Can one define own indexing function/mapping to be used for an Array

*To*: mathgroup at smc.vnet.net*Subject*: [mg113338] Can one define own indexing function/mapping to be used for an Array*From*: "Nasser M. Abbasi" <nma at 12000.org>*Date*: Sun, 24 Oct 2010 06:05:29 -0400 (EDT)*Reply-to*: nma at 12000.org

I am trying to implement something where it is more natural to use an index that starts at 0 instead of the default 1 for vectors and matrices as since this will match the problem I am looking at. If I write u={0,1,2} u[[0]] This will return the Head of u. So have to write u[[1]] to get the first entry. I'd like to write u[[0]] to get the first entry. I thought about using Array: In[8]:= u = Array[U[#1] & , 4, 0] Out[8]= {U[0], U[1], U[2], U[3]} But this does not do much, I still have to write u[[1]] to access U[0] I could write my own function to implement a 'get' and 'set' operations as in: In[4]:= get[u_, i_] := u[[i + 1]] In[5]:= get[u, 0] Out[5]= U[0] So, everywhere in the code, where I would have liked to write u[[i]], I will replace that by get[u,i], and now my i's will match the textbook i's since those are implemented using 0-index arrays. In an OO setting, I could have defined my own "[[ ]]" function on object of type Array, then I can write more u[[i]], where now u's own function "[[ ]]" will be used. Other languages also allow one to define an array with different starting index than the default. Is there a way to do something like this for Array at least. For general Lists, I think that might not be possible? It will break everything I would imagine. I am looking at this report: http://library.wolfram.com/conferences/devconf99/lichtblau/ "Data Structures and Efficient Algorithms in Mathematica", But thought to also ask here, to see if there might be a simple trick to do this for Array, by unprotecting it, and changing something? and then protecting the definition again, before I try to implement a data struct with the help of the above article to do what I want. thanks --Nasser