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Re: What is @@@?

• To: mathgroup at smc.vnet.net
• Subject: [mg87472] Re: What is @@@?
• From: AES <siegman at stanford.edu>
• Date: Fri, 11 Apr 2008 01:45:25 -0400 (EDT)
• Organization: Stanford University
• References: <ftkbe8$bov$1@smc.vnet.net>

In article <ftkbe8$bov$1 at smc.vnet.net>,
 Bill Rowe <readnews at sbcglobal.net> wrote:

> ><http://documents.wolfram.com/mathematica/book/section-A.2.7>
> 
> >A.2.7 Operator Input Forms
> 
> >Characters that are not letters, letter-like forms or structural
> >elements are treated by Mathematica as operators.
> 
>
> >So Mathematica treats "3" as an operator???
> 
> No, Mathematica does not treat the "3" in either expression
> above as some kind of operator.  . . . . . . . . . . . there are
> other parts of the documentation covering what is regarded as a
> number, expression, variable etc that takes precedence over the
> portion you quoted.

Look, after using Mathematica extensively since, literally, version 1.0, 
I know full well that "3" is not an operator!

But, it sure seems to me that the quote given above unambiguously 
implies that it is -- otherwise the sentence would have (and could have, 
and should have) said something like

      Characters that are not letters, NUMBERS, letter-like forms, or
      structural elements are treated by Mathematica as operators.

This is, after all, supposedly Wolfram's precise, detailed, absolutely 
complete and accurate documentation for its product -- right?

This branch of this thread started with my query about where in the 
documentation I could learn about all the non-alphameric operators that 
are so ubiquitous, and confusing, in Mathematica.  

I use and understand some of these; I know that I don't know all of 
them; I would like to have a brief overview (3 or 4 pages max) giving a 
quick list of all of them (or least the most important of them) and a 
brief (few sentence), so that I might learn what the rest of them are, 
and perhaps improve my skills.

I was pointed to Section A 2.7.  It doesn't really do what I want -- and 
seems to be inaccurate (or at least imprecise) to boot.

Finally, you mention "precedence" for Mathematica's documentation.  
Precedence implies _precedence rules_ (otherwise it's meaningless).  
So, if you'll pardon a little sarcasm:  Where in the Mathematica 
documentation are these precedence rules for the Mathematica 
documentation itself given?  

My bottom lines:

1)  Writing totally precise, complete, detailed, absolutely accurate 
_reference_ documentation, of the sort needed by experts, for any system 
as massive and complex as Mathematica, is very hard -- a very difficult 
task.  

Wolfram works hard, I believe, at providing this kind of reference 
documentation -- as they more or less have to -- but don't do a perfect 
job, as the opening sentence of A 2.7 illustrates in an admittedly 
pretty minor way.

2)  Writing less precise, less complete, much shorter, simpler, less 
detailed, and very differently organized and structured _user_ 
documentation, for  the benefit of beginners and/or ordinary non-expert 
users of a system like Mathematica is at least equally hard -- in fact, 
perhaps an even more difficult task.

Wofram has thus far, at least in my view, _totally_ failed at performing 
this task and providing this kind of _user-oriented_ documentation for 
version 6.0; and deserves severe criticism for this failure.  Their 
product is superb and in many ways amazing.  But the "ordinary user 
oriented" documentation that they provide for it is not so much lousy as 
essentially nonexistent -- and I can't believe they've done this.