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}.