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Re: How to delay action of ...[[i]] (Part[...,i]) until appropriate time?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112252] Re: How to delay action of ...[[i]] (Part[...,i]) until appropriate time?
  • From: Greylander <greylander at gmail.com>
  • Date: Tue, 7 Sep 2010 01:59:50 -0400 (EDT)
  • References: <i627rm$9c$1@smc.vnet.net>

I have answered my own question!  And understand a bit more how to
'think' in Mathematica...

The problem is that Part[[]] acts on any expression.  What I have
finally figured out is that I need a version of part (or a version of
[[...]]) that acts *only* on lists (i.e. expressions with "List"
head), and searching and exploring the documentation, I eventually
learned how to do that.  This will have exactly the desired result.

Here is what I did:

      VPart[expr_List,k_] :=Part[expr,k]

And I also define subscripting in an expression to invoke VPart[]:

     expr_List[Ctrl+-]k_ :=VPart[expr,k]

Above the [Ctrl+-] means literally press the Ctrl key and the -
(minus) key, so that "k_" will then be a subscript.

Now I have one remaining question:  why is there not something like
this already defined in the core of Mathematica?  It seems obvious (to
me) that one would want a version of Part[] (element selection)
restricted to List expressions only.




On Sep 6, 4:13 am, Greylander <greylan... at gmail.com> wrote:
> Consider the following toy example:
>
> in> goo[v_] := v.{1, 1}*(3 v)
> in> foo[k_][v_] := goo[v] [[k]]
>
> in> goo[nnn]
> out> 3 nnn nnn.{1, 1}
>
> in>foo[1][{2, 3}]
> out>30
>
> in> foo[2][nnn]
> out>nnn
>
> Notice how in this last output, because the parameter nnn is
> undefined, [[k]] ends up acting on the structure of the expression in
> goo, but the intuitive behavior would be for evaluation of [[k]] to
> also be delayed.  The output I would like to see is:
>
> in>foo[2][nnn]
> out> ( 3 nnn nnn.{1,1} ) [[2]]
> in> nnn = {4,5}
>      %
> out> 135
>
> But of course it does not happen that way.
>
> I realize that Mathematica is a specification rather than procedural
> language, but surely there is some reasonably elegant way to to delay
> the effect of [[2]] above so it acts on the eventual result of
> goo[nnn] and not on the structure of the expression.
>
> This is related to my other questions about using NDSolve on dependent
> variables that have arbitrary structure and therefore require some
> kind of indexing.
>
> There must some basic aspect of the Mathematica language that I have
> missed which makes indexing and list manipulation more intuitive.  (I
> hope!)
>
> Anyone have any insights?



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