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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
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