Re: "vector" Map[] / functional outer product?
- To: mathgroup at smc.vnet.net
- Subject: [mg83773] Re: "vector" Map[] / functional outer product?
- From: Mitch Murphy <mitch at lemma.ca>
- Date: Fri, 30 Nov 2007 05:19:11 -0500 (EST)
- References: <fim8tq$rmd$1@smc.vnet.net> <474ED0C0.9030008@gmail.com>
based on the solution from Jean-Marc Gulliet, here's a slight
improvement based on overloading Map[] for List arguments. this solves
my issue perfectly without having to type in esc sequences for infix
operators
Unprotect[Map];
Map[f_List, a_List] := Transpose@Outer[Compose, f, a]
Protect[Map];
{f, g} /@ {a, b, c}
-> {{f[a],g[a]},{f[b],g[b]},{f[c],g[c]}}
cheers,
Mitch
On Nov 29, 2007, at 09:46, Jean-Marc Gulliet wrote:
> 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