Re: ListDimension function
- To: mathgroup at smc.vnet.net
- Subject: [mg72587] Re: [mg72595] ListDimension function
- From: Adriano Pascoletti <pascolet at dimi.uniud.it>
- Date: Thu, 11 Jan 2007 03:04:34 -0500 (EST)
- References: <200701100907.EAA13288@smc.vnet.net>
On 10 gen 2007, at 10:07, carlos 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.
Carlos,
this works on your examples.
Adriano Pascoletti
In[1]:= h[{}] = 1;
h[l_List] := 1 + Max[h /@ l];
h[l_] /; Head[l] =!= List := 0;
In[4]:= h[a + b]
Out[4]= 0
In[5]:= h[{1, 2, x*y}]
Out[5]= 1
In[6]:= h[{1, 2, {3, 0, 1}}]
Out[6]= 2
In[7]:= h[{{}, {}, {}}]
Out[7]= 2
In[8]:= h[{{}, {{1, 2}}, a}]
Out[8]= 3
- References:
- ListDimension function
- From: carlos@colorado.edu
- ListDimension function