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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



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