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MathGroup Archive 2007

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RE: ListDimension function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72592] RE: [mg72595] ListDimension function
  • From: "David Park" <djmp at earthlink.net>
  • Date: Thu, 11 Jan 2007 03:24:41 -0500 (EST)

Carlos,

Will the following work?

test1 = a + b;
test2 = {1, 2, x*y};
test3 = {1, 2, {3, 0, 1}};
test4 = {{}, {}, {}};
test5 = {{}, {{1, 2}}, a};

ListDimension[expr_] := Max[Length /@ Position[{expr}, {___}]]

ListDimension /@ {test1, test2, test3, test4, test5}
{0, 1, 2, 2, 3}

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 



From: carlos at colorado.edu [mailto:carlos at colorado.edu]

Hi - I need a short function ListDimension that
given a list returns its "brace dimensionality" =
max number of brace levels to reach deepest entry.
Examples

   List         ListDimension
   a+b                   0
   {1,2,x*y}             1
   {1,2,{3,0,1}}         2
   {{},{},{}}            2
   {{},{{1,2}},a}        3

Built-in functions dont seem to be of help.
Dimensions is restricted to matrix or tensor type of lists.
Depth (minus 1) doesnt help as it is entry type dependent:

   Depth[{1,2,3}] -> 2
   Depth[{1,2,3+a}] -> 3
   Depth[{1,2,3+a+Sqrt[x+y]}] -> 5

For the above three, ListDimension=1.



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