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MathGroup Archive 2006

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64926] Re: [mg64909] Listable functions with two brackets f[][] (SubValues)
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 8 Mar 2006 00:59:37 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

ClearAll[f];
f[vec_][a_Line]:=Line[(#+vec&)/@a[[1]]];
f[vec_][a:{_Line..}]:=f[vec][#]&/@a;

b=Line[{{1,2},{3,4},{5,6}}];

f[{1,3}][b]

Line[{{2, 5}, {4, 7}, {6, 9}}]

c={b,Line[{{2,3},{5,6},{9,3}}]};

f[{1,3}][c]

{Line[{{2, 5}, {4, 7}, {6, 9}}], Line[{{3, 6}, {6, 9}, {10, 6}}]}


Bob Hanlon

> 
> From: "Goyder Dr HGD" <h.g.d.goyder at cranfield.ac.uk>
To: mathgroup at smc.vnet.net
> Date: 2006/03/07 Tue AM 06:12:03 EST
> Subject: [mg64926] [mg64909] Listable functions with two brackets f[][]  (SubValues)
> 
> 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
> 
> -- 
> This message has been scanned for viruses and
> dangerous content by the Cranfield MailScanner, and is
> believed to be clean.
> 
> 


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