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Re: pure function puzzle
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Re: pure function puzzle
*From*: John Lee <lee at math.washington.edu>
*Date*: Tue, 13 Jul 93 15:01:32 -0700
Martin McClain <wmm at chem.wayne.edu> writes:
> I need a pure function that operates on
> {x,{a,b,c}},
> where x, a, b, and c are all simple lists. The output must be
> {Ints[x,a],Ints[x,b],Ints[x,c]},
> where Ints means Intersection. You would think this could be based on
> Thread, but when a,b,c,and x are all lists, Thread seems to get confused.
> Map also has a problem: it needs a function as its argument, and apparently
> nested pure functions are not allowed. I can do the required
> transformation with a compound statement
> f1 = Intersection[x,#]&;
> f2 = Map[f1,#]&
> and then apply f2 to my input, but x is not known ahead of time. I want
> this function as one step in a long Composition, and I really need a clean,
> single function of a single argument, producing a single object. Maybe some
> clever use of Hold, or Evaluate, or something like that ??? Any ideas?
Here's one fairly simple solution:
In[38]:= f = Apply[ Intersection,
Transpose[{Table[#[[1]], {Length[#[[2]]]}], #[[2]]}],
1 ] &;
In[39]:= list = {{1, 3, 5, 7}, {{1, 2, 3}, {3, 4, 5, 6}, {5, 6, 7, 8}}};
In[40]:= f[list]
Out[40]= {{1, 3}, {3, 5}, {5, 7}}
On the other hand, if you're willing to forego the requirement that f be a
pure function, here's a much more straightforward definition:
In[46]:= f2[ {x_, y_} ]:= (Intersection[ x, # ]&) /@ y;
In[47]:= f2[list]
Out[47]= {{1, 3}, {3, 5}, {5, 7}}
Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA
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