Re: Indexed Slot in a Rule - How to do it??

• To: mathgroup at smc.vnet.net
• Subject: [mg100323] Re: Indexed Slot in a Rule - How to do it??
• From: Szabolcs <szhorvat at gmail.com>
• Date: Mon, 1 Jun 2009 07:06:44 -0400 (EDT)
• References: <gvtme0\$gct\$1@smc.vnet.net>

```On May 31, 1:33 pm, Alan <alan.st... at yahoo.com> wrote:
> Here's the problem.  Convert a vector (list) with symbol names into
> indexed slots.  I'm doing this so that I can turn the vector into
> function that takes a list.  Here's an example of the desired
> behavior:
>
> eqs = {0, 5*x1, 1, 10*x3, 3*x2};
>
> convert this to:
>
> indexedeqs = {0, 5*#[[1]], 1, 10*#[[3]], 3*#[[2]]};
>
> T[q_]:=indexedeqs;
>
> T[{1,2,3}] = {0,5,1,30,6}
>
> I can't for the life of me figure out how to do this.  I've been
> performing meta-Mathematica all week.  Here's the closest I've come:
>
> xvars={x1,x2,x3};
> MapIndexed[Rule[#1, #[[First@#2]]] &, xvars]
>
> But, this treats the second # literally, and puts in the current item
> from xvars.  I need a way for the second # to just be # without it
> really taking a value.
>
> So, I tried doing it as a string:
> xvars={x1,x2,x3};
> MapIndexed[Rule[#1, "#[[" <> ToString[First@#2] <> "]]"] &, xvars]
>
> And this creates a rule that looks correct, but, its right hand side
> of the rule is a string instead of an expression.
>
> I can't figure this out!!!  Any help is greatly appreciated.
>

It is certainly possible to do this, and I'm sure several people will
post a solution.

So here's an alternative suggestion:

Instead of #[[1]], etc. use #1, #2, ... and then Apply the function
with @@ (or apply it at level one with @@@ instead of mapping with /@,
etc.)

In[1]:= eqs = {0, 5*x1, 1, 10*x3, 3*x2};

In[2]:= f = With[{fun = eqs /. {x1 -> #1, x2 -> #2, x3 -> #3}}, fun &]
Out[2]= {0, 5 #1, 1, 10 #3, 3 #2} &

In[3]:= f @@ {x, y, z}
Out[3]= {0, 5 x, 1, 10 z, 3 y}

```

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