Re: strange behavior with Map

*To*: mathgroup at smc.vnet.net*Subject*: [mg116421] Re: strange behavior with Map*From*: Robert Rosenbaum <robertr at math.uh.edu>*Date*: Mon, 14 Feb 2011 04:28:01 -0500 (EST)

Oh, I see. I didn't realize that Map[f,x,n] applied f to levels 1 through n. I had intended to do: Map[Function[x, 2], {{1, 2}, {1, 2}}, {2}] which indeed gives the same result as Map[Function[x, 0 x + 2], {{1, 2}, {1, 2}}, {2}] Thanks for the help. Best, Robert On Feb 13, 2011, at 2:07 AM, Leonid Shifrin wrote: > Hi Robert, > > It's a bit subtle indeed. The key observation is this: > > In[23]:= Map[f, {{1, 2}, {1, 2}}, 2] > > Out[23]= {f[{f[1], f[2]}], f[{f[1], f[2]}]} > > Since things evaluate from the bottom, the interesting part happens after we > have this: > > {f[{2, 2}], f[{2, 2}]} > > (schematically - in reality, the first f completely evaluates, and only then > the second). Now, > consider: > > In[27]:= Function[x, 0 x + 2][{2, 2}] > > Out[27]= {2, 2} > > In[28]:= Function[x, 2][{2, 2}] > > Out[28]= 2 > > which is, the functions *are* different, because multiplication by a scalar > (zero included) preserves the > dimensionality of the second factor, for the first function, while the > second function simply replaces the > argument by 2, whatever it is. > > Regards, > Leonid > > > On Sat, Feb 12, 2011 at 1:20 PM, Robert Rosenbaum <robertr at math.uh.edu>wrote: > >> This doesn't seem right: >> >> >> In[181]:= Map[Function[x, 2], {{1, 2}, {1, 2}}, 2] >> >> Out[181]= {2, 2} >> >> In[180]:= Map[Function[x, 0 x + 2], {{1, 2}, {1, 2}}, 2] >> >> Out[180]= {{2, 2}, {2, 2}} >> >> >> Best, >> Robert >> >>