Hermite Normal Form

Question

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?

Answer 1

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