       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

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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