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A Sum-like notation for iteration

  • To: mathgroup at
  • Subject: [mg102237] A Sum-like notation for iteration
  • From: cca at
  • Date: Sun, 2 Aug 2009 05:59:38 -0400 (EDT)

For a future version of Mathematica, a would like to suggest a Sum-like 2D 
notation for Table and related constructs. By this I mean, for exemple, 
that an expression like 

RawBoxes@RowBox[{UnderoverscriptBox["Table", RowBox[{"i", "=", "m"}], "n"],
   RowBox[{"f", "[", "i", "]"}]}] 

could be interpreted as 

Table[f[i], {i, m, n}] 

and, of course, in full generality (and due embellishments for list 
iterators and steps). By using this notation, for example, I have been able 
to make some people understand Table with many iterators much more easily. 

Setting the Notation package aside (which I refuse to use) I think it is 
possible to do this in many ways (using MakeBoxes, CellEvaluationFunction, 
etc.), but I have not attempeted beyond 3 iterators. 

Carlos Cesar de Araujo
Gregos & Troianos Educacional
Belo Horizonte, MG, Brasil
(31) 3283-1122

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