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StyleBox[\(An\ Interview\ with\ Stephen\ Wolfram\),
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\(Associate\ Editor\ Hal\ Varian\ Talks\ With\ the\ Creator\ of\
Mathematica\ about\ Version\ \(3.0.\)\),
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" You've talked about using precedents in Mathematica design. Which \
precedents were really important to maintain in moving from Version 2 to \
Version 3?"
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Cell[TextData[{
"SW: Well, the first thing to say is that we've worked hard to maintain \
compatibility, so that any program written with an earlier version of ",
StyleBox["Mathematica",
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" can run without change in 3.0, and any notebook can be converted. I guess \
the good news is that we didn't make any big mistakes in the design of \
earlier versions of ",
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" that we'd have to go back on now. There are a few very small incompatible \
changes\[LongDash]I really doubt most people will ever run into them\
\[LongDash]that are listed at the very back of my book (and in the online \
help).\n\nAs far as new functionality is concerned, yes, I tried hard to \
follow design precedents that were already set up in ",
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", because that way people have to learn the smallest number of new \
concepts in order to use the new functionality. The most important precedents \
deal with the whole idea of symbolic programming\[LongDash]the notion of \
setting up symbolic expressions that can represent anything one wants, and \
then having functions that operate on both their structure and content.\n\n\
One of the things I think is interesting about Version 3 is the extent to \
which it validates the generality of symbolic programming. There are \
certainly some new programming constructs in Version 3, but the fundamental \
ideas of symbolic programming in ",
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" already existed even in Version 1. There, though, they were mostly used \
for setting up mathematical kinds of things, together with graphics and so \
on. But now, in Version 3, they're used for a lot more things, like setting \
up notebook documents and user interface elements. The fact that the same \
symbolic programming primitives work for those as work for math kinds of \
things, I think, really validates the idea of symbolic programming being \
something pretty general."
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" What were the components of Mathematica that were changed the most? ",
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"? ",
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"?"
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"SW: We worked on Version 3 for about five years, and a huge amount of new \
stuff is in it. Actually, I think the source code for ",
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" more than doubled in size from Version 2 to Version 3. I guess in \
general the idea in Version 3 was both to deepen and broaden the capabilities \
of ",
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". Deepen in the sense of taking functions like ",
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" whose basic description was already set, and making them cover more \
cases, work more efficiently, and so on. Broader in the sense of adding \
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" able to do a wider range of things."
}], "Text",
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Cell[TextData[{
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" I understand that ",
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" now handles vectors and matrices. What kinds of performance increases \
are you seeing?"
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Cell[TextData[{
"SW: Yes, we've extended ",
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" quite a bit. It can now handle lots of array operations, list \
manipulation, functional programming, and so on. Pretty much any operation \
where the structure of the output can be predicted just by looking at the \
structure of the input. (It can't handle functions like ",
StyleBox["Cases",
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" where the form of the output depends not only on the structure, but also \
on the data, in the input.)\n\nThe speed increases one sees depend on a lot \
of details, but they're quite often factors of twenty or more. In fact, \
compiled ",
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" code now often seems to be faster than at least the most straightforward \
custom implementations in C. At least, that's what I've found for some of my \
cellular automaton programs. And actually, we've discovered some pretty \
interesting general things from studying the behavior of ",
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", that I think we'll be able to use to do some rather spectacular things \
for the speed of numerical operations on large data sets in ",
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" in general. But that's for the next version..."
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StyleBox["HV:",
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" How has the Graphics system changed?"
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Cell[TextData[{
"SW: The main changes have to do with integrating different kinds of \
elements into ",
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" graphics, and being able to import and export graphics easily. There are \
a few new basic options and things, mostly to help people produce top-quality \
publication graphics. An example is ",
StyleBox["Offset",
FontFamily->"Courier"],
", which lets one place objects in graphics with a certain absolute offset \
from a particular point. Other examples have to do with fonts, which can now \
be controlled in much more detail.\n\nAs you know, one of the big things in ",
StyleBox["Mathematica",
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" 3.0 is the typesetting system, and an important feature of graphics in \
3.0 is that you can now put fully formatted expressions, with whatever \
special characters, styling, etc. you want right into graphics.\n\nAnother \
thing in graphics in ",
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" 3.0 is that you can use the ",
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" function to tell ",
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" to output your graphics in a whole collection of formats \[LongDash] EPS, \
TIFF, GIF, etc. You can also tell ",
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" an absolute size that you want a graphic to show up in a notebook, or an \
absolute resolution."
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"The new programmable notebook system in ",
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" gives some more capabilities as well; for example, you can generate a \
collection of graphics, then immediately send a command to the front end to \
have ",
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" start an animation of these graphics."
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Cell[TextData[{
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" How about upward compatibility?"
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Cell[TextData[{
"SW: As I already said, programs should be essentially 100% compatible; \
notebooks should be 100% convertible. One thing that's happened in ",
StyleBox["Mathematica",
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" 3.0 is that we've been able to get rid of platform-dependent .mb cache \
files. Now all notebooks are in .nb files, and the .nb files are identical \
from one platform to another. When you try to open a .ma file, ",
StyleBox["Mathematica",
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" will let you convert it to a .nb file that will then work on any \
platform. By the way, the Notebook Conversion dialog also has an option for \
letting you convert all the notebooks in a particular directory. The option \
is just a check box, and it's rather easy to miss. But I've found it very \
useful."
}], "Text",
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Cell[TextData[StyleBox["Typesetting",
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" Can you tell us a bit about the typesetting capabilties?"
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Cell["\<\
SW: What we wanted to do was to create a \"no compromises\" typesetting \
system that would make things look great on screen and on paper, and allow \
everything to be edited and interacted with very easily. We wanted the system \
to work with math, with tables, with text, and so on.\
\>", "Text",
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Cell["\<\
I think it all worked out extremely well. It's easy to enter things. And \
you can evaluate what you've entered. And then you can edit or reuse any \
part of your results.\
\>", "Text",
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Cell[TextData[{
"Being able to do what we did with typesetting isn't easy, and in fact it \
wouldn't have been possible if it wasn't for the symbolic programming \
language that we already have inside ",
StyleBox["Mathematica",
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". In fact, even doing something as seemingly straightforward as breaking \
a mathematical expression across lines requires a kind of understanding of \
the structure and meaning of the expression that makes use of a lot of \
symbolic programming ideas."
}], "Text",
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Cell[TextData[{
StyleBox["HV:",
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" What about the World Wide Web capabilties?"
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Cell[TextData[{
"SW: You can use ",
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" or ",
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" to save a ",
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" notebook as an HTML document. Of course, when the notebook is converted \
to HTML it's not nearly as good as when it's a live notebook. The formulas \
have to get turned into bitmaps, for example, because there's no way to \
represent math in HTML. And of course you can't evaluate a piece of HTML."
}], "Text",
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Cell[TextData[{
"I find that the best way to interact with ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" on the web is to store everything as a notebook, and then to set my \
browser so that ",
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" or ",
StyleBox["MathReader",
FontSlant->"Italic"],
" is a helper app that is used to open anything with a .nb file extension. \
This works well. And actually ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" notebooks can have hyperlinks that go to http addresses, so you can get \
back into your web browser even once you've gone off into the notebook."
}], "Text",
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Cell[TextData[{
"In addition to ",
StyleBox["Mathematica",
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" documents, it's also possible to interact with ",
StyleBox["Mathematica",
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" computations on the web. We've got an example of that at \
http://www.integrals.com. It's a site where people type in integrals, and ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" does the integrals, and displays the result. The site works by connecting \
the web server via ",
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" to the ",
StyleBox["Mathematica",
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" kernel."
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Cell[TextData[{
"It turns out that the ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" language is actually a very good way to specify not only the form but \
also the function of a web site, and we've been working for some time on a \
major new technology called ActiveSites that takes advantage of that. But \
that's for another interview. [Editor's Note: See the column by Matthew \
Thomas, this issue.]"
}], "Text",
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Cell[TextData[{
StyleBox["HV:",
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" How easy is to to convert an archive of papers in TeX to Mathematica \
3.0?"
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Cell[TextData[{
"SW: It depends. We do have quite a bit of technology for converting from \
TeX to ",
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" that we'll be making available sometime early next year, and on many \
kinds of TeX documents it works very well. In fact, we used it to convert my \
whole ",
StyleBox["Mathematica",
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" Book \[LongDash] which was originally in TeX \[LongDash] into ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" notebooks. But we can only be sure that our convertor will work if the \
TeX you use is fairly stylized. It's the same issue as when you submit a \
paper in TeX to most journals \[LongDash] they don't want you to have your \
own macros and so on, because they want to be able to treat TeX like a markup \
language, where you indicate a section head by \\section, not by a bold, \
larger, font change. "
}], "Text",
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Cell["\<\
So, the basic answer to your question is: If your TeX is well stylized \
enough, our automated convertor should work well. And in fact, it'll have \
ways that you can extend it for your own documents, etc. as well. \
\>", "Text",
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StyleBox["HV:",
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" How do you see these new capabilities affecting technical \
communications?"
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"SW: Gosh. Well, the biggest thing is that I'm hoping we'll see more and \
more interactive papers being produced: papers where you can not only read \
about something, but also do something \[LongDash] right there in the \
notebook. I think that a lot of things that we've done with ",
StyleBox["Mathematica",
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" and with ",
StyleBox["Mathematica",
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" notebooks have blurred the boundaries between documents and programs. And \
that's going to mean that it's increasingly realistic for people to publish \
programs as well as descriptions of things. "
}], "Text",
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Cell[TextData[{
"What I'm hoping is that in the future papers will routinely include not \
only words and pictures, but also data, programs, user interface elements and \
so on. So if I want to do something with the contents of a paper \[LongDash] \
say run my own model on the data it describes, or use its program on my data \
\[LongDash] I can immediately and seamlessly do that. And the availability \
of ",
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" as a kind of universal language is critical to making that possible. "
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Cell[TextData[{
StyleBox["HV:",
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" How has the Help system been improved?"
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Cell[TextData[{
"SW: One thing is that we've now got my complete ",
StyleBox["Mathematica",
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" Book, as well as the complete ",
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", and all the other standard ",
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" documentation, online, as ",
StyleBox["Mathematica",
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" notebooks. So you can read them on the screen, evaluate or copy examples \
from them, print them, and so on. You can also search them, directly or by \
using a master index. "
}], "Text",
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Cell[TextData[{
"There's really a lot in the help system now. One thing I encourage you to \
look at are the demos. They are kind of buried under ",
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". But I think people will find them pretty interesting \[LongDash] both \
as examples of what ",
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" can do, and for actual material they discuss. "
}], "Text",
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Cell[TextData[{
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" Can you give us some examples of unusual notebook designs using the new \
palettes and hyperlink examples?"
}], "Text",
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Cell[TextData[{
"SW: The best place to look for these is in the demo area I just mentioned. \
One thing to look at is the ",
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". It's a palette-based notebook that lets people explore operations on \
polyhedra. It's fun and educational, and it's also a good example of how one \
can build a custom user interface in ",
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" 3.0. "
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"I might also mention that the ",
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" for ",
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" 3.0 is just another notebook. But like many of the demo notebooks, it \
doesn't look or act much like a traditional notebook."
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" What role do you see palettes playing in mathematical education?"
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"SW: One of the big things about palettes is that they let one use ",
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" just by pushing buttons. So that means that it's easy to set up lots of \
operations, and have students try them out just by pushing buttons, without \
ever having to figure out how to type anything. "
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"I'm sure we'll see some really neat things done with palettes over the \
course of this year. I know that quite a few of the courses that are based \
on ",
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" are planning to do revisions using palettes, and I think it'll be \
exciting to see what gets done."
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" Are there brand new capabilties that didn't exist in previous versions?"
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"SW: Lots and lots! We've worked hard on ",
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" 3.0 for five years, and actually we've more or less doubled the size of \
the internal code for the system in that period of time. So there'd better be \
a lot of new things!"
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Cell[TextData[{
"A good way to find out what's new is to look at my ",
StyleBox["Mathematica",
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" Book. In the Reference Guide, every new function \[LongDash] and there \
are hundreds of them \[LongDash] is indicated by a +. There's also a summary \
of what's new in the front of my book, and at the back of the First Look \
booklet that's excerpted from my book."
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Cell[TextData[{
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" What demands does Mathematica place on the platform? I understand that \
you have some clever ways to deal with disk space issues."
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Cell[TextData[{
"SW: The amazing thing is that even though ",
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" 3.0 does much, much more than ",
StyleBox["Mathematica",
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" 2.2, it ends up not needing a bigger computer. The reason is some clever \
software engineering tricks that we invented to save memory. And what I think \
we can say on all platforms is, that if you can run the current version of \
your operating system, you'll also be able to run ",
StyleBox["Mathematica",
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"."
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" 2.2 did. To store the whole on-line ",
StyleBox["Mathematica",
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" Book and everything typically takes 100 megabytes or so. To store only \
programs takes much less \[LongDash] perhaps 20 megabytes. But one neat thing \
we've done is to set everything up so that if you want to, you can run with \
zero megabytes of hard disk space \[LongDash] you execute ",
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" directly off a CD-ROM. Once it's started up, this actually works quite \
well, and I myself have used this capability quite a few times."
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"Associate Editor Hal R. Varian is the Dean of the School of Information \
Management and Systems at the University of California at Berkeley. He is \
also a Professor in the Haas School of Business, a Professor in the \
Department of Economics, and holds the Class of 1944 Professorship. \n\nHe \
received his S.B. degree from MIT in 1969 and his MA (mathematics) and Ph.D. \
(economics) from UC Berkeley in 1973. He has taught at MIT, Stanford, Oxford, \
Michigan and other universities around the world. \n\nAmong his publications \
are: ",
StyleBox["Economic and Financial Modeling with Mathematica",
FontSlant->"Italic"],
" \n(editor) A collection of articles showing how to use the computer \
language ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" for economic and financial applications. TELOS/Springer-Verlag, 1992. \n",
StyleBox[
"Computational Economics and Finance: Modeling and Analysis with \
Mathematica",
FontSlant->"Italic"],
" \n(editor) A collection of articles showing how to use the computer \
language Mathematica for economic and financial applications. \
TELOS/Springer-Verlag,1996. \n\nHal R. Varian\nUniversity of California, \
Berkeley\nhal@sims.berkeley.edu"
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}, Open ]],
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Cell[TextData[{
"Stephen Wolfram is president and founder of Wolfram Research, Inc. the \
company that developed ",
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". He is the principal architect of the ",
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was the author of its main documentation, including ",
StyleBox["The Mathematica Book",
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", Third Edition, Wolfram Media/Cambridge University Press (1996). His \
publications include ",
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