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

• To: mathgroup at smc.vnet.net
• Subject: [mg64909] Listable functions with two brackets f[][] (SubValues)
• From: "Goyder Dr HGD" <h.g.d.goyder at cranfield.ac.uk>
• Date: Tue, 7 Mar 2006 06:12:03 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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

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

In:=
f[{1, 3}][b]

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

In:=
f[{1, 3}][c]

Out=
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:=
SetAttributes[f, Listable]

In:=
f[{1, 3}][c]

Out=
{f,f}[{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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