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Re: what actually is in the WRI "functions" database?

• To: mathgroup at smc.vnet.net
• Subject: [mg48699] Re: what actually is in the WRI "functions" database?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 10 Jun 2004 02:45:03 -0400 (EDT)
• References: <20040608153448.46653.qmail@web81005.mail.yahoo.com> <40C5E6C7.6080704@cs.berkeley.edu> <p06110400bcec42b09adc@[130.95.6.184]> <40C724B2.3090200@cs.berkeley.edu>
• Sender: owner-wri-mathgroup at wolfram.com

On 9/6/04, Richard Fateman wrote:

>Since the standard form and the mathematica input form can be, and 
>apparently ARE different, you cannot check consistency between the 
>standard form and the computer-algebra form this way!

I still do not follow you. If I go to

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

and copy the Input Form and Standard Form (long box form) expressions 
into Mathematica, and enter both expressions, or convert both 
expressions to a common format (StandardForm or TraditionalForm, 
which I prefer) I get _exactly_ the same output. See

  http://physics.uwa.edu.au/pub/Mathematica/MathGroup/FunctionFormats.nb

where I have tried to make this clear.

I agree that either expression is not evaluatable until the Ellipsis 
is defined but, once this is done, either expression evaluates 
correctly.

OTOH, copying and pasting the MathML form into a Mathematica session 
and converting to StandardForm one encounters the MathML conversion 
problem.

>I am concerned only with the CAS form errors.  So far as I can tell, EVERY
>formula with an ellipsis is wrong.  Probably wrong wrt InputForm as 
>well as MathML.

They are not "wrong". They are incomplete: the ellipsis needs to be defined.

>One must deduce the pattern of each ellipsis and make the 
>appropriate substitution.  This is not something that can be done 
>automatically.

Agreed.

>There may be other issues as well.  When we attempted to convert 
>G&R's TeX into a CAS language, the largest group of problems were, I 
>think, ellipsis, but there were others. see 
>www.cs.berkeley.edu/~fateman/papers/parsing_tex.pdf

I've downloaded this.

>This is truly pointless because, even if there was a mechanism to 
>translate automatically from StandardForm to MathML and back, all 
>that would do is check the TYPESETTING, not the semantics.

It is not pointless. It would, at least, identify the conversion 
error encountered here.

>I am reporting the kind of error that requires at least revisiting 
>every formula with an ellipsis in it and a change to the design.

All it requires is for the ellipsis to be defined (on a case-by-case 
basis). I expect that intelligent use of symbolic pattern-matching 
and the Notation package could be used together to reduce the number 
of cases to be handled to a manageable number.

Cheers,
Paul