Talk:Mathematica

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[edit] Screenshot request

Someone please post a nicer screenshot. Preferably one with expressions which are hierarchically nested. Ninjagecko 16:12, 13 December 2006 (UTC)

I would like a screenshot showing something in the notebook, some numbers, maybe a 3-D graph, something other than just a blank window. PrimeFan 23:41, 13 December 2006 (UTC) P.S. I'd do it myself but I haven't upgraded to the latest version.

[edit] How Lisp-like?

Can someone elaborate on how Mathematica is Lisp-like? (And by the way, I'm curious to know where Ar found the information that Mathematica was implemented in Objective-C, that's very interesting!) Dysprosia 00:53, 1 Aug 2004 (UTC)

I no longer know where I found the information a precise indication that it was written in Objective-C; I think it is common knowledge on MathGroup etc.. A hint can be found in the Background and Acknowledgments section of Version 1 of the book Mathematica: A System for Doing Mathematics by Computer:
Mathematica is a C-language program, about 150,000 lines long. ... The original source code of Mathematica was actually written in our object-oriented extension of C.
As for similarity to Lisp, there are many aspects one may cite. IMO, the underlying reason is that symbolic expressions are naturally represented as a hierarchy of sub-expressions where the zero-th part (the Head of the subexpression) determines how the remaining arguments are to be interpreted; the difference to Lisp is merely that instead of head[arg1, arg2] you write (head arg1 arg2), which is just a difference in syntax. Just as Lisp derives much of its power from the ability to control the time when arguments are evaluated, Mathematica does the same: In Lisp the distinction is between function and macro, in Mathematica it is the presence or absence of the Hold...-attributes. The similarities extend to control structures: e.g., the (rarely used) GoTo as well as Catch and Throw in Mathematica resemble their respective Lisp counterparts; Block works very much like let (except for the difficulty of constructing closures, which is something you can simulate with With). In both cases, symbols are central to the language for accessing the information that is associated with them, although the referenced data structures are actually independent of them (which is why building specialized Mathematica code at run-time in the form of, e.g., pure functions already holding large amounts of pre-calculated data - think of Currying - typically is very efficient despite the seemingly large expressions one so obtains). Add to this the impure functional character: Mathematica tries to imitate a functional system, and the functional style is very much idiomatic in Lisp, though the main reasons are different in either case (in Mathematica it is important for the semantics of "infinite" evaluation, in Lisp this is one way of reducing excessive copying, aka "consing"; the latter is, of course, also an issue for Mathematica efficiency). The Lisp heritage (some of which is discussed in a thread on comp.lang.lisp) can also be seen from the read-eval-print-loop that was still somewhat exotic at the time.
There are, however, also some very important differences, e.g., as far as scoping or performance characteristics are concerned. Also, rule-based transformations are not typical of Lisp, and Common Lisp at least has a much sharper distinction of the various times (load time, read time, compile time, run time...).
All this is just what comes to mind immediately. I don't think it would be good to put these things into the article, at least in the present form. Ar 14:15, 1 Aug 2004 (UTC)
That's very interesting stuff. It should perhaps deserve it's own section in the article, but you're right about not in the current form. Re the Objective-C thing, Objc is not a Wolfram Research creation, so it could still be a proprietary extension... Dysprosia 23:12, 1 Aug 2004 (UTC)
In fact, I was quite sure about objc, so the formulation in the Mathematica book was a surprise. So I now looked further: V3 of the book states in [http://documents.wolfram.com/v3/MainBook/1.12.4.html

| section 1.12.4]:

The C code in Mathematica is actually written in a custom extension of C which supports certain memory management and object-oriented features. The Mathematica code is optimized using Share and DumpSave.
I will therefore go back and change the objc-part. Ar 20:41, 2 Aug 2004 (UTC)
Just to note, the difference in syntax is that of S-expressions (Lisp style with parens) versus M-expressions (Mathematica style with bracks). M-expressions were actually an early proposed syntax for Lisp, but were abandoned in favor of the S-expressions which have become so representative of Lisp.

[edit] Version history

Just curious, is there a place where Mathematica's version history is listed? PrimeFan 22:18, 7 September 2005 (UTC)

Wolfram Research has a version history here: Quick Revision History of Mathematica Robertd
Thanks. PrimeFan 16:58, 13 September 2005 (UTC)

How is about this overview ?

  • Short Version:

[edit] Release history

Version Platforms Release date
SMP (Symbolic Manipulation Program)  ? 1983 - 1988
0.x  ? 1986
1.0 DOS, VMS, … (?) 1988
1.2 DOS, Mac OS, NeXTStep, … , VMS (?) 1989
2.0 DOS, Mac OS, NeXTStep, … , VMS (?) 1991
2.1 DOS, Windows 3.1, Mac OS, NeXTStep, … , VMS (?) 1992
2.2 DOS, Windows 3.1, Mac OS, NeXTStep, … , VMS (?) 1993
3.0 Windows, Mac OS, NeXTStep, Linux, Sun OS, Solaris, IRIX, AIX, HP-UX, OSF/1 1996
4.0 Windows, Mac OS, Linux, Solaris, IRIX, AIX, HP-UX, … (?) 1999
4.1 Windows, Mac OS, Linux, Solaris, IRIX, AIX, HP-UX, … (?) 2000
4.2 Windows, Mac OS, Linux, Solaris, IRIX, AIX, HP-UX, … (?) 2002
5.0 Windows, Mac OS, Linux, Solaris, IRIX, AIX, HP-UX, … (?) 2003
5.1 Windows, Mac OS, Linux, Solaris, IRIX, AIX, HP-UX, … (?) 2004
5.2 Windows, Mac OS X, Linux, Solaris, IRIX, AIX, HP-UX, Tru64 2005
  • Long Version:

[edit] Release history

Version Platforms Release date
1.0 16bit:(?) DOS x.x
32 bit: VMS x.x
1988
1.2 16bit:(?) DOS x.x
32 bit: Mac OS x.x, NeXTStep x.x, VMS x.x
1989
2.0 16bit:(?) DOS x.x
32 bit: Windows NT x.x, Mac OS x.x, NeXTStep x.x, VMS x.x
1991
2.1 16bit:(?) DOS x.x, Windows 3.0 - 3.11
32 bit: Windows NT x.x, Mac OS x.x, NeXTStep x.x, OS/2 x.x, VMS x.x
1992
2.2 16bit:(?) DOS x.x, Windows 3.0 - 3.11
32 bit: Windows NT x.x, Mac OS x.x, NeXTStep x.x, OS/2 x.x, VMS x.x, NeXTStep x.x (Intel, Motorola), Sun SUN/OS x.x
64 bit:(?) Solaris x.x (?), SGI IRIX x.x, IBM AIX x.x, HP-UX x.x, Digital OSF/1 x.x(?)
1993
3.0 32bit: Windows 95, Windows NT x.x - 4.0, Mac OS 7.1 - 7.5 (68k(?), PPC), Linux 1.2 - 2.0 (x86), NeXTStep 3 (Intel, Motorola, HP-PA RISC, SPARC), SUN/OS 4.1.1
64 bit:(?) Sun Solaris 2.5, SGI IRIX 5.3, IBM AIX 4.1, HP-UX 10.10, Digital OSF/1 3.0
1996
4.0 32 bit: Windows x.x/98/Me, Windows NT x.x, Mac OS, Linux (x86)
64 bit:(?) Sun Solsris x.x., SGI IRIX x.x, IBM AIX x.x, HP-UX x.x
1999
4.1 32 bit: Windows x.x/98/Me, Windows NT x.x, Mac OS, Mac OS X 10.0, Linux (x86, PPC)
64 bit:(?) Linux (Alpha)
2000
4.2 32 bit: Windows x.x/98/Me, Windows NT x.x, Mac OS, Mac OS X x.x, Linux (x86, PPC)
64 bit:(?)
2002
5.0 32 bit: Windows x.x/98/Me, Windows NT x.x, Mac OS X x.x, Linux (x86)
64 bit:(?)
2003
5.1 32 bit: Windows x.x/98/Me, Windows NT x.x, Mac OS X x.x, Linux (x86)
64 bit:(?)
2004
5.2 32bit: Windows 98/ME, Windows NT 4.0/2000/XP/2003 (x86), Mac OS X 10.2 - 10.4 (PPC), Linux (x86)
64 bit: Windows XP/2003 (x86-64), Mac OS X 10.4 (PPC G5), Linux (x86-64, IA-64), Sun Solaris 8, 9, 10 (UltraSPARC), Sun Solaris 10 (x86-64), SGI IRIX 6.5, IBM AIX 5.1 - 5.3, HP-UX 11, HP Tru64 UNIX 5.1
2005


I very much dobut that version 2.2 was 64-bit on any platform, which is implied by the above table. The history at http://www.wolfram.com/products/mathematica/history.html firsts mentions 64-bit on version 5. Drkirkby 20:46, 18 June 2006 (UTC) Links: [Short Version Overview] [Platforms for Version 5.2] [Platforms for Version 3.0]

84.153.84.73 17:22, 4 February 2006 (UTC)

[edit] POV? Mathematica is not robust nor reliable

This was recently added to the article:

Mathematica has a strong following in the academic market, especially undergraduate students, however industrial users tend to prefer more reliable and robust tools such as MATLAB and Maple.

Does this mean that Mathematica is not robust or reliable enough for industrial use?

Also, does this mean that at universities Mathematica is usually available but not MATLAB? Because that would be wrong, American universities usually have both programs available to their engineering students. Anton Mravcek 20:29, 4 November 2005 (UTC)


As an industrial practitioner of scientific computing for over a decade, I've never met anyone who uses Mathematica (though I knew plenty of them when I was in college). Matlab's numerical libraries are universally acknowledged as more robust, and people who do heavy symbolic manipulation have a strong preference for Maple.

--GaeusOctavius 20:49, 4 November 2005 (UTC)

In my experience, Maple is favored in math departments due to the large amount of purely symbolic manipulation, MATLAB is favored in more applied departments like engineering, and Mathematica has quite a following in non-computational physics. — Laura Scudder 22:30, 7 November 2005 (UTC)
For purely theoretical math and for "recreational" math, Mathematica is perfect. I guesstimate half of the contributors to the OEIS use Mathematica and provide Mathematica programs whenever they send in a sequence. PrimeFan 22:35, 8 November 2005 (UTC)
You may have some point about Matlab's numerical libraries, but to say that symbolic manipulation in Maple is somewhat superior to Mathematica is nonsensical in my opinion (Yes, I have used both). Just my 2c. Dysprosia 01:51, 11 November 2005 (UTC)
I can confirm Anton's statement about Mathematica in universities, at least in the case of Wayne State University. In the Undergraduate Library, the Windows XP computers have a folder called "Engineering Applications," which contains Mathematica 4.2, MATLAB 6.5, MathCAD 11, etc. (but no Maple). The computers in the College of Engineering, however, don't have Mathematica (but they do have MATLAB, MathCAD, PolyMath, etc.) When some engineering students tackled the problem of face recognition, they turned to MATLAB.
So just using WSU, I'm not sure this qualifies as "a strong following in the academic market, especially undergraduate students." Del arte 22:36, 12 November 2005 (UTC)

I have recruited mathematical software users for various math intensive corporate tasks - usually initial technical or financial project testing and development. What I have found is that Mathematica is the corporate preferred package for theoretical testing - primarily looking at various routes that can be taken, whilst Matlab is preferred for hands on development. I personally prefer Mathcad but corporate pressures being what they are the two main packages for maths within the corporate world are Mathematica - high end and Matlab - hands on. As for Maple this is seen as an academic use package and there has been little transition to the corporate market. Just check technical and high end recruitment sites and you will find this to be the case.

[edit] Authorship of Mathematica

The article says Mathematica was "originally developed by Stephen Wolfram". It is true that Stephen Wolfram initiated the project to develop Mathematica, but the first released version of Mathematica included contributions from a team of 8 developers: Stephen Wolfram, Daniel Grayson, Roman Maeder, Jerry Keiper, Henry Cejtin, Steve Omohundro and Dave Ballman collaborated on the Mathematica kernel (the computational core of Mathematica), while Theo Gray designed and implemented the front end that established the distinctive interaction style of Mathematica and provided the ability to create "live" interactive, executable mathematical notebooks. Some of these people were involved in the development of Mathematica for 2 years prior to its debut as a commercial product, so the expression "originally developed by" would surely apply to them as much as to Wolfram. My authority for this is personal recollection: I was one of the earliest employees of Wolfram Research, and I personally knew 7 of the 8 original developers (all but Omohundro). (I wasn't one of the developers myself, but I was one of the first 10 or so people hired when the company was being organized in preparation for the initial commercial release.) In the interest of historical accuracy and fairness, I suggest that the article text at least be amended to read "originally developed by a team assembled and led by Stephen Wolfram". I realize that doesn't flow as smoothly as the current wording; maybe someone else can find a better way to say it. I will wait a day or two for comment before proceeding with the edit. --Logician1989 06:23, 16 February 2006 (UTC)

I'll let you do the honours. You should reference this page (or some other) somewhere when you do, maybe even just in the edit comment, as a verifiable source. Dysprosia 08:23, 16 February 2006 (UTC)
Thanks for the link. I'm new to editing Wikipedia and am still learning the rules and customs. By the way, I noticed that the article describes Mathematica as a "computer algebra system". Swolf hated this term and forbade employees of WRI from using it. He said that "computer algebra system" placed undue emphasis on symbolic manipulation, and overlooked 2/3 of what Mathematica could do (high-precision, rapid numerical calculation, and graphics/visualization) -- and more importantly, obscured the fact that these three aspects of the system were tightly integrated with each other. The subtitle of the Mathematica book is "A System for doing Mathematics by Computer", and we were allowed to call Mathematica a "computer mathematics system" or a "computer math system" (although that suggests that Mathematica does "computer mathematics" as opposed to the "regular" kind, so was also frowned upon) but NOT a "computer algebra system". As an evangelist who spoke frequently to potential customers and large audiences, I had to keep this restriction firmly in mind. Nevertheless I realize that the terms "computer algebra system" and "CAS" are entrenched, and furthermore are used canonically in Wikipedia (as an article title, for example) as the designation for a class of software which certainly does (or should) include Mathematica, so I'm thinking I shouldn't change this usage in the Mathematica article. --Logician1989 16:54, 16 February 2006 (UTC)

[edit] Map vs. threading

I argue that using map is much more lucid than using Mathematica's inbuilt threading, in the example of "Map[Apply[Log, #] &, {{2, x}, {3, x}, {4, x}}]". Using threading isn't wrong, it's just less clear, and we should strive for clarity if we are to write an illustrative example. Dysprosia 00:37, 6 June 2006 (UTC)

The code: "Map[Apply[Log, #] &, {{2, x}, {3, x}, {4, x}}]" uses the terms "Map", "#", "&", each of which requires a somewhat lengthy definition. These definitions were completely absent from the pre-existing Wikipedia article containing this code. Therefore, the example was not readily comprehensible to someone who did not already know the subject well, making it an undesirable encyclopedia entry. Fixing this up by including lenthy definitions for these terms would make the example overly long, especially since this aspect of the program is unnecessary, as my rewrite shows.

On the other hand, the code which I wrote has a self-contained explanation following it. Moreover, my program is shorter, does not require any extraneous function definition, and it illustrates how the numerous options for Mathematica functions, in this case a third argument to Apply, produce shorter and cleaner programs.

For these reasons, my code should remain.

-ilan

You haven't responded at all to the clarity or otherwise of using threading. It's obscure, and not all functions, especially user defined functions, support it. Dysprosia 13:38, 6 June 2006 (UTC)

And you haven't responded to using numerous undefined symbols in an example. As for the clarity of threading and your statement: "It's obscure," I disagree with it. This is only an opinion, as is your own statement. Indeed, it is just a question of style and cannot be proved rigourously. However, as I implied on my Wikipedia homepage discussion, if there were a Mathematica manual of style, then my book would be a good candidate, so my claim has an authoritative basis. For example, I consider your ad hoc function definition to be a good example of bad style, especially when it can be avoided by writing a simpler program. In conclusion, since I considered it obvious that your point was stylistic, I felt that objective issues, such as your use of many undefined symbols, had priority in the discussion.

-ilan

The point about undefined symbols can be easily rectified by expanding the article in a reasonable fashion. If there were a Mathematica manual of style, your book would still be your opinion, and thus would not be quite "authoritative". Dysprosia 21:41, 6 June 2006 (UTC)

This appears to be an implicit admission that your version of the article was incomplete and that my changes made it self-contained. Normally, someone would accept that as being an improvement. Instead you make vague plans for a longer version. As for your second point, it is incorrect but I don't have the time or energy to explain to you these things that you should already know. I am starting to wonder whether Wikipedia even makes sense if everything comes down to this type of bickering. The only solution seems to be to appeal to a referee or editorial board.

-ilan

If you find reasonable discussion about making reasonable improvements to the article that tiring, then this is a reflection on yourself, not on me. My second point is not incorrect -- like I mentioned on your talk page before you removed it (it is still in the article history), Wikipedia doesn't work on a "defer to the authority" basis, and furthermore, matters of style are fundamentally based on opinion and not on objectivity. When I get some time, I'll make an attempt to address both concerns and feature both methods in the article. Dysprosia 00:34, 7 June 2006 (UTC)

[edit] Mathreader License

The sentance

"Starting with version 3.0 of the software, notebooks are represented as expressions that can be manipulated by the kernel, and the typesetting features of the front end were deemed sufficiently important to warrant the availability of a dedicated reader software for displaying Mathematica notebooks, the MathReader software that is not tied to a commercial license."

is rather long, but I feel is also inaccurate too. There is a commercial license on MathReader, despite the fact the software is a free download. Drkirkby 00:16, 12 June 2006 (UTC)

[edit] Connections with other applications

The article says communication with other programs occurs with MathLink. But that is not the only way - one can use the file pointers stdin and stdout. i.e. to get Mathematica to evaluate things output from myprog1 one can use

myprog1 | math.

Is that not communication? I guess it is only one-way (myprog1 to math, and not the other way too). Do others think something like that should be added? Or perhaps 'bidirectional' inserted into the header/description.

MathLink is clearly sophisticated and quite complex - there is not always the need for such complexity. Drkirkby 07:32, 12 June 2006 (UTC)

[edit] Icon

I belive the Mathematica icon is for version 4, whereas the latest version is quoted as 5.2. It would seem sensible for a version 5 icon. But I have some concerns about exactly how an icon may be used (copyright), so are not going to add one myself Drkirkby 18:13, 25 June 2006 (UTC)

I have updated the icon. It classifies as "fair use". —Mets501 (talk) 20:44, 18 August 2006 (UTC)

[edit] Unfounded criticism

This remark (from the Criticisms section) just has to be from a programmer and non-mathematician:

In breaking with most popular programming languages, Mathematica indexes its lists starting from one. […]

Mathematica is first and foremost a tool for doing mathematics; therefore it makes sense to follow the conventions of mathematics. The observation that it is also a programming language doesn't mean that suddenly the conventions of programming should take precedence. For example, the upper left element of a matrix A is usually written A11; it would be a Bad Thing if Mathematica forced us to write A[[0,0]] instead.

The remark is also factually incorrect—you can index a list with index 0. What you get is the list's head, as already mentioned earlier in the article. So in a certain sense, Mathematica elegantly honors the conventions of mathematics and of programming.

Since the remark is totally unfounded as criticism, I removed it from the article.
Herbee 03:14, 27 August 2006 (UTC) (I'm a programmer, btw)

[edit] Is every price tag inherently worthy of criticism?

In the Criticisms section, we have a fact that reads: ... Wolfram Research sells the software for a price of $1880 to $3135 for a standard license.

The nature of the criticism is not clear to me. (There's no citation, so I can't verify this.) Is the criticism that the price is not less than $1880? Or is the criticism that it has a price tag at all? If the former, I think this should either be removed as POV (whether or not this is an excellent is clearly a matter of opinion) or else cited as to who is making this specific criticism. If the latter, I think this should be removed on the basis of redundancy or just plain sillyness — should every commercial product in Wikipedia have a Criticism section added because someone doesn't want to pay for it?

Just thinking out loud before I remove it. Either way, we're missing a citation so the reader can verify where this criticism is coming from. And please consider that for each review of "it's too expensive", we may also be able to find an "it's an excellent value" review for a Praise section. That might escalate. Or maybe not. Anyways, thanks for your thoughts on this. --Ds13 16:12, 9 October 2006 (UTC)

You raise an interesting point. However, in the context of the full paragraph there, I would vote against deletion. As it also points out that the product is proprietary, a point to be had might be that while the product does a lot of good things, it only allows for the things which the designers want to allow. This would be at odds with, say, an otherwise similar but open source product. I admit this point does not come across much at all as written, but is an extraordinarily valid criticism. "I am paying such and such, and yet an arbitrary design decision prevents me from doing what I wish to do." A rewrite would (IMO) be far preferable to deletion.
As to citing prices: before deleting them, please try to find sources yourself; they're on the manufacturer's website (albeit are likely to change not infrequently). I always rather look first, then either i) correct what is wrong; ii) add ref to correct info; iii) as last resort, delete unfixable content.
Baccyak4H 16:41, 9 October 2006 (UTC)
I can't find a reference for the criticism that the single-user license "places the software out of the hands of many who could benefit from using it", so I've tagged this.
I've also split the criticism of being proprietary from the criticism of the Standard version costing too much.
Additional weasel-wording in this section includes: "a policy some find draconian" and "which some argue slows down the speed". --Ds13 18:36, 9 October 2006 (UTC)

Here are links [1] [2] to two software reviews complaining about the price. I didn't bother to include the random newsgroup comments regarding Mathematica's high price. If you know of any reviews claiming that Mathematica is an excellent value for the price, please let me know; I didn't find any during my search.

I don't believe that any software which charges a price should be criticized on that fact alone, but nor do I believe that any price set for a piece of software is automatically reasonable just because the market will bear it. I agree that finding verifiable citations is the way to establish which side of the fence Mathematica sits on. -- Four Dog Night 20:14, 9 October 2006 (UTC)

I didn't find any reviews that said it was good value. I guess it's just me, but I'll accept that. (Personally, I think that $140 for students as long as they're in school is a great value. And any for-profit entity that needs to spend the $1,880 for their license is probably spending tens of thousands in hardware and, especially, salary to operate the system, so the difference between $1,880 and free may not be as significant for that target buyer as it might seem.) Anyways, that's my POV and there doesn't appear to be a reliable source that feels the same way.
I've bolstered the "proprietary" criticism with some context and a link to comparisons with competitive software, after an anonymous user blanked it. Thought technically, that criticism is still without reference to a reliable, notable source — it almost appears as an original argument. Thoughts? --Ds13 15:57, 10 October 2006 (UTC)

Here is the abstract of a paper by Richard Fateman and Derek Lai:

Users of computers for scientific and mathematical computation have become more aware of computer algebra systems through recent commercialization of the technology. However, the proprietary nature of most such systems makes the software unavailable to computer scientists and systems developers for "dissection" and for certain kinds of experiments or applications. In an attempt to provide appropriate software for such purposes, and especially for interaction in the Common Lisp environment, we have developed a simple mathematical display package. This program produces conventional notation - raised superscripts, fraction bars, and similar features, from an internal notation that is quite natural in Lisp. This module fits into the model begun by earlier programs at Berkeley consisting of a "clone" parser for one common proprietary system (the Mathematica (TM) language), and a simplifier for rational functions.The entire package is written in Common Lisp, and some of its main features are described in this document.

The actual paper (click on the "full text" link) goes a bit further regarding the problems of proprietary CAS systems.

P.S. Just FYI, my POV is that $800 (instead of $1880) would be a reasonable full list price. But either way, it is out of my price range, so I will be sticking with the free stuff. -- Four Dog Night 19:10, 10 October 2006 (UTC)

Interesting you cited Fateman. He has on several occasions posted to MathGroup on how one can write some code that does not do what it is documented to do. He would then often state how unacceptable this was, to the effect of this isn't in the documentation, and I cannot see under the hood. Someone else (name escapes me) does that a lot as well, quite a bit less adversarially I might add (and both use remarkably contrived constructions). I am not sure how to use this to better the article, but felt it worth mentioning. Baccyak4H 19:37, 10 October 2006 (UTC)
Ironically, I can't read the paper due to the proprietary nature of its ownership and/or distribution. ;) I agree with your point though, especially when the user of an algebra package is expertly capable of reading/using/modifying/evaluating its source, then being open can be a significant benefit. But I suspect the portion of users who need a computer algebra system and who are actually capable of expertly reading/modifying/evaluating its source code (were it to be made available) is very small. --Ds13 19:58, 10 October 2006 (UTC)
I don't know what I would have done to have special access to that paper, but who knows. Interesting. Fateman also wrote a technical critique of Mathematica in 1991. I don't know to what extent the problems he describes still exist in the current version of Mathematica. -- Four Dog Night 23:46, 10 October 2006 (UTC)