Re: Confusing results with N[expr]?

*To*: mathgroup at smc.vnet.net*Subject*: [mg62412] Re: Confusing results with N[expr]?*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Wed, 23 Nov 2005 01:13:03 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

On 11/22/05 at 4:41 AM, Steven.Hancock at cern.ch (Steven HANCOCK) wrote: >There may be a clue in the following, equally distressing >nonsense... >In[1]:= $Version >Out[1]= 5.1 for Microsoft Windows (October 25, 2004) >(* Map[f, expr] or f /@ expr applies f to each element on the first >level in expr. *) >In[2]:= Map[f, a^b] >Out[2]= > f[b] >f[a] >In[3]:= f /@ a^b >Out[3]= > b >a >(* MapAll[f, expr] or f //@ expr applies f to every subexpression >in expr. *) >In[4]:= MapAll[f, a^b] >Out[4]= > f[b] >f[f[a] ] >In[5]:= f //@ a^b >Out[5]= > b >f[a] The issues above with Map and MapAll is simply an operator precedence issue. The expression f/@a^b can be taken as either f/@(a^b) or (f/@a)^b. Likewise, the expression f//@a^b can be taken as (f//@a)^b or f//@(a^b). In both cases, Mathematica applies the operators in the order in which they appear. But the precendence with either Map[f, a^b] or MapAll[f, a^b] is different. This grouping makes it clear Power is to be done first. The following shows more clearly this is what is occurring In[1]:=Hold[f/@a^b]//FullForm Out[1]//FullForm= Hold[Power[Map[f,a],b]] In[2]:=Hold[Map[f,a^b]]//FullForm Out[2]//FullForm= Hold[Map[f,Power[a,b]]] In[3]:=Hold[f//@a^b]//FullForm Out[3]//FullForm= Hold[Power[MapAll[f,a],b]] In[4]:=Hold[MapAll[f,a^b]]//FullForm Out[4]//FullForm= Hold[MapAll[f,Power[a,b]]] -- To reply via email subtract one hundred and four