Re: & without #
- To: mathgroup at smc.vnet.net
- Subject: [mg73090] Re: & without #
- From: dh <dh at metrohm.ch>
- Date: Thu, 1 Feb 2007 04:32:05 -0500 (EST)
- References: <epp68i$cv0$1@smc.vnet.net>
$Version 5.1 for Microsoft Windows (October 25, 2004)
Hi Kristen,
the usage of & and #: f[#]& is an abbreviation for: Function[x,f[x]]
with the default argument #. Therefore, Random[Integer,10]& is a
function that returns, when called, a random integer between 1 and 10.
Array[Random[Integer,10]&,20] will call Random[Integer,10]&[x] with x
set succesively to 1,2,..10. Note that in this case the argument is
never used.
On the otherhand, Array[Random[Integer,10],20] will call
Random[Integer,10][x]. This is a strange construct, the Head is:
Random[Integer,10], evaluating to a random integer. The argument is
still an integer from 1..10. We have e.g. 5[3]. This can not be
evaluated any further.
Daniel
Kristen W Carlson wrote:
> Hi,
>
> From Built-in Functions/Cases, here is this (undocumented?) usage of &
> without #:
>
> L=Array[Random[Integer,10]&,20]
>
> {4,5,9,6,8,5,4,0,9,4,5,2,10,6,3,7,4,2,2,8}
>
> Here is what happens without the &:
>
> L=Array[Random[Integer,10],20]
>
> {3[1],3[2],3[3],3[4],3[5],3[6],3[7],3[8],3[9],3[10],3[11],3[12],3[13],3[
> 14],3[15],3[16],3[17],3[18],3[19],3[20]}
>
> Can someone who understands this please explain as completely as you
> can, including how & and # work
> together, given the behavior of & alone. And is this documented anywhere?
>
> This might help and I also post it to help illuminate for those who
> haven't seen this & usage; it is from Andrzej a while ago (Andrzej I
> hope you don't mind):
>
> In general it means a constant function. For example 3& will return 3
> with any argument. But the are at least two "special" functions,
> which will work like "variable constants" when used in this way. One
> of them is Random[]& (and various variants of it). Another is Unique
> [symbol]&, which on every evaluation will produce a unique name based
> on "symbol".
>
> Kris
>
>
$Version