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MathGroup Archive 1996

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Re: How to think about Map[ ] ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4685] Re: How to think about Map[ ] ?
  • From: wagner at motel6.cs.colorado.edu (Dave Wagner)
  • Date: Sun, 25 Aug 1996 18:23:13 -0400
  • Organization: University of Colorado, Boulder
  • Sender: owner-wri-mathgroup at wolfram.com

In article <4ve91p$l93 at dragonfly.wolfram.com>,
AES <siegman at ee.stanford.edu> wrote:
>I can understand that  
>
>   Map[f,{a,b,c}] --> {f[a], f[b], f[c]}
>
>But would someone want to give a little tutorial on how to understand 
>the (what seem to me) bizarre results I get when I try various
>combinations like
>
>   Map[f, a + b + c]
>
>   Map[f, a + b - c]
>
>   Map[f, a * b * c]
>
>   Map[f, a / b / c]

The seemingly inscrutable results that you get in some cases are due
to the way the those expressions are represented internally.
If you look at the internal forms of these expressions you will
see that the way Map works is quite simple and consistent:

In[1]:= FullForm[{a,b,c}]
Out[1]//FullForm= List[a, b, c]

In[2]:= FullForm[Map[f, {a,b,c}]]
Out[2]//FullForm= List[f[a], f[b], f[c]]

In[3]:= FullForm[a+b+c]
Out[3]//FullForm= Plus[a, b, c]

In[4]:= FullForm[Map[f, a+b+c]]
Out[4]//FullForm= Plus[f[a], f[b], f[c]]

I'll leave the rest to your own explorations.

		Dave Wagner
		Principia Consulting
		(303) 786-8371
		dbwagner at princon.com
		http://www.princon.com/princon

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