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MathGroup Archive 2007

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Re: How to make delayed functions from text info

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81149] Re: How to make delayed functions from text info
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Fri, 14 Sep 2007 03:32:20 -0400 (EDT)
  • References: <fcb39b$fca$1@smc.vnet.net>

P_ter wrote:
> Hello,
> I have a list like this t1= {{"AA", {15.}, {19.}, 4.}, {"AC", {17.}, {21.}, 4.}}
> It means: AA[b_,t_]:= If[15<t<=19,b,0] Etc.
> The problem is that I have a few hundred of these elements in a list. But when I do:
> (ToExpression[#[[1]]][b_,t_]:= Evaluate[If[#[[2,1]]< t<= #[[3,1]],b,0]])& /@ t1
> I get out {Null, Null}, although AA and AC exist with ?AA,?AC

This is because SetDelayed[] (i.e. :=) evaluates to Null when the 
assignment was successful.

> But I want to see these delayed functions in a list:
> lst = {AA[b_,t_]:=If[15.<t<=19.,b,0],AC[b_,t_]:=If[17.<t<=21.,b,0]
> ...}
> I would like to say: lst[[1]] and get this delayed function. Is that possible?
> Also I wonder if ?(AA,AC) could be done, such that I get all the definitions in a row. Any idea?

The simplest solutions I can think of are the following (after the 
functions "AA", "AC", etc. have been defined):

Information /@ t1[[All, 1]]

DownValues /@ ToExpression /@ t1[[All, 1]]

If you really need a list of expressions that *look like* function 
definitions (but do not actually define the functions), try

t1 /. {name_, {min_}, {max_}, _} ->
   HoldForm[name[b_, t_] := If[min < t <= max, b, 0]]

(The argument renaming is caused by SetDelayed being embedded in Rule.)

-- 
Szabolcs


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