Contents

• Mathematica on the World Wide Web

• Wolfram Research in Japan

• Pattern Matching with Mathematica

• The Quintic Poster

• New Mathematica Applications and Links

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 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 0207-278.

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

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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

Wolfram Research, Inc.
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phone: 217-398-0700; fax: 217-398-0747
orders: 1-800-441-MATH (6284)
customer service: 217-398-5151
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Wolfram Research Europe Ltd.
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Oxfordshire OX8 8LN, UNITED KINGDOM
phone: +44-(0)1993-883400
fax: +44-(0)1993-883800

Wolfram Research Asia Ltd.
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3-2-15 Misaki-cho
Chiyoda-ku, Tokyo 101, JAPAN
phone: +81-(0)3-5276-0506
fax: +81-(0)3-5276-0509

Internet email addresses
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On the Cover

The cover shows elements taken from the quintic poster; see the article on page 8.

(C)1994 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.

Wolfram Research on the World Wide Web

An extensive assortment of news and information about Mathematica is available to millions of Internet users on the Web.

Mathematica users have always been quick to take advantage of the many Internet services offered by Wolfram Research. The ease of automated software registration and password generation through email has been very popular with customers. So has email-based technical support--our customers' preferred way to get technical support for many years. And MathSource uploads and downloads have generated heavy traffic from the start, partly because MathSource can be accessed via email as well as anonymous FTP, Gopher, and direct dialup. Now, certain to be avidly used by customers and visitors alike, the new Wolfram Research Web site is filled with helpful information about Mathematica.

From the first page of the new Web site, you can access Mathematica Products

Information, including descriptions about Mathematica applications and publications. You can also get current news and company information.

Also through the Wolfram Research Web site, you can download MathReader, the Mathematica notebook reader. Once MathReader is installed, the Web server allows you to take an electronic tour of Mathematica and to view notebooks from other Web sites or from MathSource.

The Web site provides information about registration and passwords, technical support, customer service, Mathematica training, user groups, and more. In the Gallery, you can hear Mathematica-generated sounds or view graphics and animations. MathSource, which is already available via CD-ROM and other Internet access systems, is fully accessible through the Web site as well.

1994 Is an Outstanding Year for Wolfram Research

As we enter the last quarter of 1994, MathUser caught up with chief operating officer Prem Chawla, who is responsible for day-to-day operations at Wolfram Research.

*How has Wolfram Research fared as a company in 1994?

Chawla: 1994 has been a very good year for us. We have always followed a clear strategy: to make products that are very solid and that will enhance the productivity of our users for many years. Following this strategy, Wolfram Research has continued to increase its revenues over the years. In fact, the company has been profitable every single quarter since its inception. Furthermore, we have been able to grow the business aggressively without requiring any outside investment.

*What does the financial success of Wolfram Research mean for Mathematica users?

Chawla: Most important, it means that we can provide high-quality support for our users, now and in the future. This year, for example, we have significantly expanded services and technical support for users in Europe and Asia. In addition, our profitability has allowed us to invest heavily in both short-term and long-term research and development. Nearly a quarter of our staff works directly on developing our core Mathematica technology. In addition, this year we have added substantial staff in application products development.

1995-1996 Grants Available to Academics and High School Educators

Mathematica grant recipients will get free software and support for developing courseware and packages--apply by February 1995

Wolfram Research has introduced two new Mathematica grant programs designed to support educators who are developing Mathematica-based courseware and application packages.

The Visiting Scholar Program is open to experienced Mathematica users from universities or high schools who have already begun developing Mathematica-based courseware or application packages. Award recipients will be invited to spend up to eight weeks at company headquarters to consult with Wolfram Research staff and collaborate with fellow award recipients. Advanced training, technical and project development support, office space, and travel expenses and living accommodations during that period will be provided by Wolfram Research.

The High School Courseware Grant Program is open to high school teachers who plan to use Mathematica in the classroom. Award recipients will receive up to 20 Mathematica High School Version licenses for their high school computers, free updates during the 1995-96 academic year, and courseware development and technical support.

Recipients will also be invited to attend a special three-day courseware training seminar at Wolfram Research headquarters in Champaign, Illinois.

Grant applications are due by February 15, 1995, and award winners will be announced by April 15, 1995. For more information or to request a Mathematica grant program application, contact Wolfram Research.

Wolfram Research Opens New Office in Japan

Wolfram Research Asia Ltd. officially opened its doors on August 1 of this year. Centrally located in the business district of Tokyo near the Tokyo Dome (home of the Tokyo Giants), this new office brings Wolfram Research closer to the many Mathematica users in Japan, Korea, Taiwan, and China.

The most immediate benefit for users in Japan is that the new office provides direct technical support to resellers, who in turn can provide more comprehensive technical support to their customers. Close contact with resellers also helps Wolfram Research stay abreast of special technical issues associated with Asian operating systems and hardware, so our development team can make sure necessary modifications are made to keep Mathematica running efficiently on these systems.

Staff in the new office speak both Japanese and English, and are focusing on bringing timely information to regional customers about new developments. They also plan to organize speaking tours and training seminars for users at all levels of expertise.

Mathematica for Microsoft Windows Manual Now Available in Japanese

Customers in Japan who purchase Mathematica for Microsoft Windows will now receive two main components of the system's documentation in Japanese. The user interface manual has been translated into Japanese to accompany the previously translated main documentation, Mathematica: A System for Doing Mathematics by Computer by Stephen Wolfram. To make Mathematica as easy to use as possible, other translations into Japanese are underway. To order Japanese documentation, contact one of the Mathematica resellers in Japan.

Mathematica Seminar Tour in Japan

Presenters Theodore Gray, director of User Interface Development (Wolfram Research), and Paul Wellin, mathematics professor at Sonoma State University (USA), will accompany Wolfram Research Asia Ltd. staff and local resellers as they visit universities and organizations throughout Japan later this year to introduce Mathematica and to discuss developments in forthcoming versions of the system. All but the Mitsubishi Electric event are open to the public.

Several hundred users are expected to attend the second annual Mathematica User's Group Meeting at Waseda University in Tokyo on December 10. The talks by Theodore Gray and Paul Wellin will be translated simultaneously, and in addition, users will present various applications of Mathematica in such areas as biology, statistics, data analysis, and differential geometry. Programming with Mathematica will also be a focus of several presentations.

For more information about any of these presentations, contact Wolfram Research Asia Ltd.; email: info-asia@wri.com or phone: +81-(0)3-5276-0506. For registration information for the User's Group Meeting, contact Scientist-sha, phone: +81-(0)3-3253-8992.

Tour Schedule

December 2
University of Tokyo

December 3
Science University of Tokyo

December 5
Reseller office in Osaka

December 6
Mitsubishi Electric, Amagasaki (staff only)
Kyoto Sangyo University

December 7
Kobe University

December 10
User's Group Meeting at Waseda University

1994 European Mathematica Conference for Advanced Users

Many of Europe's most advanced Mathematica users recently met in Oxford, England, to learn more about the system and to share their ideas. The first Mathematica Conference for Advanced Users to be held outside the U.S. was a great success, with over a hundred users coming from all over Europe and as far away as Australia.

Stephen Wolfram, President of Wolfram Research, opened the event with an outline of the new technology being developed for the forthcoming release of Mathematica and a discussion of the underlying design principles.

Users went on to learn from a series of tutorials and discussion sessions. Many of Wolfram Research's development staff were available to answer questions about their work and to offer help. "I am already making use of what I learned," said Michael Quinlan of the Department of Mathematical Physics at University College, Cork.

Many new Mathematica packages were demonstrated, and users presented their work in areas as diverse as financial analysis, high energy physics, education, and shrimp-peeling machines. Business sessions explained the support available from Wolfram Research to enable package developers to market their work.

"These events give us valuable feedback on the direction that we are taking," said Stephen Wolfram. "The attendees' response was very encouraging."

The event was organized by Wolfram Research Europe Ltd. "It is important for the European office to strengthen its relationship with its growing base of European users," said Jon McLoone, conference organizer. "This was a great opportunity for us to learn more about what people want in the many countries of Europe."

Wolfram Research offers events such as Mathematica Days and Advanced User Conferences to support the use of Mathematica. We are keen to hear suggestions from users about future events. Contact Wolfram Research Conference Organizers at 217-398-0700 or +44-(0)1993-883400, or send email to conference@wri.com.

MathSource on CD-ROM

The MathSource CD-ROM contains the entire MathSource collection of packages, notebooks, courseware, examples, book supplements, and more on a single CD-ROM.

Formats available: ISO-9660/Rock-Ridge; Macintosh HFS. To order, see "How to Contact Us".

Did You Get your Mathematica Products Catalog?

The very first edition of the Mathematica Products Catalog was mailed earlier this year, and we want to make sure you received your copy!

The catalog contains descriptions and ordering information for Mathematica application products as well as a broad selection of books, courseware, MathLink applications, MathSource information, and miscellaneous items.

If you didn't get your free copy, or would like us to mail one to a friend, please contact Wolfram Research.

Subject to availability.

UK Office Moves

On July 29, Wolfram Research Europe Ltd. expanded to occupy new offices, more than tripling their office space. The new offices are now integrated with the European warehouse for promotional materials and Mathematica stock for UK and Ireland customers.

"The move has increased efficiency and provides room for the expansion of Wolfram Research services in Europe: both enable support enhancements for the growing European Mathematica community," said Conrad Wolfram, general manager, Wolfram Research Europe Ltd.

For the new address and telephone numbers, see "How to Contact Us".

New Versions

OS/2
A native OS/2 version of Mathematica (Version 2.2.3) is now available. This version features full 32-bit addressing and includes a text-based interface with built-in editing. The next version of Mathematica OS/2 (Version 2.2.4), currently in development, will include support for remote computing and interprocess communication via MathLink and TCP/IP. A Microsoft Windows-based notebook front end will be included in this version. It will provide an alternative user interface for users who have Windows and TCP support installed on their OS/2 systems. Customers who purchase the current version of Mathematica for OS/2 will be entitled to a free upgrade to the one in development.

Windows NT
Mathematica 2.2.3 for Windows is now available for Intel-based systems. This version is compatible with both Windows NT and Windows 3.1. Mathematica for the MIPS and DEC Alpha versions of Windows NT are now in development.

DEC OpenVMS
Mathematica 2.2.3 is now available for Digital Equipment Corporation's 64-bit Alpha AXP systems running OpenVMS.

DEC OSF/1 AXP
The X notebook front end will soon be available as a 32-bit application for Digital Equipment Corporation's 64-bit Alpha AXP systems running OSF/1 2.0 or above. This front end is compatible with other notebook versions and runs under Motif.

Linux
A version of Mathematica for Linux is in the initial stages of development. For further information as development progresses, please email info@wri.com.

Pattern Matching with Mathematica

Pattern matching is perhaps the most distinctive feature of the Mathematica programming language. Very few programming languages include pattern matching at all, and none approach the flexibility and seamless integration of pattern matching in Mathematica. Although pattern matching is often unfamiliar to users of other languages, the pattern matching facilities in Mathematica are very easy to learn, and often provide simple and intuitive solutions to problems that can be difficult to handle by any other means.

One of the more common applications of pattern matching is in replacing parts of expressions with other expressions. If you can write a pattern that matches the expressions you want to replace, you can use that pattern to make the desired replacements.

Here, for example, is a pattern that matches the logarithm of a power.

Log[x_^a_]

Using this pattern, the following rule can be used to replace the logarithm of a power in the usual way.

powerrule = Log[x_^a_] -> a Log[x];

Rules can be applied using the slash-dot operator.

Log[Sqrt[2]] - Log[1/Pi] + Log[(x + y) ^ 3] /. powerrule

This is the result.

Log[2]
------ + Log[Pi] + 3 Log[x + y]
  2

All uses of pattern matching to make replacements are little more than variations on this theme. If you understand this example, you are ready to start using pattern matching in your own programs. You can see more examples and functions in Section 2.3 of The Mathematica Book.

Patterns in Function Definitions

You can often simplify the definition of a function by putting the arguments in a suitable form and naming the important parts. In this example two of the variables do not have to be named because they are not used on the right-hand side.

f[(_ z_ + _) / (c_ z_ + d_)] := (c z + d) ^ (-2 m) f[z]

To make this definition without pattern matching you would have to use a module, local variables, conditionals, and some complicated constructions to get at the right pieces.

f[(2 + 5 x) / (1 + 2 x)]

This is the result.

    f[x]
------------
         2 m
(1 + 2 x)

Using FullForm

Pattern matching is a fundamental computational operation that is used very broadly, not just in mathematics. Its generality prevents it from making use of mathematical knowledge beyond axioms like commutativity and associativity--were it to try to do that, it would have to attempt many theoretically undecidable questions.

The output that you see from Mathematica is designed for human eyes. Expressions that look the same may be structurally different. FullForm reveals the internal representation of expressions.

FullForm[2 / 3]

Rational[2, 3]

FullForm[2 / 3.]

0.6666666666666666667

FullForm[2 / x]

Times[2, Power[x, -1]]

In the next example, notice that the second Sqrt[x] is not transformed to become 1/s.

Sqrt[x] + 1/Sqrt[x] /. Sqrt[a_] -> s

       1
s + -------
    Sqrt[x]

FullForm shows that the representation of Sqrt[x] depends on whether it is in the numerator or the denominator.

FullForm[ Sqrt[x] ]

Power[x, Rational[1, 2]]

FullForm[ 1/Sqrt[x] ]

Power[x, Rational[-1, 2]]

Sqrt[x] + 1/Sqrt[x] /. 

        {Sqrt[a_] -> s, 1 / Sqrt[a_] -> 1/s}

1
- + s
s

A Graphics Example

When midpointrule is applied it will "average" a polygon, replacing the polygon with vertices v1, v2, v3, I by the polygon with vertices (v1+v2)/2, (v2+v3)/2, I.

midpointrule = Polygon[x_] :> Polygon[(x + RotateRight[x]) / 2];

The rule is applied once and then twice to a polygon p.

p = Polygon[{{1,0}, {5,1}, {4,4}, {1,5}, {0,2}}];

Show[Graphics[{
        Hue[.8], p, Hue[.4], p /. 

        midpointrule
        }]];

Here the rule is used twice.

Show[Graphics[{
        Hue[.8], p, 

        Hue[.4], p /. midpointrule,
        Hue[.2], p /. midpointrule /. midpointrule
        }]];
 

The ParametricPlot3D command outputs a three-dimensional graphics object, which is abbreviated to -Graphics3D-. Some of its elements are polygons. (The graphic is produced as a side effect.)

ParametricPlot3D[{Sin[t], Cos[t], u}, {t, 0, 2Pi}, {u, 0, 2}];

This lets you see the cuboid hidden inside the cylinder.

Show[ {%, Graphics3D[Cuboid[-{1/3, 1/3, 1/3}]]} /. midpointrule /. midpointrule];

Make Room on Your Office Wall for Solving the Quintic Order Your Poster Today--Supplies Are Limited!

All mathematicians know that there is no formula for the solution of the general quintic equation,

a x^5 + b x^4 + c x^3 + d x^2 + e x + f = 0.

Or do they?

The story of the solution of the quintic didn't end when Ruffini, Abel, and Galois showed that there is no algebraic solution to the quintic. That's because later in the 19th century, Hermite, Kronecker, and Brioschi independently discovered solutions in terms of elliptic modular functions, and Klein discovered a solution in terms of hypergeometric functions.

The hypergeometric functions are built into Mathematica and the elliptic modular functions are being implemented for the forthcoming release. It seemed only natural for Wolfram Research's Research and Development group to program the methods of these mathematicians as an acid test of the new technology. Little did they know how difficult this would be! They were very fortunate to have the extensive library resources of the University of Illinois.

The result appears in the poster, "Solving the Quintic with Mathematica," which features the history behind several solutions to the quintic. Included is a description of how formulas for the quintic were derived and their implementation in Mathematica. The poster also includes a detailed historical time line of the solution of polynomial equations in one variable. It shows portraits of many of the world's most famous mathematicians and describes their contributions to our understanding of this important subject.

Created for the International Congress of Mathematicians held this summer in Zurich, Switzerland, the poster was distributed to over 3,000 attending mathematicians at the conference computer lab, which was sponsored by Wolfram Research. A limited supply of these posters is now available--for just $2 each plus the cost of shipping (which varies according to where you live)--to whomever reaches us first with their orders! To order see "How to Contact Us".

This 27" by 38" poster is an impressive and informative addition to any mathematician's office. You can also find the complete text for the poster, as well as the extensive bibliography, on MathSource, item 0207-199.

The circular graphics are contour plots of theta functions.

Conferences

International Mathematica Symposium IMS '95

Applications of Mathematica in science, mathematics, technology,
business, and education

July 16-20, 1995
LSU College of Higher Education
Southampton, England

Submissions are invited for a two-page abstract, a poster presentation, a software demonstration, or a discussion panel. Contributions will be refereed by an international program committee, and accepted papers will be included in the proceedings. Mathematica tutorials will take place on July 15-16, 1995.

The fee, 350 pounds sterling, includes registration, accommodations, meals, refreshments, entertainment, and proceedings.

Submission deadlines:

Two-page abstracts to be submitted by January 30, 1995. Notification of acceptance to authors by February 28, 1995. Final copy of accepted eight-page papers by May 8, 1995. Registration and fees due by May 8, 1995. Further details may be obtained from the conference organizers:

Peter Mitic (Chair), Department of Mathematics
LSU, The Avenue, Southampton, ENGLAND SO9 5HB
phone: +44-(0)703-228761; fax: +44-(0)703-230944;
email: p.mitic@soton.ac.uk

Veikko Ker
Rovaniemi Institute of Technology
Jokivayla 11, 96300 Rovaniemi, FINLAND
phone: +358-60-331311; fax: +358-60-3313322;
email: veikko.keranen@rotol.fi

Gautam Dasgupta, Department of Civil Engineering
Columbia University, 620 SW Mudd
New York, NY 10027, USA
phone: 212-854-3102; fax: 212-854-6267;
email: dasgupta@columbia.edu

Mathematica Conference

July 8-10, 1995
University of Tasmania in Hobart

More information will be in future issues of MathUser. For further details contact:

Desmond Fearnley-Sander

Department of Mathematics, University of Tasmania,
GPO Box 252C, Hobart, Tasmania 7001, AUSTRALIA
phone: +61-(0)02-202445; fax: +61-(0)02-202867;
email: dfs@hilbert.maths.utas.edu.au

Applications & Links

New Mathematica Applications Give Users More Ready-to-Use Tools

*New Applications

Mathematica's hundreds of commands and high-level programming constructs make it easy for you to design your own custom functions and to combine them into a versatile system to solve a given class of problems. Many users have contributed the results of their programming to MathSource. An increasing number have focused their efforts on particular application areas to produce complete add-on packages that are available as separate products.

Here are two of the latest applications products.

• EnergyWorker
  EnergyWorker is an analysis package designed to help both engineers and nonspecialists solve day-to-day thermal and energy-related problems. EnergyWorker calculates thermal resistances and heat flows due to convection, conduction, and thermal radiation for common structures and surfaces. It also calculates temperatures throughout a nodal network of thermal components.

  For more information or to order EnergyWorker, contact Goth, Goth, and Chandleri Ltd., by telephone +44-(0)1323-832683, by fax +44-(0)1323-832588, or by email 100070.3267@compuserve.com.

• OPERA (TM)
  (Options Pricing Environment for Research and Analysis)
  OPERA is an options pricing analysis product designed for individual investors and investment banking firms. The package integrates the Mathematica kernel as its computation engine with a presentation manager and a derivative securities manager. The computation engine uses methods of stochastic calculus and the standard Black-Scholes options pricing model. The results of computation are massaged, manipulated, and displayed using the presentation manager. The derivative securities manager acts as an inventory of securities. OPERA comes with the consulting services offered by Evolving Technologies.

  For more information contact Evolving Technologies Corporation at 212-425-1566 or send email to evolvingtech@applelink.apple.com.

*Applications Update

• Optica
  Optica, a design, analysis, and modeling tool for customized optics systems (featured in the last issue of MathUser) will be available soon for Microsoft Windows, Macintosh, the X Window System, and NEXTSTEP.

• MathLive
  MathLive, a real-time visualization extension for 3D Mathematica graphics, is now available for the Power Macintosh.

  You can view a real-time demonstration of MathLive on the Web. The URL is http://www.render.com/oneday/true-d/true-d.html

• Time Series Pack
  Time series are used in research in fields ranging from biology and finance to engineering and astronomy. The functions and utilities in the Time Series Pack, developed by Wolfram Research's Applications group, help users study univariate and multivariate time series models, analyze and visualize real data, fit models to data, and forecast future values. Statistical data analysis, visualization, and modeling tasks are all made easier with tools from this pack. The Time Series Pack will be available soon.

• MathLink Connects Mathematica to All Kinds of Programs
  Given the multitude of ways to use Mathematica, it is no surprise that people use the system in combination with a wide variety of other software.

  MathLink, the system's built-in communication protocol, makes seamless connections between Mathematica and other programs possible. You can use Mathematica as the interface to another program or as the powerful computing engine behind another program. You can even use MathLink to have Mathematica communicate with other programs running on different computers connected on a network.

  You don't have to be a programmer to benefit from MathLink, because Mathematica users, Wolfram Research, and other software companies are continually developing new links to popular programs. Many of these links are available free of charge.

  • MathLink for GraphRight The MathLink connection between Mathematica and the NEXTSTEP application GraphRight lets users send and receive lists of data between the two. While working in Mathematica, you can access GraphRight to create a chart of the data. (Available free of charge from MathSource item 0206-187.)

  • MathLink for IRIS Explorer
    This module allows users to deliver data to Mathematica to perform calculations and to return results to the scientific visualization package IRIS Explorer for further processing or graphical display. (Available free of charge from MathSource item 0205-805.)

  • MathLink for MATLAB
    MathLink made it simple to create the connection between Mathematica and MATLAB, and using the connection couldn't be easier!

    The Mathematica Symbolic Toolbox for MATLAB lets you call Mathematica to solve a problem that requires symbolic or high-precision numeric capabilities, pass matrices between MATLAB and Mathematica, and mix Mathematica code and MATLAB code without having to write M-files. (Available free of charge from MathSource item 0205-951.)

    A second package allows Mathematica users to call MATLAB from within Mathematica. (Available free of charge from MathSource item 0206-143.)

    The MATLAB MAT-File Reader/Writer allows Mathematica to directly read and write MATLAB MAT-files, which are compact binary files for numerical matrices. (Available free of charge from MathSource item 0206-200.)

  • MathLink for AVS
    This link lets users transmit data sets and three-dimensional objects from Mathematica to AVS and import data sets from AVS into Mathematica. (Available free of charge from MathSource item 0203-678.)

  • MathLink for Xmath
    Now users of the analysis and visualization software Xmath can access
    Mathematica's symbolic capabilities without leaving the Xmath interface. (Available free of charge from MathSource item 0207-133.)

  • MathLink for Spyglass Transform
    This link lets you send arrays and commands from Mathematica to the data visualization software Transform, so that you can visualize functions as publication-quality images and plots. (Available free of charge from Spyglass, Inc., 1800 Woodfield Drive, Savoy, IL 61874; phone: 217-355-6000; fax: 217-355-8925.)

  • MathLink for LabVIEW
    VIs ("virtual instruments") for the laboratory control and data acquisition system LabVIEW 3.0 have been developed to let users pipe data through Mathematica for advanced analysis and visualization. (Available free of charge from MathSource item 0207-166.)

  • MathLink for Excel
    Are you a Microsoft Excel user? Are you comfortable with Excel's interface, but want Mathematica's computing power? Do you find yourself creating data files in Excel and reading them into Mathematica? If so, then you should take advantage of MathLink for Excel from Wolfram Research!

    MathLink for Excel lets you access Mathematica with Excel macros in several different ways. The M.VALUE macro is the default macro for sending a Mathematica command. For example, this is how to see what version of Mathematica you are using.

    =M.VALUE("$Version")

    The macros M.EXCELGET and M.EXCELPUT allow you to send and receive a range of Excel cells as Mathematica arrays with a given name. This example shows how you would send a 2 by 5 range of cells named myarray to Mathematica.

    =M.EXCELGET(myarray, A1..B5)

    There are more than 150 convenient predefined Excel macros that let you call Mathematica automatically; examples include M.COS, M.ERF, and M.FACTORIAL.

    To use MathLink for Excel, you need Version 4.0 or later of Excel, and a version of Mathematica that supports MathLink. For the Macintosh, this is Mathematica Version 2.2 or later, and for Windows this is Mathematica Version 2.2.2 or later. Many Windows users have Version 2.2.1; this will not work because MathLink was not included with that release. To find which version of Mathematica you have, look for the version number on the splash screen that appears when you first start up the front end, or else select the About Mathematica item from the Apple menu on the Macintosh or from the Help menu on Windows. Contact Wolfram Research for information on an upgrade. To order your copy of MathLink for Excel and Mathematica see "How to Contact Us".

    Here are two tips for users who already have MathLink for Excel.

    Mathematica can handle larger numbers and expressions than Excel. Since Excel can only handle a maximum of 255 characters in a cell, your output may sometimes be garbled at the end. However, Mathematica keeps the correct result with which you can continue to work.

    You can load packages using MathLink for Excel by combining =M.VALUE( ) with any one of << (the abbreviation for Get), Get, or Needs. For example, to load the package Miscellaneous`CityData` using MathLink for Excel you could enter the following command in an Excel cell.

    =M.VALUE("<<Miscellaneous`CityData`")

    Depending on whether or not the load was successful, the cell will contain the value Null or $Failed, respectively.

    However, although the next command seems equivalent, it generates the Excel dialog box "Error in formula".

    =M.VALUE("Needs["Miscellaneous`CityData`"]") =M.VALUE("Needs[""Miscellaneous`CityData`""]")

    This applies when using any Mathematica function that needs double quotes. For example, this is how to get city coordinates using the CityData function.

    =M.VALUE("CityData[""Saint Louis"", CityPosition]")

Upcoming Mathematica-related products will focus on the analysis of mechanisms, engineering, tensor analysis, signal processing, access to databases, fuzzy logic, clinical medicine, physics, operations research, and financial analysis. Continue to look for regular announcements of new applications products in future issues of MathUser!

Books

*New Books:

Mathematica Graphics: Techniques and Applications
Tom Wickham-Jones (TELOS/Springer-Verlag)
ISBN 0-387-94047-2
This is a step-by-step, comprehensive instructional book on visualization and computer graphics using Mathematica. It provides detailed information on how to solve common problems that confront users and contains a vast range of graphics examples. It appeals to all levels of users as it works its way from basic problems to advanced topics.
This book includes 32 pages of full-color pictures carefully integrated with the text. It also contains more than 1000 black-and-white illustrations, as well as a comprehensive reference section. A companion diskette contains packages of Mathematica code and MathLink binaries that are described in the book.

Mathematica: An Introduction to Statistics and Probability
Michimasa Kobayashi (Toppan)
ISBN 4-8101-8932-5 (in Japanese)
A primer on fundamental statistical techniques in Mathematica. Includes diskette.

Engineering Mathematics with Mathematica
John S. Robertson (McGraw-Hill)
ISBN 0-07-053171-4
A supplementary text for junior/senior-level college courses in applied mathematics where Mathematica is used in a laboratory setting. Covers topics found in courses on ordinary and partial differential equations, vector analysis, and applied complex analysis.

Applied Electronic Engineering with Mathematica
Alfred Riddle and Samuel Dick (Addison-Wesley)
ISBN 0-201-53477-0
Shows how to use Mathematica to solve a wide range of problems in electrical engineering. Presents an overview of electrical engineering problems and solution methods. Also shows how the abilities of Mathematica combine to make it easier to solve electrical engineering problems. Includes diskette containing a demo version of the Nodal package and code for the book's examples.

*Translations:

Mathematica
(Mathematica: A Practical Approach)
Nancy Blachman (Academic Service)
ISBN 90-395-0016-9 (in Dutch)

*Forthcoming Books:

Beginner's Mathematica
Wien Hong (Unalis Corporation, 1994) (in Chinese)
A detailed introduction to Mathematica covering all of the system's major capabilities. Also includes a comprehensive description of Mathematica's operation under the Microsoft Windows operating system.
To order, telephone 886-2-704-2762 or fax 886-2-700-1006.

Mathematica for Scientists and Engineers
Thomas B. Bahder (Addison-Wesley)
ISBN 0-201-54090-8
A comprehensive guide to Mathematica focusing on the specific needs of scientists and engineers. Provides numerous real-world examples in differential equations, boundary value problems, vector field theory, and tensors. Gives a thorough treatment of evaluation issues that affect long running times and memory management. Includes MathLink tutorial for installing FORTRAN and C programs into Mathematica.

Mathematica for Physics
Robert L. Zimmerman and Fredrick I. Olness (Addison-Wesley)
ISBN 0-201-53796-6
Designed as a supplement for any of the core advanced undergraduate and graduate physics courses. Covers essential problems in mechanics, electrodynamics, quantum mechanics, special and general relativity, cosmology, elementary circuits, and oscillating systems. Emphasizes the graphical capability of Mathematica to develop the reader's intuition and visualization in problem solving.

Differential Equations: An Introduction with Mathematica
Clay C. Ross (Springer-Verlag)
ISBN 0-387-94301-3
Covers standard topics for an introductory differential equations course, using Mathematica to enhance students' problem-solving abilities and understanding of the subject.

Mathematica Graphics Guidebook
Cameron Smith with Nancy Blachman (Addison-Wesley)
ISBN 0-201-53280-8
Tutorial for constructing high-quality mathematical and scientific graphics in Mathematica. Includes numerous examples and practical advice for printing displayed graphics.

*CD-ROM:

Illustrierte Mathematik: Visualisierung von mathematischen Gegenst (Illustrated Mathematics: Visualization of Mathematical Objects)
Oliver Gloor, Beatrice Amrhein, and Roman E. Maeder
(BirCom/Birkhauser)
ISBN 3-7643-5100-4 (in German)
A CD-ROM containing a collection of Mathematica graphics and animations, along with Mathematica programs for creating additional examples. Designed to enhance a high school or undergraduate mathematics curriculum.

With nearly 100 books in nine languages, two journals in both print and electronic formats, an electronic magazine, and MathSource, Mathematica users have a tremendous fund of published information available to support their work. The recent Frankfurt Book Fair was the scene of numerous meetings between Wolfram Research and publishers from all over the world interested in expanding their Mathematica publishing or in starting new lists. Authors interested in referrals to publishers, or seeking assistance in preparing their publications, should contact us at devsupport@wri.com.

Customized Training

Wolfram Research, Inc.
Wolfram Research is now offering "Mathematica Basic Training" each month at the University of Illinois, Urbana-Champaign, or on-site for groups of five or more. The one-day course will introduce new users to the system's numeric, symbolic, graphical, and programming features through problem solving. Additional courses are being considered--please email training@wri.com with your comments or suggestions.

Principia Consulting
David Wagner offers Mathematica training, consulting, and custom programming, as well as specialized instruction in stochastic modeling. For information call 303-786-8371 or email wagner@cs.colorado.edu.

International Solutions Research and Development and Consulting Corporation, Inc. (ISD)
Franco Reyes-Amoroso offers training and customized Mathematica courses. For information call 303-758-3952.

Variable Symbols, Inc.
Nancy Blachman gives introductory and intermediate Mathematica workshops, as well as specialized instruction in programming with Mathematica and Mathematica graphics. She is the author of Mathematica: A Practical Approach, The Mathematica Quick Reference, and The Mathematica Graphics Guidebook. For information call 510-652-8462 or email nb@cs.stanford.edu.

Oxford System Solutions (OSS)
Consultants William Shaw, co-author of Applied Mathematica: Getting Started, Getting It Done, and Vanessa Thomas regularly offer Mathematica training workshops for all levels in Oxford, and on-site training is available for groups anywhere in Europe. OSS also presents specific courses on individual topics such as modeling derivative securities. For information call +44-865-784270 or fax +44-865-784004.

Many colleges and universities sponsor workshops and seminars year-round.

Opportunities at Wolfram Research

Wolfram Research continues to expand and to look for outstanding people to join the firm. Positions are open in project management, research and development, software localization engineering, and technical writing, editing, and translating. We are also looking for Mathematica programmers with several years of experience to develop commercially applicable packages in engineering and business. Send applications for all positions to Personnel Department, Wolfram Research (resumes@wri.com). A current list of job openings and descriptions is available on Wolfram Research's World Wide Web site.

Wolfram Research is an affirmative action/equal opportunity employer.

International Mathematica Student and Professional Consultants Wanted Wolfram Research is searching for experienced Mathematica users and programming experts for part-time work worldwide. Consultants will respond to questions via the Internet and demonstrate Mathematica at trade shows, conferences, and other events in their country. If interested, please send your resume to resumes@wri.com.

Workshops

Mathematica Basic Training
Upcoming dates: December 3, January 28, February 25, March 25, and April 22. At the University of Illinois, Urbana-Champaign. For information call Wolfram Research at 1-800-441-6284, ext. 245, or email training@wri.com.

Mathematica Workshops by International Solutions Research and Development and Consulting Corporation, Inc. (ISD)
Introduction to Mathematica, November 4, December 2, and January 6; Intermediate Mathematica, November 11-12, December 9-10, and January 13-14; Advanced Mathematica, November 18-19, December 16-17, and January 20-21; Professional Mathematica, November 25-26, December 23-24, and January 27-28. For more information contact Franco Reyes-Amoroso, Denver, CO, at 303-758-3952.

Pragmatic Introduction to Mathematica
Essen, Germany, November 18. Munich, Germany, December 9. Contact Markus van Almsick, telephone: +49-(0)201-41944 or QT Software, telephone +49-(0)89-332970.

Madison Mathematica Workshop
Mathematica Basics, Problem Solving with Mathematica, Mathematica Programming. Madison, WI, December 9-11. For more information contact New Horizons Computer Learning Center at 608-223-4377 or George E. Hrabovsky at 608-256-4021.

Mathematica Workshop by Variable Symbols, Inc.
Intermediate Level Mathematica training taught in Spanish by Nancy Blachman. Instituto Tecnologico y de Estudios Superiores de Monterrey (ITESM), Monterrey, Mexico, December 12-16. For information contact Cesar Vaccari, ITESM, by telephone at 52-8-358-2000 ext. 3906-3911, or fax 52-8-359-3150, or email cvaccari@campus.mty.itesm.mx.

Mathematica Training Courses by Computer Algebra Netherlands
Hands-on introductory course, December 15; Introduction to Programming, December 16. For more information contact CAN Expertise Centre, Kruislaan 419, 1098 VA, Amsterdam; telephone: +31-20-5608-400, fax: +31-20-5608-448, email: can@can.nl.

Mathematica Workshop by Variable Symbols, Inc.
Nancy Blachman will be teaching Problem Solving with Mathematica. Stanford University, Winter Quarter. For those not at Stanford, call 415-723-3618 for information.

Q&A

Q:How can I use the packages that come with Mathematica?

A:The packages included with Mathematica are grouped together in directories by topic: Calculus, Graphics, Statistics, and so on. When a package is loaded, it uses Mathematica's programming language to define new functions.

You can load a package with Get["name"] (or equivalently with the shorthand notation <<name) or else with Needs["name"]. The double quotes are left out when using the short form of Get.

Needs acts like Get except that it will not load the same package twice. It is not harmful to reload a standard package, although it takes time and may clutter the screen with warning messages.

You can refer to the package either by its file name or by specifying its context. Using a context allows you to use the same command to load a package no matter what the platform; Mathematica will convert the context to the correct file name, then open the package and evaluate it. (For more information on contexts see page 333 of The Mathematica Book.)

FilledPlot is a package that allows you to color the regions between graphs; either of these commands loads the package.

Get["Graphics`FilledPlot`"]

or

<<Graphics`FilledPlot`

You can list the functions now available by typing the following command.

?Graphics`FilledPlot`*

AxesFront      Curves         Front
Axis           FilledPlot     ListFilledPlot
Back           Fills

ListFilledPlot[data] generates a plot with the area between
   the x axis and the curve given by the data filled.
   ListFilledPlot[data1, data2, ...] generates a plot with
   the areas between the curves given by data1 and data2,
   data2 and data3, etc. filled. The shade of the fill and
   other specifications can be given by the Fills option.

ListFilledPlot[{9, 7, -2, 5, -4, 7, 5, 9}];

The Guide to Standard Mathematica Packages describes the more than 150 packages that come with Mathematica.

Q:On my Macintosh, Mathematica crashes right after I start. What is wrong?

A:The most likely cause is that your Mathematica preferences file is damaged.

The preferences file can sometimes become damaged during an operating system upgrade, or if you have an older version of this file when installing Mathematica. If it is damaged, Mathematica crashes immediately upon startup. If you throw away the file, a new preferences file will be created the next time you start Mathematica and this should work.

The file to throw away is System Folder:Preferences:Mathematica V2.2 Prefs. Do not throw away System Folder:Preferences:Mathematica Kernel Prefs or Mathematica 2.2.2:Defaults:Mathematica Prefs.

Another possibility is that there may be a conflict with either the Apple LaserWriter 8.0 driver or the HP LaserJet driver 8.0. If you are using the Apple LaserWriter 8.0 driver, you can either move back to the 7.1.2 driver or upgrade to the 8.1.2 driver. If you are using an HPLJ-4M printer, you were probably given the 8.0 driver to run it. Contact HP Customer Service at 208-323-2551 to get Version 8.1.1 of the driver software.

Q:How do I use the function Chop?

A:Chop is a function used to convert real numbers that are relatively close to zero to the exact integer 0.

 x = 4.1 10^(-16)

      -16
4.1 10

{Head[x], Chop[x], Head[Chop[x]]}

{Real, 0, Integer}

Chop[{1., 2., 3., 4., 5., 6.}, 4]

{0, 0, 0, 4., 5., 6.}

N[ (-1)^(1/3) ] ^ 3

                -18
-1. + 9.21572 10    I


{Head[%], Chop[%], Head[Chop[%]]}

{Complex, -1., Real}

Q:How can I make all of the functions in the Electrical Engineering or Finance Pack available without having to load each individual package?

A:Loading the Master package makes all the symbols declared in packages in the application accessible, without actually loading the packages. Assuming the directory containing the applications is on Mathematica's $Path, all you need to do is enter:

Needs["EE`Master`"]

or

Needs["Finance`Master`"]

Whenever a function that has not been loaded is called, the package containing it will be loaded transparently and the function will be evaluated. Memory is not taken up by the packages until they are actually needed.

Q:How can I get command-line editing in the Unix version of Mathematica?

A:There is a public domain program called "fep" that wraps any application with editing features. HP ships an equivalent program on its Unix computers called "ied". You type "fep math" or "ied math" to make Emacs or vi work. MathSource item 0207-267 contains "fep".

There is also an Emacs interface for Mathematica, by David Jacobson. Mathmode lets you run Mathematica under GNU Emacs and provides a functionality somewhat similar to the notebook interface available on Macintosh, Microsoft Windows, X, and NEXTSTEP. The input is divided into cells. MathSource item 0202-093 contains Mathmode.

Q:Can I save the inputs from my notebook so that they can be read in as a package by someone without a notebook front end?

A:You can load any notebook into the kernel using <<filename. All input statements that are contained in Initialization cells will be evaluated when the file is read in. Everything else in the file is treated as a comment. If you want to save the notebook in a package format (i.e., no graphics, no output, text enclosed in comment delimiters, etc.), just select the "Package" setting in the Save as Special dialog box.

Q:Our university recently purchased several copies of Mathematica. Can these copies be rolled into a Mathematica site license?

A:For schools that already have a site-license arrangement and want to make Mathematica even more widely available, recent purchases can be counted toward an unlimited site license.

Technical Support Addresses

U.S. and non-European technical support
email: support@wri.com
fax: 1-217-398-0747
telephone: 1-217-398-6500

Monday, Tuesday 8:30am-5:00pm
Wednesday 9:00am-5:00pm
Thursday, Friday 8:30am-4:00pm
U.S. Central Time (GMT -6)

Registration/password requests
email: register@wri.com
telephone: 1-217-398-5151

Monday-Friday 8:00am-5:00pm

European technical support
email: support-euro@wri.com
fax: +44-(0)1993-883800
telephone: +44-(0)1993-883400

Monday-Friday 9:00am-5:00pm (GMT -0)

Mathematica Miscellany

This is a star chart with the orbit of Mars superimposed (the red line). It shows that Mars can have retrograde motion as seen from the Earth. The other line is the ecliptic, the path of the Sun.

The Planetarium.ma notebook for Mathematica, MathSource item 0206-132, by Terry Robb contains over 30 commands including 14 graphics commands. You can display star charts, compute planet positions, determine eclipses, and much more.

Win a $100 Gift Certificate for extraordinary Mathematica code! Have you written a unique or creative short solution to a problem using the features of Mathematica? Here is your opportunity to enter a contest. Send us your best Mathematica programs--one liners welcome! All winning entries receive a $100 gift certificate for any item marked "wri" in the Mathematica Products Catalog. For contest entry details, contact MathUser today.

Give Mathematica to Your Favorite Student for the Holidays

Our festive gift wrap and ribbons are ready and waiting as we prepare to send a special Mathematica for Students to your favorite student this holiday season!

Mathematica for Students is a full-function version of Mathematica for currently enrolled high school and college students. Students find that Mathematica helps them understand concepts better in any course that requires mathematics. If you'd like to give students you know a holiday gift that will help them on their way to a successful future, be sure to include a copy of Mathematica for Students on your list!

To order, call Wolfram Research and ask for the "Student Version Holiday Offer." Let us know the student's name, address, and school; we can send the order to you or directly to the student with a personalized holiday card. To ensure delivery by December 25, order no later than December 16.

Mathematica for Students is available for Macintosh and Microsoft Windows systems. Student identification is required for registration. Numeric coprocessor support is not included. MathLink support is not included on the Windows version. Subject to availability.