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