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what actually is in the WRI "functions" database?

• To: mathgroup at smc.vnet.net
• Subject: [mg48587] what actually is in the WRI "functions" database?
• From: Richard Fateman <rfateman at sbcglobal.net>
• Date: Sat, 5 Jun 2004 19:58:08 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I was browsing through the WRI function database, actually
to see what indexing method was being used.  But then I
began to wonder how some of
the specific formulas fit into Mathematica. I tried
(the first) equation I picked on in Mathematica 5.0.

It was formula
http://functions.wolfram.com/01.09.23.0002.01

which has a condition that n is a positive integer.

This is displayed on the functions web site as  n \[element] 
?[DoubleStruckCapitalN]^{+}  where I've made up some of
the notation there, using TeX notation. Mathematica has a superscriptbox
notation, I think..

The InputForm on the functions web site says to type this into Mathemaitca as

n \[Element] Integers && n > 0

which is not the same.

Then I looked further, nearby..

http://functions.wolfram.com/ElementaryFunctions/Cot/23/01/0005/

where there is a formula containing an ellipsis ...

and the InputForm basically is not computationally equivalent
at all to the semantics of the formula.  It just has an ellipsis!

To summarize:
1. There is a typeset formula T, using typical math notation.

2. There is an InputForm, S which is not the same as T, and probably 
cannot be automatically mapped onto T from Mathematica.

3. S, in general, does have the semantics of T either.

4. (oh, also), There is a MathML form.  It seems to have a typeset
component that looks like T, but very verbose, and a MathML content
that is (I guess) supposed to translate into S.
In the example http://functions.wolfram.com/01.09.23.0002.01
it is NOT the same as S, at least if you believe there is
a difference between the integers and the POSITIVE integers.


Question: Has anyone (else) found this troublesome?  Is there just a
disconnect between the Functions web site and what (I think)
was the intention of making it meaningful to automated mathematics?

The idea that a table or encyclopedia of computerized mathematics
should be a collection of typeset math and an inaccurate rendition
of it in some computer algebra system is not particularly attractive.

RJF