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