Re: Matrices Over Z/NZ
- To: mathgroup at smc.vnet.net
- Subject: [mg39049] Re: [mg39043] Matrices Over Z/NZ
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 26 Jan 2003 05:22:41 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On Saturday, January 25, 2003, at 03:32 PM, flip wrote:
> Hello,
>
> If I want to create a matrix A mod 2, which is a matrix of 0's and
> 1's, how
> do I do that?
For example:
In[27]:=
Array[Random[Integer]&,{3,3}]
Out[27]=
{{0,1,0},{1,0,0},{1,0,1}}
>
> So, if I want all 2x2 matrices, A mod 2, there would be 2^4 = 16 such
> matrices consisting only of 0's and 1's.
>
> These will be:
>
> {{{0, 0}, {0, 0}}, {{1, 0}, {0, 0}}, ..., {{1, 1}, {1, 1}}}
>
> I looked at permutations, discrete and combinatoria, but didn't see
> anything
> obvoius (but I just missed it probably).
In[28]:=
Partition[#,2]&/@Distribute[Table[{0,1},{4}],List]
Out[28]=
{{{0,0},{0,0}},{{0,0},{0,1}},{{0,0},{1,0}},{{0,0},{1,1}},{{0,1},{
0,0}},{{0,1},{0,1}},{{0,1},{1,0}},{{0,1},{1,1}},{{1,0},{
0,0}},{{1,0},{0,1}},{{1,0},{1,0}},{{1,0},{1,1}},{{1,1},{
0,0}},{{1,1},{0,1}},{{1,1},{1,0}},{{1,1},{1,1}}}
>
> Laslty, I'd like to be to do any size matrix (that is, 2x2, 3x3, where
> it is
> user selectable) and any mod n.
"Any size" is obviously a pipe dream because of memory limitations.
However, here is the same thing with 3 by 3 matrices mod 3.
Partition[#, 3] & /@ Distribute[Table[Range[0, 2], {3^2}], List]
This has 19683 elements, each a 3 x 3 matrix, in all a list of 177147
elements. With normal amounts of RAM can compute a one or two larger
cases, but displaying probably be a problem.
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/