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

*To*: mathgroup at smc.vnet.net*Subject*: [mg113365] Re: Can one define own indexing function/mapping to be used for an Array*From*: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>*Date*: Mon, 25 Oct 2010 06:41:53 -0400 (EDT)*References*: <ia10d7$opu$1@smc.vnet.net>

You could define your own index brackets using the Notation package Cheers -- Sjoerd On Oct 24, 12:05 pm, "Nasser M. Abbasi" <n... at 12000.org> wrote: > 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