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Does anyone know an approach to finding the Hermite Normal Form for smaller matrices, like

$ A =\begin{pmatrix} 6 & -6 & 9\\ 3 &2 & 2 \end{pmatrix} $

Or does one just have to shuffle around more or less randomly?

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There is a similar algorithm to the usual reduced row echolon form for the Hermite Normal form, see e.g. here on wikipedia: https://en.wikipedia.org/wiki/Hermite_normal_form

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    I don't see it? – 2017-02-11
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    I recommend the search funciton to search for "Algorithm" on that site. You'll find e.g. [this](http://www.math.tamu.edu/~rojas/kannanbachemhermitesmith79.pdf) or [this](https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm) one. – 2017-02-11
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    Ah yes, I was hoping for something a little less complex. – 2017-02-11
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    @1233023 If you are not interested in the algorithm itself, Mathematica has a function (called HermiteNormalForm) that you could use. – 2017-02-12