• To: mathgroup at smc.vnet.net
• Subject: [mg3619] Re: [mg3566] addressing matrix elements
• From: Richard Mercer <richard at seuss.math.wright.edu>
• Date: Thu, 28 Mar 1996 00:11:50 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```>  The Mma language sometimes drives me crazy.  If I don't
>  practice it regularly, I seem to forget everything.
>  Here's what I want to do, but can't.
>

>  Say M is a matrix of integers.  I want to func[M, k] to
>  return a matrix same dimensions as M, each entry
>  consisting of the corresponding entry of M taken modulo
>  k.  For instance, func[{{22,33}, {44,55}}, 10] should
>  return {{2,3}, {4,5}}.  I would like this to work for
>  arbitrary rectangular integer matrices, but am not having
>  much luck.  It seems like this should be easy,  but I'm
>  stumped.
>

>  More generally, I would like to be able to apply a
>  function f to each element in a matrix of arbitrary size
>  and dimensions, without worrying about the particulars
>  of the matrix representation via lists.  I want func[M,
>  g] to return a matrix of the same size and shape as M,
>  with elements formed by applying g to corresponding
>  elements of M.  Is there nice way to do this?  Seems like
>  some combination  of Map, Apply, Thread, SetAttributes
>  Listable, Outer, etc. could do the job, but I am lost in
>  the morass of possibilites.   Any help would be
>  appreciated.
>

>  Thanks,
>

>  -- David Cabana    drc at gate.net
>

Here is one semi-elegant way:
Attributes[ModAll] = {Listable};
ModAll[m_,n_]:= Mod[m,n];

Then use it as follows
list = {34,{56,82},{90,25,{61,77}}};
ModAll[list,7]

{6, {0, 5}, {6, 4, {5, 0}}}

You could alternatively

Unprotect[Mod]
SetAttributes[Mod,Listable]
and then Mod itself would behave in the desired fashion.
I prefer the former method as it does not alter the original Mod.

If you feel that using the Listable attribute is "cheating" (I don't
know why), another alternative is

ModAll[ls_List,n_]:= ModAll[#,n]& /@ ls;
ModAll[m_,n_]:= Mod[m,n];

Richard Mercer

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```

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