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MathGroup Archive 2006

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Re: Listable functions with two brackets f[][] (SubValues)

  • To: mathgroup at
  • Subject: [mg64931] Re: Listable functions with two brackets f[][] (SubValues)
  • From: dh <dh at>
  • Date: Wed, 8 Mar 2006 00:59:43 -0500 (EST)
  • References: <dujrti$923$>
  • Sender: owner-wri-mathgroup at

I can not see the benefit of using f[a_][b_] instead of f[a_,b_]. But if 
you insists on using f[][]:
Consider f[a][b]: f[a] returns a function that takes [b] as argument.
Only a symbol can have the attribute "Listable". Therefore, f[a] can not 
have the arttribute "Listable". It followes, that the definition has to 
be done in 2 stages. First we define the "inner" function and make it 

f1[fun_,a_Line]:=Line[fun /@ a[[1]]];
SetAttributes[f1, Listable]

now we define the final function f2[][] using f1:

f2[vec_][a_]:= f1[#+vec &, a]

this will now work as you want:

f2[{1, 3}][c]
f2[{1, 3}][b]


Goyder Dr HGD wrote:
> I would like to use a double bracket function f[][] as, I believe,
> originally promoted  by David Park. The second bracket is called the
> SubValues of f.  My problem is that I would like the second bracket to
> be Listable. Is this possible.?
> The following is a toy example by way of illustration.  Suppose I wish
> to make a function that translates the graphics primitive Line. Then I
> can make a function as follows and it works for one Line[].
> In[1]:=
> ClearAll[f]; 
> f[vec_][a_Line] := Line[(#1 + vec & ) /@ a[[1]]]
> In[3]:=
> b = Line[{{1, 2}, {3, 4}, {5, 6}}]; 
> In[4]:=
> f[{1, 3}][b]
> Out[4]=
> Line[{{2,5},{4,7},{6,9}}]
> However, if I have a list of Lines[]  it does not work because the
> second bracket does not have the Attribute Listable. 
> In[5]:=
> c = {b, Line[{{2, 3}, {5, 6}, {9, 3}}]}; 
> In[6]:=
> f[{1, 3}][c]
> Out[6]=
> f[{1,3}][{Line[{{1,2},{3,4},{5,6}}],Line[{{2,3},{5,6},{9,3}}]}]
> Attempts to make the function f[][] Listable fail because it makes the
> first and not the second bracket Listable.
> In[7]:=
> SetAttributes[f, Listable]
> In[8]:=
> f[{1, 3}][c]
> Out[8]=
> {f[1],f[3]}[{Line[{{1,2},{3,4},{5,6}}],Line[{{2,3},{5,6},{9,3}}]}]
> Is there a solution?
> Thanks 
> Hugh Goyder

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