About MathUser

MathUser is published by Wolfram Research to provide news and information about Mathematica to registered Mathematica users. MathUser is also available free of charge to other people interested in Mathematica. To be added to the list of subscribers or to submit a change of address, send your postal address information to mathuser@wri.com, or call +1-217-398-5151. (In Europe, fax +44-(0)1993-883800.) Note that MathUser is sent to your registration address, the same address where all other Mathematica information and mailings are sent.

Electronic copies of this and earlier issues of MathUser are available on MathSource. This issue of MathUser is MathSource item 0207-863.

The MathSource item numbers of prior issues are:

1. Spring/Summer 1992 0202-655

2. Fall/Winter 1992 0204-477

3. Spring/Summer 1993 0205-759

4. Fall 1993 0205-827

5. Winter 1994 0206-907

6. Spring 1994 0205-771

7. Fall 1994 0207-278

8. Spring 1995 0207-593

Your comments and suggestions are important to us. Send letters to the editor at the address below. We are always interested in hearing ideas for topics to be covered in MathUser.

How to Contact Us

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On the cover

"Transitions", Mathematica graphic by Igor Bakshee. One of a series of images to be included in the Graphica book.

1995 Wolfram Research, Inc. MathUser (ISSN 1062-7030) is published several times a year by Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237, USA; email: mathuser@wri.com.

Mathematica, MathLink, and MathSource are registered trademarks, and MathUser is a trademark of Wolfram Research, Inc. Mathematica is not associated with Mathematica Policy Research, Inc. or MathTech, Inc. All other product names mentioned are trademarks of their producers.

Mathematica for Microsoft Word

Now in testing, this new product will be available soon for the Macintosh and Microsoft Windows

Microsoft Word, the world's most powerful and popular word processor, will soon be available as an interface to Mathematica. If you are already using Word to create technical documents and want to incorporate live mathematical calculations, this will be an ideal combination.

You work directly in Word, entering calculations and receiving results (including graphics) in a notebook-style interface like the familiar Mathematica front end. In addition, you can use all of Word's features for advanced document processing and page layout. These features include spelling and grammar checking (which automatically ignore Mathematica input and output), equation and figure numbering, indexing and cross-referencing, multicolumn layout, text flow around graphics and frames, and a drawing environment for customizing graphics.

The Mathematica input cells are "live" and can be edited and reevaluated. Corresponding output cells will be updated in place, even if they have been moved to distant locations in the document. You can also automatically hide or delete all the inputs, outputs, or prompts. This means that you could have the output distributed throughout your document, perhaps in movable, resizable frames, with all of the input collected at the end. Hide the input, and you have a publication-ready manuscript; show it, and you have a live mathematical document.

Those who want an alternative to the traditional Mathematica notebook interface can take advantage of Word's easy-to-use macro language, WordBasic, to create interface elements like custom dialog boxes, toolbars of common functions, on-screen forms with buttons and pop-up menus, and so forth. The interface itself is written in WordBasic, and access to the full source code allows you to modify or enhance it.

Mathematica for Microsoft Word will be announced on our Web site as soon as it is available. Check the site for the latest news and ordering information.

First Asian Technology Conference in Mathematics

December 18-21, 1995 National Institute of Education, Singapore

Among the plenary talks will be one by Jerry Uhl (University of Illinois), co-author of Calculus&Mathematica: "Visual Interactive Learning through Electronic Courseware". There will be several other talks by Mathematica developers and Mathematica users from Japan, Hong Kong, and other Asian countries. Wolfram Research, Inc. will also hold training and lab sessions at the conference.

For more information, contact Ho Kheong Fong at +65-(0)460-5310, send a fax to +65-(0)469-8952, or email fonghk@nievax.nie.ac.sg. Or contact David Washburn at Wolfram Research, 217-398-0700, or email washburn@wri.com.

1995 Mathematica Developer Conference

The Inside Track for Advanced Mathematica Users

October 5-8, 1995
University of Illinois, Illini Union
Urbana-Champaign, Illinois

The 1995 Mathematica Developer Conference will give advanced users an opportunity to meet Wolfram Research staff and other Mathematica experts to share and exchange experiences and ideas. The conference will feature workshops, forums, luncheons, a computer lab, and a series of informative, practical sessions. Many of the sessions are dedicated to helping users create Mathematica packages, MathLink applications, Mathematica books, and interactive texts. Attendees will be introduced to new features of Mathematica currently in development, and will be encouraged to integrate these features into their work.

For further information or to register, call Donna Lents-Johnson at 217-398-0700, send email to devconf@wri.com, or visit our Web site at http://www.wri.com/devconf.

New Version of Mathematica Now in Testing

With over a million people around the world depending on Mathematica for fast, reliable results, Wolfram Research takes product testing very seriously. Every new version of Mathematica is subjected to an exhaustive battery of automated and human testing. The goal of this long and creatively demanding testing process is to make sure that the software is of the highest quality.

The next major new version of Mathematica, which has been under development for the past three years, is now completing its final alpha test. Although alpha testing is primarily internal, a small group of external Mathematica developers have participated in three of the alpha tests. As we had hoped, many testers' reports describe bugs and problems that will be fixed before the next stage of testing. Their constructive criticism is also helping to shape the design of the product. We received encouraging comments concerning both the front end and the kernel: "Beautiful... congratulations."; "Breakthrough!"; "The front end is just marvelous!"; "A fine accomplishment. Thanks!"

Mathematica Plus subscribers will receive the upcoming version automatically as soon as it is released. For more information about this program, contact Wolfram Research.

World Wide Web

Mathematica Courseware Directory Available on the Web

Visit the Wolfram Research Web site (http://www.wri.com/) to discover how educators around the world are using Mathematica in the classroom. The new on-line directory contains courseware descriptions from educators at colleges, universities, and high schools who have integrated Mathematica into their teaching programs. From algebra and calculus to physics and graduate-level courses, the programs in the directory provide useful examples that cover a wide range of disciplines.

You can also find information on the Web site about Wolfram Research's flexible academic purchase programs, Mathematica for Students, Mathematica for High Schools, and other resources and products designed specifically for educators and students.

Interactive Mathematica Demo Premieres on the Web

(http://www.wri.com/demo/)

A revolutionary interactive demo has been added to the Wolfram Research site. It allows Web users without a copy of Mathematica to sample Mathematica's capabilities.

When you click to start the demo from your Web browser, a Mathematica kernel is launched on a computer at Wolfram Research in Champaign, Illinois. Your input is sent to the kernel for processing and the output is returned to your screen.

New Mathematica Notebook to HTML Conversion Program Available Free

math2html is now available free on MathSource as item 0207-829.

Now you can easily put your Mathematica notebooks on the World Wide Web. The math2html program, written by H. Edward Donley from Indiana University of Pennsylvania, is a PERL program that converts Mathematica notebooks to HTML format for viewing on the Web.

math2html creates an evaluated or an unevaluated version of your Mathematica notebook in the form of an HTML document. Closed cell groups are placed in their own HTML documents and are linked to their parent documents. You can specify which series of adjacent graphics are combined into MPEG movies and which are converted to individual GIF images (math2html does not convert sounds or bitmap images). Input cells can be converted into HTML forms that can be sent to a Mathematica kernel.

New Versions of Mathematica

NEXTSTEP for SPARC
Mathematica 2.2 will be available soon under NEXTSTEP for SPARC. This new version is functionally identical to Mathematica for NEXTSTEP Motorola, Intel, and HP PA-RISC computers, and is compatible with all other notebook front end versions.

LINUX
Mathematica 2.2 is now available under LINUX. This new version includes a text-based interface and support for interprocess communication and remote computing via MathLink.

Windows 95
An update for Mathematica 2.2.3 for Microsoft Windows 95 users who did not install TCP/IP is now available on MathSource, item 0207-841. This update replaces Mathematica's local protocol.

Acquire New Mathematica Skills in a Training Course near You

Sign up soon for one-day courses in Boston, New York, and Washington, DC September 25-29 and November 6-10, 1995

Mathematica training courses are going on an east coast U.S. tour, and if you live nearby, you won't want to miss it! The courses cover practical skills that you can take back to work and use the very next day. It's the fastest way to learn how to apply Mathematica efficiently and to increase your productivity on the job.

Space is limited, so register early! For specific course dates or to register, call 1-800-441-6284, ext. 244 (U.S. and Canada only), or email training@wri.com for an electronic registration form. For more information, you can also check the training section on our Web site: http://www.wri.com/services/training/traintour/

Introduction to Mathematica ($400)

Ben Friedman, Robert Dickau, Todd Ramsburg
Wolfram Research staff

This basic training course gives new users a thorough introduction to using the system's numeric, symbolic, graphical, and programming features. In this problem-solving, hands-on session, you will learn just what you need to know to start applying Mathematica to technical problems you encounter on a daily basis.

Programming with Mathematica ($400)

Richard Gaylord
Professor, Department of Materials Science, University of Illinois at Urbana-Champaign
Co-author, Introduction to Programming with Mathematica and Computer Simulations with Mathematica

Learn to use the Mathematica programming language by discovering how pattern matching works and how expressions are evaluated. Learn tips and techniques for writing Mathematica programs that are much shorter than in C or Fortran.

Data Analysis with Mathematica ($500)

William Shaw
Principal Consultant, Oxford System Solutions
Co-author, Applied Mathematica: Getting Started, Getting It Done

Professionals in engineering, physics, biology, finance, and other applied sciences can benefit by learning to use Mathematica effectively for data analysis. This course covers methods for importing data, data modeling, how to use 2D and 3D visualization tools, regression, how to incorporate functions from the new Time Series Pack, and more.

Financial Modeling with Mathematica ($500)

William Shaw
Principal Consultant, Oxford System Solutions
Co-author, Applied Mathematica: Getting Started, Getting It Done

Discover how to harness Mathematica as a tool for complex analytical modeling, rapid development, verification for testing code, and visualization. Sections include data import mechanisms and regression tools, derivatives, portfolio covariance analysis and optimization, and enhancements for the Mathematica Finance and Time Series Packs, MathLink for Excel, and MathLive. This course is ideal for quantitative analysts and other financial engineering professionals.

Additional Mathematica Training

Mathematica Training Courses by Principia Consulting
Anaheim, CA, September 19-21.
For more information, contact Dave Wagner at 303-786-8371.

Mathematica Training Courses by Allan Hayes
Introduction to Mathematica, Intermediate Graphics and Visualization, Intermediate Programming. De Montfort University, Leicester, UK, September 13-15.
For more information, contact Jackie Mackay at +44-(0)171-490-1609, or email jackie@ledge.co.uk.

Mathematica Training Courses by CorporateU
Computation and Data Analysis, September 19-October 10; Mathematica Programming, October 17-November 11. For more information, contact CorporateU, Philadelphia, PA, at 215-988-2150.

Mathematica Training Seminar by Additive
Friedrichsdorf, Germany, September 29.
For more information, contact Beate Reif at +49-(0)6172-77015.

Principles of Mathematica by Uni Software Plus
Hands-on introductory course.
Hagenburg, Austria, September 28Ð30.
For more information, contact Herbert Exner at +43-(0)723-63-338, or fax +43-(0)723-63-33830, or email usp@unisoft.co.at.

How to Become a Mathematica Master
A one-day systematic introductory course for beginners and intermediates. For exact seminar dates (October/November) and locations in Germany, contact QT Software at +49-(0)89-33297-0, or email 100614.350@compuserve.com.

Mathematica on Wall Street: Derivatives Analysis Workshops
New York, NY, October 2; Chicago, IL, November 13; London, UK, December 20.
For more information, contact Variable Symbols, Inc. at 510-652-8462.

Mathematica for Students Is Just What Students Need for School This Fall

Now Includes Free World Wide Web Browser--A Limited-Time Special Offer*

As more and more colleges incorporate Mathematica into the curriculum, more and more students want a copy of their own to take home. At a specially reduced price, Mathematica for Students fits the bill perfectly--it's a full-function version of Mathematica, at a price that's just right for the student budget. And for a limited time only, Mathematica for Students comes with a free copy of the renowned World Wide Web browser, Enhanced Mosaic 2.0.

As students use Mathematica to delve deeper into mathematics than they ever could before, concepts become clearer and easy-to-create graphics bring ideas to life. The connection to real-world applications makes math more exciting to learn, and knowing how to use Mathematica is a valuable skill that students can put to use immediately for homework in all kinds of engineering and science courses.

Students who use Mathematica in school find they have a head start when it comes to looking for a job after graduation. Since Mathematica is what the professionals use, including it on your resume can certainly give you an advantage!

*Special offer in U.S. and Canada only.

1995-1996 High School Grants Awarded

Recipients Develop Mathematica-based Courseware to Share with Educators Worldwide

As was the case with the response to last fall's announcement of a new Visiting Scholar Grant Program, response to our new High School Grant Program was far greater than we had imagined! High school teachers around the world are bringing Mathematica into their classrooms in record numbers, and sending their students off to college very well prepared.

Grant recipients attended a three-day workshop at Wolfram Research headquarters in Champaign this summer. A Mathematica basic training course, presentations by experienced Mathematica courseware developers, and discussion time with fellow grant recipients and Wolfram Research staff gave recipients inspiration and practical information as they continue to develop their own courseware projects.

As part of the award, grant recipients also received copies of Mathematica for the computers in their school labs, so they can actually put the courseware they develop to the test with their students this fall. Plans so far include creating lessons in the form of Mathematica notebooks to teach topics in algebra, trigonometry, geometry, calculus, physics, statistics, and computer science. The resulting courseware will be published on a sample courseware CD-ROM, and will be available free of charge to high school educators.

"Mathematica is an invaluable tool for the next generation of scientists, engineers, and business leaders. I look forward to exposing my students to this top quality software product."
Gordon Locke-Scobie
High School Grant Recipient

1995-1996 High School Grant Recipients

• Daniel Boice
  Southwest Research Institute
  San Antonio, Texas

• James Button
  Antilles School
  Charlotte Amalie, Virgin Islands

• Carol Castellon
  University Laboratory High School
  Urbana, Illinois

• Sergey Feofanov
  Filer High School
  Filer, Idaho

• Sally Illman
  Roosevelt High School
  Seattle, Washington

• Michael Grasse
  Elk Grove High School
  Elk Grove Village, Illinois

• Richard Kick
  Hinsdale Central High School
  Hinsdale, Illinois

• Gordon Locke-Scobie
  Vienna International School
  Austria

• Thomas Ramsey
  Mentor High School
  Mentor, Ohio

• Reinhard Simonovits
  University of Graz
  Graz, Austria

• Christopher Thiel
  St. Francis High School
  La Canada, California

• John Tinnin
  Kaycee Junior/Senior High School
  Kaycee, Wyoming

• Rock Island High School
  Rock Island, Illinois

High School Teachers Get Mathematica for Less

Major Discounts Make It Affordable for High School Classrooms

Mathematica for High Schools contains a full-function version of Mathematica, a user interface guide, and Mathematica: The Student Book, a comprehensive manual filled with practical math and science examples that teachers and students can use in class. Substantial educational discounts make this special high school version of Mathematica available to high school teachers for up to 80% off the price of the professional version!

Using Mathematica makes it possible for teachers to present students with more real-world examples and to incorporate two- and three-dimensional graphics that are too time-consuming or complex to draw on the blackboard. In Mathematica's interactive environment, students discover how to explore math on their own, and often find that they suddenly understand concepts that were otherwise too difficult to grasp. Equipped with an alternative approach to presenting information, teachers can enhance their students' understanding of all kinds of topics in math and science classes.

Those who have the opportunity to use Mathematica in school tell us they are pleased they did. As one Illinois high school student who was in the Calculus&Mathematica Distance Education Program explained, "Most of all, Mathematica is great because it applies EVERYTHING to real situations. I feel that traditional math courses I have taken have fallen short in this area. This course is showing me how math is everywhere in the real world. I can't wait to get out there and put it to the test."

5-Packs and 10-Packs Are Perfect for School Labs

If you teach with Mathematica in a school computer lab, consider a Mathematica for High Schools 5-pack or 10-pack for significant savings off the already-low price of Mathematica for High Schools. (District-wide site licenses are also available.)

Mathematica for High Schools is available for Macintosh and Microsoft Windows.

"I find that students are more willing to 'play' with the mathematics using Mathematica than they would if they had to grind each example out on their own. Many students become more independent problem-solvers as a result of working with Mathematica."
Mike Chupa, math instructor
Tower Hill School, Delaware

"Now I know more about calculus than just definitions. I could take calculus and apply it to a situation really well."
Matthew Stanley, student
Camp Point Central High School, Illinois

"When it's presented to you on the computer, sometimes it's like you're seeing in a different way and it clicks. That was the way it was for me. Our teacher would explain something to us. Then I would come over and look at it in a different way, and then I understood."
Maria Monge, student
Fairfield Community High School, Illinois

Visiting Scholars' Progress Will Benefit Others

Grant recipients work on projects at Wolfram Research headquarters Mathematica-based application packages, courseware, and texts are the focus of projects that earned a select group of researchers and educators invitations to collaborate with Wolfram Research staff at the company's headquarters. Among the grant recipients who visited us this summer two took advantage of the expertise of nearby staff to make headway on some exciting educational projects.

Phillip Kent from Imperial College (London) spent time developing strategies for World Wide Web-based Mathematica educational materials. He organized a meeting that brought together Wolfram Research staff and the director of the U.S. Department of Energy's Undergraduate Computational Engineering and Sciences project, Thomas Marchioro. The discussion focused on courses that use Mathematica to teach problem-solving skills and on the development of public-domain software for publishing Mathematica materials in an interactive form on the Web. This spurred the establishment of an active email group as a forum for continuing discussion on these topics. You can access more information on the Web at URL http://uep.ameslab.gov/dev/tlm/uces_wri.html.

Grant Keady from the Department of Mathematics at the University of Western Australia worked on developing a series of instructional Mathematica notebooks to accompany the well-known text, Advanced Engineering Mathematics, by Zill and Cullen. You can access these notebooks on the Web site at URL http://www.pws.com/diffeq.html. He also used the time to pursue his interests in links between numerical computing and computer algebra, particularly using MathLink.

For information on the Mathematica Visiting Scholar Grant Program, email grants@wri.com.

Mathematica at the top!

For the past two years, Stan Wagon, author of several Mathematica books, has organized a highly successful workshop in Colorado called "Mathematica in the Mountains". This year, Stan's workshop attracted more than 30 high school and college teachers. Participants scaled new heights in the use of Mathematica while on a hike to the summit of Torreys Peak (14,267 ft.) in the middle of a hailstorm.

The World of Mathematica Graphics on Display

Be among the first to receive this new series of art books. Since the introduction of Mathematica seven years ago, the system's powerful graphics capabilities have earned it widespread recognition as an essential tool for effectively communicating complex scientific and mathematical ideas.

Quickly adopted by researchers and scientists, Mathematica is commonly used to create the graphics now seen in standard textbooks and appearing in technical journals around the world. Even beyond the scientific community, however, many have tapped its powerful capabilities to create stunning images that have captured the attention of technical and nontechnical people alike. Soon the talents of a few people who have become experts in creating elaborate and impressive images using Mathematica will be showcased in the Graphica books, a new series of hardcover, large-format, full-color art books.

This is not the first time images created using Mathematica have ventured outside purely scientific applications. Mathematica graphics have found their way into Hollywood special effects, architecture, sculpture, and industrial and graphic design. Images by the physicist and artist whose works are featured in Graphica 2, for example, have been reproduced on clothing fabrics, wallpaper, and automobile upholstery, and not surprisingly, as fine art prints.

Now this spectacular series can be made a part of your own library collection at home or work. The images in these books may even inspire you to realize the aesthetic potential in your own Mathematica-based creations.

As a Mathematica user, you are invited to register for a special Graphica charter offer. For more information, send email to info@graphica.com.

Many of these and other images are available for licensing. For more information, email licensing@graphica.com.

Reading and Writing External Files

Sometimes users have to work with data stored not in a notebook but in some external file. Mathematica has many facilities for dealing with external files. Text or binary data can be read in, manipulated in some way, and then written back out.

*Viewing the Contents of a File

Before reading a file into Mathematica, you can look at the contents with the !! command.

!!polyfile

1 + 2*x + x^2

*Reading and Writing Expressions

The Get command is the basic command for reading a file into Mathematica. The commands in the file are read in as if you had typed them into your session directly.

Get["polyfile"]

1 + 2 x + x²

This is the equivalent short form.

<<polyfile

1 + 2 x + x²

We can use the corresponding Put command (or the short form >>) to write an expression out to a file.

Factor[x^2 + 2 x + 1] >>: factorfile
!!factorfile

(1 + x)^2

*Reading in Data

Mathematica input/output commands are often used to read data that are in tabular form. The ReadList command reads in each row as a sublist of a larger list.

!!matrixfile

1 2 3 
4 5 6

mymatrix = ReadList["matrixfile",
          {Number, Number, Number}]

{{1, 2, 3}, {4, 5, 6}}

pairmatrix = ReadList["matrixfile", {Number, Number}]

{{1, 2}, {3, 4}, {5, 6}}

We can also read in the numbers as a flat list.

mylist = ReadList["matrixfile", Number]

{1, 2, 3, 4, 5, 6}

If you don't know ahead of time how many columns of data you have, you can add the RecordLists option. If this option is set to True, then each line of data is read into a separate sublist.

mymatrix = ReadList["matrixfile", Number, 
    RecordLists -> True]

{{1, 2, 3}, {4, 5, 6}}

mystream = OpenRead["matrixfile"]

InputStream[matrixfile, 11]

The Read command reads data from the stream, one line at a time.

line1 = Read[mystream, 
       {Number, Number, Number}]

{1, 2, 3}

line2 = Read[mystream, 
       {Number, Number, Number}]

{4, 5, 6}

Close[mystream]

matrixfile

Putting the lines into a list gives the same matrix as the one we got using ReadList.

mymatrix = {line1, line2}

{{1, 2, 3}, {4, 5, 6}}

*Reading More Complicated Files

In the previous simple example, it was more efficient to use ReadList than to open a stream and use Read. However, streams let you read complicated files that ReadList cannot handle. We need to know the structure of the file before being able to read it properly.

!!polymatrixfile

Here is a polynomial:
1 + 2x + x^2

Here is a matrix:
1 2 3
4 5 6

As before, we open a stream to this file.

mystream = OpenRead["polymatrixfile"]

InputStream[polymatrixfile, 7]

We use the Read command to read off the first piece of text as a string.

mystring1 = Read[mystream, String]

Here is a polynomial:

We use Read again, specifying that an expression (the polynomial) is to be read.

mypoly = Read[mystream, Expression]

1 + 2 x + x²

Reading an expression does not advance us to the next line, so we need to read the newline character to throw it away.

Read[mystream, Character];

Now we can read the second piece of text as a string.

mystring2 = Read[mystream, String]

Here is a matrix:

Since we know that a table of data is next, we can use ReadList on the stream.

mymatrix = ReadList[mystream,           
        Number, RecordLists -> True]

{{1, 2, 3}, {4, 5, 6}}

Close[mystream]

polymatrixfile

*Reading Comma-Separated Data

Mathematica does not have a built-in command for reading comma-separated data.

!!commafile

1,2,3
4,5,6

There are several ways to read this data in as a matrix. You need to know the number of columns to use the following combination of commands.

Partition[Map[First, ReadList[
  "commafile", {Number, Character}]],
    3]

{{1, 2, 3}, {4, 5, 6}}

Map[ToExpression, ReadList[
  "commafile", Word, 
  RecordLists -> True, 
  WordSeparators -> {",", " "}], {2}]

{{1, 2, 3}, {4, 5, 6}}

Map[ToExpression[
  StringJoin["{", #, "}"]]&,
    ReadList["commafile", String]]

{{1, 2, 3}, {4, 5, 6}}

Suppose we want to write out the following matrix.

mymatrix2 = {{10, 20, 30}, {40, 50, 60}};

There is no built-in command analogous to ReadList for writing a list or matrix of data to a file. However, we can use the following sequence of commands. The OpenWrite command creates an OutputStream that allows us to write data to a file.

mystream = OpenWrite["matrixfile2"]

OutputStream[matrixfile2, 4]

The following converts the matrix into one string; the numbers are separated by spaces and the rows are separated by a newline character.

matrixstring = ToString[ 
  TableForm[mymatrix2, 
    TableSpacing -> {0,1}] ] 

10 20 30
40 50 60

FullForm[%]

"10 20 30\n40 50 60"

WriteString[mystream, matrixstring]

We tidy up by closing the stream.

Close[mystream]

matrixfile2

We check that the data are in the file.

!!matrixfile2

10 20 30
40 50 60

While this routine is short, only spaces are allowed to separate the columns of data. The more flexible function WriteMatrix requires two arguments: a filename and a matrix. The optional third argument specifies the column separator, with the tab character as the default.

WriteMatrix[file_String, matrix_List, 
        separator_String:"\t"] :=
   With[{myfile = OpenWrite[file]},
   Scan[(
     WriteString[myfile, First[#]];
     Scan[
       WriteString[myfile, separator,      
         #]&, Rest[#]];
      WriteString[myfile, "\n"]
   )&,    
   matrix];
   Close[myfile]
]

WriteMatrix["tabfile", mymatrix2]

tabfile

!!tabfile

10      20      30
40      50      60

WriteMatrix["commafile", mymatrix2, ","]

commafile

!!commafile

10,20,30
40,50,60

Rieman Zeta Poster

A special edition of the six-foot-long poster on the Riemann zeta function (originally produced in 1990) has been re-created to honor the work of Jerry Keiper (1953-1995). Keiper was the leader of the numerics research and development group at Wolfram Research and author of many numerical algorithms in Mathematica. Posters are available at cost from Wolfram Research ($15 U.S., $20 outside the U.S.; includes shipping and handling).

Mathematica Publishing Support

The Mathematica Developer Support program contributes to Mathematica book development by giving authors access to the technical publishing expertise of the Wolfram Research staff. We encourage authors to contact us for advice on book production and electronic publishing issues, as well as for critical readings of manuscripts and information about how upcoming changes in Mathematica will affect their projects. If you are writing a book, the Developer Support program can help you do things right, from technical and production issues to connections with potential publishers.

At Wolfram Research we put great value on the many books and articles that show people how to use Mathematica to learn, discover, and to get things done, as well as those authors who use Mathematica to get their results. More than 100 books about Mathematica are now in print (see http://www.wri.com/mathematica/books/index.html, and MathSource item 0203-825); and some 2000 articles using Mathematica have appeared in scientific journals (see MathSource item 0205-018 for selective bibliography).

As Mathematica expands in every field where mathematics is applied, Wolfram Research works with publishers to identify subject areas for needed new Mathematica books, and locates authors to write them. And to ensure that published material is widely distributed in the Mathematica community and beyond, Wolfram Research regularly promotes Mathematica books through trade shows and mailings. If you have a Mathematica book or article, we would very much like to receive a copy of it (send to Librarian, Wolfram Research, Inc.; in return we will send you a free Mathematica T-shirt).

Some contact points for Mathematica authors:
Developer Support program devsupport@wri.com
Permissions Editor permissions@wri.com
WRILaTeX (documentation kit) wrilatex@wri.com
Notebook-to-TeX converter nb2tex@wri.com
Or call 217-398-0700

Mathematica's Popularity in Japan Explodes

Corporate and research organizations, universities, and high schools alike discover its advantages

From high school students first learning algebra to experienced researchers at scientific institutions and universities, Mathematica is becoming firmly established as the technical computing system of choice. Considered an indispensable productivity tool at major corporations and research centers, Mathematica is being increasingly applied in finance, optics, and all areas of engineering, with users at organizations such as Matsushita Electric Company, Mitsubishi Electric, NTT, Nikon, Olympus, and the National Lab for High Energy Physics.

Waseda University regularly uses Mathematica in science classes for over 1900 first-year students, and recently hosted a training session for 800 students, organized by Mathematica reseller Japan Information Processing Service (JIPS). Customized academic purchase programs have made Mathematica affordable for all types of universities. Among the over 80 universities that participate in academic site programs are: the University of Tokyo, Tohoku University, Waseda University, Science University of Tokyo, Kobe University, Aizu University, and Chuo University.

Mathematica User Group in Japan Hosts Annual Meeting

Over 400 expected to attend

Mathematica User Conference
December 2, 1995
Tokyo Denki University-Hatoyama campus

Featuring keynote speakers from Wolfram Research's research and development team, user presentations, and an on-site computer lab.

For more information or to register, contact:
Scientist-sha
Yamazaki Building, 3-2 Kanda Surugadai
Chiyoda-ku, Tokyo 101, JAPAN
phone: 81-(0)3-3253-8992; fax: 81-(0)3-3255-6847;
email: info-asia@wri.com

The Mathematica Book Now Available in French

ISBN 2-87908-035-5

To get a copy of Mathematica: Le systeme informatique pour les mathematiques, the French translation of the definitive text on Mathematica by Stephen Wolfram, visit your local bookstore or contact the publisher:

Addison-Wesley France
41, Rue de Turbigo, 75003 Paris, France
phone: +33-(0)1-4887-9797; fax: +33-(0)1-4887-9799

Also available in German and Japanese. For more information contact:

Addison-Wesley Deutschland GmbH
+49-(0)228-98-5150
(Mathematica: Ein System fŸr Mathematik auf dem Computer; ISBN 3-89319-371-5)

Addison-Wesley Japan Ltd.
+81-(0)3-3291-4581
(Mathematica: A System for Doing Mathematics by Computer, in Japanese; ISBN 4- 7952-9614-6)

Fuzzy Logic

What is it, and why do engineers and researchers use it in their work?

by Marian S. Stachowicz and Lance Beall, authors of the recently released Mathematica Fuzzy Logic Pack

Mathematics based on classical set theory is only able to describe situations where a sharp boundary distinguishes elements having a certain property from those that do not. In terms of logic, a proposition is either true or false, with nothing in between.

More commonly in the real world, however, we have to deal with "unsharp" phenomena--imprecise situations in which it is difficult to find a boundary between truth and falsehood.

Fuzzy logic extends conventional Boolean logic to handle the concept of partial truth, so that truth values can be between "completely true" and "completely false". Fuzzy logic can be used to describe complex systems involving human linguistic descriptions, where Aristotelian two-valued logic is ineffective. With fuzzy set theory it is possible to relate linguistic information to a computer, allowing us to communicate with computers more naturally.

*Applications of Fuzzy Logic

Fuzzy logic is being applied increasingly over a wide range of fields. This technology is particularly popular in Japan, where over 1000 patents have been filed in the last few years. These fuzzy logic-based products have grossed billions of dollars in sales around the world.

One of the first applications of fuzzy logic was to control a cement kiln in Denmark. Michio Sugeno displayed the power of fuzzy logic control by using it to fly a model helicopter. Some classic examples of problems that can be solved with fuzzy control include truck-backing, balancing an inverted pendulum, and controlling a hanging crane. Recently, fuzzy logic has been used to control everything from consumer electronics to the Sendai subway.

*Advantages of Fuzzy Logic

Fuzzy systems offer a number of benefits over traditional systems; it is often possible to develop solutions for complex, ill-defined problems quickly. This is especially true if there is a good deal of expert knowledge about a process or if the problem is easy to describe linguistically. Neither exact system parameters nor complicated equations describing physical processes are needed to find a solution to a problem. Furthermore, once the system is designed and working, the linguistic variables and rules make maintenance easier.

Another advantage of fuzzy systems is that they tend to be more robust than traditional systems; they are naturally much more tolerant of fluctuating or changing system parameters or operating conditions. This could be an important advantage if you are looking for a solution for a noisy process or a process that changes over time. Using a smaller number of general rules that describe all situations, fuzzy systems can achieve a performance better than traditional systems.

*The Future

Fuzzy systems are able to deal with vague and ambiguous information that is common in natural language. Since we live in an imprecise and uncertain world, it is pretty certain that fuzzy logic will be an important engineering tool in the next century.

*Fuzzy logic is being applied in an ever-broadening range of areas, including:

• linear and nonlinear process control (robotics, automation, tracking)

• consumer electronics (digital high-definition televisions, VCRs, microwave ovens, cameras)

• pattern recognition (image processing, machine vision)

• decision making (sensor fusion, risk analysis)

• financial systems

• information systems (database management, information retrieval)

• data analysis

• meteorology

Now Available

Fuzzy Logic Pack

Engineers and system designers can apply this pack's practical, customizable set of tools immediately to create, modify, and visualize all kinds of fuzzy logic-based systems. It's also ideal for a solid introduction on how to use fuzzy logic to quickly model nonlinear systems and systems with incomplete or ambiguous input data.

Signal Processing Pack

This set of Mathematica-based tools for working with signals and systems focuses on symbolic transforms, classical filter design, and signal analysis by transforms and graphical presentation.

These packs are available for all platforms that run Mathematica 2.2 or later. (Versions that support the notebook front end are required in order to use on-line documentation.)

Free!

For a complete listing of all Mathematica-related products--application-specific packages, courseware, books, journals, gift items, and more--check our Web site or contact Wolfram Research today for your own Mathematica Products Catalog.

Q&A

Q: How do I plot two curves on the same plot, one as a solid line and one as a dashed line? What about different colors?

A: You can graph several functions simultaneously by putting the functions into the first argument of Plot as a list.

Plot[{Sin[8 x] E^(-x), E^(-x)}, {x,0,5}, PlotRange -> All];

The PlotStyle option is used to change the way the individual curves are displayed. PlotStyle is set to a list of sublists; each sublist specifies the style for the corresponding curve. In the following plot, the first curve is not changed because the first sublist is empty, {}. The second curve is drawn as a thick, dashed, red line.

Plot[{Sin[8 x] E^(-x), E^(-x)}, {x,0,5}, PlotRange -> All,
 PlotStyle -> {{}, 
  {Thickness[.009],Dashing[{0.02}],  
     Hue[0.67]}}];

Q: How can I export a graphic from Mathematica for Windows to another program?

A: The Mathematica 2.2.2 (or later) front end provides two facilities for exporting graphics to other applications. The easiest method is to use the Windows Clipboard. To do this, select the graphic with the mouse pointer, and choose Copy under the Edit menu. Switch to the other Windows application, position the cursor where you want to insert the graphic, and choose Paste under the Edit menu. If the other Windows application supports graphics, your Mathematica graphic should show up in that application. Unlike earlier versions, the graphics pasted from Mathematica 2.2.2 (or later) can be rescaled without losing any resolution or introducing "jaggies".

The second way to export a graphic is to save it as a file. Once again, select the graphic using the mouse pointer. This time, choose Export under the File menu. A dialog box will appear. Under "File Type:" there are several kinds of files that can be saved. For a regular graphic, choose TIFF (*.TIF), Encapsulated PostScript (*.EPS), or Windows Metafile (*.WMF). Choose the appropriate format, name the file with the proper extension (*.TIF, *.EPS, or *.WMF), and click OK. In order to import these files into another Windows program, consult the documentation for that program.

Q: How do I add labels and change line styles in ContourPlot?

A: To display labels in ContourPlot, use the option FrameLabel. Axes is set to False by default, so axes labels are not rendered. The default for Frame is True, so all frame labels will be displayed.

ContourStyle modifies the appearance of the contour lines in the plot. All that you need is a list of graphics directives that affect lines.

ContourPlot[ Re[Tan[x + y I]], 
  {x,1,2}, {y,0,1},
    FrameLabel -> {"Bottom",  
     "Left", "Top", "Right"},
    ContourStyle -> 
      {Dashing[{0.02,0.02}], 
         RGBColor[1,0,0]}];

Q: How does the option LightSources affect a Graphics3D object?

A:Let's look at the usage message first.

?LightSources

LightSources is an option to Graphics3D and related functions that specifies the properties of point light sources for simulated illumination. The basic form is LightSources -> {{direction1, color1}, {direction2, color2}, ... }. The direction is specified as {x, y, z}. The color can be specified by GrayLevel, Hue or RGBColor.

FullOptions gives the default values.

FullOptions[Graphics3D[{}], LightSources]

{{{1., 0., 1.}, RGBColor[1., 0, 0]},

{{1., 1., 1.}, RGBColor[0, 1., 0]},

{{0., 1., 1.}, RGBColor[0, 0, 1.]}}

Each light source has a location and color. The coordinate systems for the locations of the light sources and Graphics3D objects are different. The origin is at the center of the screen or print image, the x axis is horizontal, the y axis is vertical, and the z axis is perpendicular to the display.

If you are sitting squarely in front of your screen, the defaults for LightSources shine a red light from your right shoulder, a green light from above your right shoulder at about head height, and a blue light from your forehead.

The next graphic shows the effect of LightSources alone and in combination. We need to load the Graphics`Shapes` package to draw a torus.

Needs["Graphics`Shapes`"]

t = Torus[];

Show[GraphicsArray[{
{
Graphics3D[t, LightSources -> 
 {{{1., 0., 1}, RGBColor[1,0,0]}}],
Graphics3D[t, LightSources -> 
 {{{1., 1., 1}, RGBColor[0,1,0]}}] 
},
{
Graphics3D[t, LightSources ->   
 {{{0., 1., 1}, RGBColor[0,0,1]}}],
Graphics3D[t]
} 
}]];

Show[GraphicsArray[{
{
Graphics3D[t, LightSources ->  
 {{{1., 0., 0.}, Hue[.8]}}],
Graphics3D[t, LightSources -> 
 {{{0., 1., 0.}, Hue[.6]}}]
},
{
Graphics3D[t, LightSources -> 
 {{{0., 0., 1.}, Hue[.4]}}],
Graphics3D[t]
}
}]];

Q: What are some techniques for speeding up Mathematica calculations?

A: Operating with Lists

If a calculation involves accessing all of the elements in a list, there are several techniques that will speed up evaluation. We will add 1 to each of the 10,000 elements of mylist in four different ways.

mylist = Table[
Random[Integer,{1,10}],{10000}];

To compare the speed of evaluation, we use the Timing command. Timing[expr] returns a list of two elements: the time it took to evaluate expr and the result of that evaluation. The following examples were done on a Macintosh IIcx.

The first way is to use the For and AppendTo commands. The For command does not return a result, so the second element is Null.

Timing[
  newlist1 = {};
  For[i = 1, i <= Length[mylist], 
    i++,
    AppendTo[newlist1, 
      mylist[[i]] + 1]]
  ]

It is faster to use the Table command to construct a new list. This time the long result is suppressed with a semicolon.

Timing[
  newlist2 = Table[mylist[[i]] + 1,  
    {i, 1, Length[mylist]}];
]

To make the calculation a little faster, you use the Map command to avoid accessing each element individually.

Timing[
  f[x_] = x + 1;
  newlist3 = Map[f, mylist];
]

Here is a more dramatic speedup. The Plus command has the attribute Listable: when a single number is added to a list, it will be added to every element of that list.

Timing[
  newlist4 = mylist + 1;
]

A simple check shows that all of the new lists are identical.

newlist1 == newlist2 == 
            newlist3 == newlist4

Compiling for Speed

The Compile function can be used to speed up commands. Here is a function of t.

f[t_] = Abs[1 +
E^(-I ((7 Pi)/12 + Pi Cos[t])) +
E^(-I ((7 Pi)/6 + 2 Pi Cos[t]))];

PolarPlot for this function takes a very long time. This function is defined to accept any expression (real, integer, or symbolic) for t. We can use the Compile command to define an associated function that will work only for real numbers. Compile has the HoldAll attribute, so we need to add the Evaluate command.

fCompiled = Compile[{{t,_Real}}, Evaluate[f[t]]];

Now PolarPlot plots the graph in 18 seconds.

Needs["Graphics`Graphics`"]

Timing[
  PolarPlot[fCompiled[t], 
   {t,-Pi,Pi}, PlotRange -> All]
]

Not all calculations can be speeded up by using Compile. However, for those that can, the savings in time can be tremendous. For more information on Compile, see page 312 of The Mathematica Book.

Second Edition of MathSource Compact Disc Now Available

The second edition of the entire MathSource collection on CD-ROM was released in April. This major revision includes the following new features:

• 20% more items
  There are nearly 700 distinct items on the CD-ROM (over 5000 files), including Mathematica tools and packages, documentation, electronic books, and journal supplements.

• table of contents with abstracts
  This notebook listing of all the items reflects how the CD is organized. Mathematica's extensive search capabilities make it easy to identify the items and files you want and to see where to find them on the CD.

• immediate access to files
  It isn't necessary to copy any archive files onto your hard disk. Tarred-and-compressed, Binhexed, and PKZipped archives are de-archived for the appropriate platform, making all the files on MathSource accessible directly from the CD.

The MathSource CD is available for Macintosh, MS DOS/Windows, and Unix/VMS. Call Wolfram Research or your nearest software dealer to order today!

Macintosh-format CD can be used on any Macintosh and any other computer that can read HFS file systems. MS DOS/Windows CD uses ISO-9660 level 1 format, and is best used on computers limited to 8.3 filenames. Unix/VMS CD can be used on any platform that recognizes ISO-9660 with Rock Ridge extensions.