MathUser
Fall 1994
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
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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:
Spring/Summer 1992 0202-655
Fall/Winter 1992 0204-477
Spring/Summer 1993 0205-759
Fall 1993 0205-827
Winter 1994 0206-907
Spring 1994 0205-771
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How to Contact Us
Wolfram Research, Inc.
100 Trade Center Drive, Champaign, IL 61820-7237, USA
phone: 217-398-0700; fax: 217-398-0747
orders: 1-800-441-MATH (6284)
customer service: 217-398-5151
technical support: 217-398-6500
Wolfram Research Europe Ltd.
10 Blenheim Office Park, Lower Road, Long Hanborough,
Oxfordshire OX8 8LN, UNITED KINGDOM
phone: +44-(0)1993-883400
fax: +44-(0)1993-883800
Wolfram Research Asia Ltd.
Izumi Building 8F
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
General and sales information, prices: info@wri.com
European information: info-euro@wri.com
Asian information: info-asia@wri.com
Customer service: orders@wri.com
User registration: register@wri.com
Technical questions and support: support@wri.com
European technical questions and support: support-euro@wri.com
Mathematica bug reports: support@wri.com
Mathematica suggestions: suggestions@wri.com
MathSource: mathsource@wri.com
This newsletter: mathuser@wri.com
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
You can then get more information about a specific function. The next
command explains the ListFilledPlot function.
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.
Here is an example.
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 can take a second argument, the tolerance. Chop[expr, tol]
replaces approximate real numbers in expr that differ from zero by
less than tol with 0. The default tolerance is 10^-10.
Chop[{1., 2., 3., 4., 5., 6.}, 4]
{0, 0, 0, 4., 5., 6.}
A common application of Chop is to remove tiny imaginary parts in
complex numbers so as to get real numbers.
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.
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