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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
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