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

*To*: mathgroup at smc.vnet.net*Subject*: [mg100362] Re: [mg100289] Indexed Slot in a Rule - How to do it??*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Tue, 2 Jun 2009 06:41:06 -0400 (EDT)*References*: <200905311034.GAA16834@smc.vnet.net>

Hi Alan, Using anonymous pure function semantics will probably be not the simplest way to achieve your goal. Assuming that your variables {x1,x2,etc} don't have global values (you must ensure it in your construction anyway) and that you know which ones and how many of them you need in advance, here is a possibility: In[1] = convertToFunction[eqs_, vars_List] := Function[Evaluate[vars], eqs]; In[2] = T = convertToFunction[{0, 5*x1, 1, 10*x3, 3*x2},{x1,x2,x3}] Out[2] = Function[{x1, x2, x3}, {0, 5 x1, 1, 10 x3, 3 x2}] In[3] = T[1, 2, 3] Out[3] = {0, 5, 1, 30, 6} This uses your variables x1, ... directly as function variables. The <Evaluate> in the code is needed to force the binding to the variables x1,etc. Note that the syntax is slightly different - you pass a sequence of arguments rather than a list. If you really need slots for the anonimous function (#...), what is your application - what is it that you want to do with them? Regards, Leonid On Sun, May 31, 2009 at 3:34 AM, Alan <alan.stone 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. > > All the best, > Alan > >