Re: ListDimension function

• To: mathgroup at smc.vnet.net
• Subject: [mg72580] Re: ListDimension function
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Thu, 11 Jan 2007 02:36:26 -0500 (EST)
• References: <eo25ue\$as5\$1@smc.vnet.net>

```car... at colorado.edu wrote:
> 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.

I'm not at a machine where I can try this, but how about something
like:

ListDim[x_?AtomQ] := 0;
ListDim[x_] := Boole[Head@x == List] + Max[ListDim /@ x]

I don't know what you want to do with lists that appear inside other
expressions, such as

{Outer[f, list1, list2], Outer[g, list3, list4]}

which I think ListDim would treat as equivalent to

{f, list1, list2, g, list3, list4}.

```

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