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MathGroup Archive 2007

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Re: "vector" Map[] / functional outer product?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83762] Re: "vector" Map[] / functional outer product?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 30 Nov 2007 05:13:14 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fim8tq$rmd$1@smc.vnet.net>

Mitch Murphy wrote:
> greetings,
> 
> is there a simpler way to express
> 
> 	{f@#,g@#}& /@ {a,b,c}
> 
> 	-> {{f[a],g[a]},{f[b],g[b]},{f[c],g[c]}}
> 
> ie. is there some mathematica function ??? such that
> 
> 	{f,g} ??? {a,b,c}
> 
> 	-> {{f[a],g[a]},{f[b],g[b]},{f[c],g[c]}}

<snip>

The following expression (In[1]) will return the desired list without 
the burden of passing explicitly any arguments to your functions.

In[1]:= Outer[Compose, {f, g}, {a, b, c}] // Transpose

Out[1]= {{f[a], g[a]}, {f[b], g[b]}, {f[c], g[c]}}

Note that if you want a nice infix notation, you could add some meaning 
to a symbol without any built-in meaning, such as CirclePlus (On the 
keyboard, you can enter the symbol CirclePlus as Esc c+ Esc --- i.e. 
escape key followed by c followed by + followed by the escape key.)

In[2]:= CirclePlus[f_, a_] := Transpose[Outer[Compose, f, a]]

In[3]:= {f, g}\[CirclePlus]{a, b, c}

Out[3]= {{f[a], g[a]}, {f[b], g[b]}, {f[c], g[c]}}

Regards,
-- 
Jean-Marc


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