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Re: Re: Mathematica skill level snippet(s)

• To: mathgroup at smc.vnet.net
• Subject: [mg104805] Re: [mg104745] Re: Mathematica skill level snippet(s)
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Tue, 10 Nov 2009 06:01:41 -0500 (EST)
• References: <200911917250.789293@jfultz2winlap>
• Reply-to: "Nasser M. Abbasi" <nma at 12000.org>

From: "John Fultz" <jfultz at wolfram.com>

"Stephen Wolfram wrote a blog post which included a ListPlot of the function
count from Mathematica's inception to version 7.

http://blog.wolfram.com/2008/11/18/surprise-mathematica-70-released-today/

The plot is about a third of the way through the post.  Note the number here is
significantly below your number because you're counting all System` symbols,
whereas he was counting System` *functions*.
"

Yes, I know about this blog (it is one of the references already on my 
page), and I actually remember spending sometime trying to find how did Dr 
Wolfram would have counted the number of functions, but I could not figure 
it out (the command used to generate the plot was not shown in the blog.)

Do you know how to find how many of the Symbols are actually Functions such 
as Sin,Cos etc.. vs. say function options or other type of symbols? Since 
the Head of a Function is a Symbol itself I can't just look at the Head of 
each symbol to find out?

In[6]:= Head[Sin]
Out[6]= Symbol
In[7]:= Head[Joined]
Out[7]= Symbol

If I filter by attribute, which I think may be the way to do it, then which 
set of attributes to use? Listable? gives only 264

Length[Select[Names["System`*"], MemberQ[Attributes[#1], Listable] & ]]
264

So, need more attributes which all apply to functions, then get a unique 
list out, then count it? But I do not know what all the attributes should 
be.

If you know  _please_ let me know, and I will add this information to the 
table.

thanks
--Nasser