On Sat, Nov 20, 2010 at 7:43 PM, zsharon <[email protected]> wrote:
> Hello all,
>
> I want to compute the "diagonalizations" of some square and non-square
> matrices over the integers.  Given M \in GL_{m,n}(Z), I want square,
> invertible matrices H,K (nxn and mxm respectively) such that M=HDK,
> where D has the same dimensions as M and is zero everywhere except for
> on the diagonal.

Isn't this Smith form?

sage: A = random_matrix(ZZ,3)
sage: A.smith_form()
(
[  1   0   0]  [   0    0    1]  [  -2   -3   -3]
[  0   1   0]  [   0    1    0]  [  -1   -2   -2]
[  0   0 316], [   1 -315 -158], [-161 -319 -320]
)
sage: A.smith_form?


William

>
> I've googled and look through the sage documentation, but I've found
> nothing.
>
> Thanks for any help!
>
> zsharon
>
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-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

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