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

  • To: mathgroup at
  • Subject: [mg48699] Re: what actually is in the WRI "functions" database?
  • From: Paul Abbott <paul at>
  • Date: Thu, 10 Jun 2004 02:45:03 -0400 (EDT)
  • References: <> <> <p06110400bcec42b09adc@[]> <>
  • Sender: owner-wri-mathgroup at

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

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

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 

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

>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 


>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 

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.


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