Re: ListDimension function

*To*: mathgroup at smc.vnet.net*Subject*: [mg72584] Re: ListDimension function*From*: Peter Pein <petsie at dordos.net>*Date*: Thu, 11 Jan 2007 02:52:31 -0500 (EST)*References*: <eo25ue$as5$1@smc.vnet.net>

carlos at colorado.edu schrieb: > 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. > Hi Carlos, with the help of Position[], it is quite easy: In[1]:= ListDimension = Max @@ (Length /@ Position[#1, List]) /. {} -> {0} & ; ListDimension/@{ a+b, {1,2,x y}, {1,2,{3,0,1}}, {{},{},{}}, {{},{{1,2}},a} } Out[2]= {0,1,2,2,3} In[3]:= ListDimension/@{ {1,2,3}, {1,2,3+a}, {1,2,3+a+Sqrt[x+y]} } Out[3]= {1,1,1} Peter