built-in MatrixRank for exact and approximate matrices. Support for large-scale linear programming, with interior point methods. New methods and array variable support in FindRoot and FindMinimum. FindFit for full nonlinear curve fitting. Constrained global optimization with N
46、Minimize. Support for n-dimensional PDEs in NDSolve. Support for differential-algebraic equations in NDSolve. Support for vector and array-valued functions in NDSolve. Highly extensive collection of automatically-accessible algorithms in NDSolve. Finer precision and accuracy control for arbitrary-pr
47、ecision numbers. Higher-efficiency big number arithmetic, including processor-specific optimization. Enhanced algorithms for number theoretical operations including GCD and FactorInteger. Direct support for high-performance basic statistics functions. Symbolic computation Solutions to mixed systems
48、of equations and inequalities in Reduce. Complete solving of polynomial systems over real or complex numbers. Solving large classes of Diophantine equations. ForAll and Exists quantifiers and quantifier elimination. Representation of discrete and continuous algebraic and transcendental solution sets
49、. FindInstance for finding instances of solutions over different domains. Printed from the Mathematica Help Browser 11988-2003 Wolfram Research, Inc. All rights reserved. Exact constrained minimization over real and integer domains. Integrated support for assumptions using Assuming and Refine. RSolve for solving recurrence equations. Support for nonlinear, par
