= Smith normal form
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For every matrix $A$ over a <principal ideal domain>, there are invertible matrices $U,V$ such that
$$
UAV=\operatorname{diag}(d_1,\ldots,d_r,0,\ldots,0),
\qquad d_1\mid d_2\mid\cdots\mid d_r.
$$
The nonzero diagonal entries are unique up to multiplication by units. Over the <integer>[integers], $U$ and $V$ are unimodular and the $d_i$ may be chosen positive; their products $d_1\cdots d_k$ are the greatest common divisors of the $k$-rowed minors.
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