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Re: Re: Prefix function syntax f @ x

• To: mathgroup at smc.vnet.net
• Subject: [mg66678] Re: [mg66651] Re: [mg66638] Prefix function syntax f @ x
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 27 May 2006 03:50:51 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200605250658.CAA03726@smc.vnet.net> <200605260817.EAA01716@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

Of course @, as in f @ g, is remarkably similar to the traditional 
mathematical symbol (a small circle) for function composition.  So using 
f@g[x] in place of f[g[x]]] ought not to be that "non-standard".

Actually, it's non-standard from the viewpoint of mathematical notation 
in one respect:  Let me use o to stand for the traditional mathematical 
small circle (in TeX: \circ).  Then

    (f o g)(x)

by definition means f(g(x))).

In Mathematica, by contrast,

    (f@g)[x]

does NOT mean the same thing as f[g[x]].  For example:

   f[x_] := x^2
   g[x_] := x + 5
   (f@g)[x] // FullForm
Power[g, 2][x]

Andrzej Kozlowski wrote:
> On 25 May 2006, at 15:58, Kristen W Carlson wrote:
> 
>> Hi,
>>
>> David Wagner emphasizes that he doesn't use the syntax
>> function@argument (p. 37n), no explanation. To me it seems very handy.
>> Any thoughts?
> 
> 
> I also never use it (although until I now have never considered why).  
> I guess the reason must be is that f[x] or f(x) is the standard  
> mathematical notation for the value of a function f at x and I am  
> used to it. I don't have this problem with @@, /@ or even @@@  
> probably because these are programming constructs that do not  
> correspond to any standard mathematical concepts.
> 
> Andrzej Kozlowski
> Tokyo, Japan
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Prefix function syntax f @ x
    • From: "Kristen W Carlson" <carlsonkw@gmail.com>
  • Re: Prefix function syntax f @ x
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>