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MathGroup Archive 2006

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Re: How to extract functions from a list and call them with any argument?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65957] Re: How to extract functions from a list and call them with any argument?
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Mon, 24 Apr 2006 06:02:19 -0400 (EDT)
  • References: <e2fkto$bp7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

dmp55 at sympatico.ca wrote:
> I have a list of functions, i.e.,
> 
> funclist = {Sin[x], x^3, Cos[x]^2}.
> 
> I can extract each of the functions, like
> 
> In[1]:=funclist[[1]]
> Out[1]=Sin[x]
> 
> , but I don't know how to call these functions with a general argument.
> If I type
> 
> In[2]:=funclist[t][[1]]
> 
> , I get
> 
> Out[2]=t
> 
> instead of Sin[t] (or t^3 or Cos[t]^2)
> 
> What I would like is to extract a function from the list and to call it
> with any argument, as it was defined in a standard way:
> f[x_]:=Sin[x].
> 
> Dom
> 
The short answer is that you don't have a list of functions - you have a 
list of expressions, so you need to replace x by whatever you want:

funclist[[1]]/. x->t

However, this is not an ideal way to work because if x gets a value 
somewhere else, that value will get substituted before you can get the 
desired replacement. It would probably be better to use a real list of 
functions - pure functions - looking like:

{Sin,#^3&,Cos[#]^2&}

Your question indicates that you are probably a beginner with 
Mathematica, and it would really help to read that big book a bit and 
try the examples. After a while, you will find that the right way to do 
things gradually soaks in!

David Bailey
http://www.dbaileyconsultancy.co.uk


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