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)

```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.

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

```

• Prev by Date: Re: Variable number of arguments
• Next by Date: How to detect 'bad' characters in expressions in the notebook?
• Previous by thread: Re: How to create a named compound 3D object?
• Next by thread: Re: Can one define own indexing function/mapping to be used for an Array