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