Editing Smith normal form (section)

===Step I: Choosing a pivot===
Choose <math>j_t</math> to be the smallest column index of <math>A</math> with a non-zero entry, starting the search at column index <math>j_{t-1}+1</math> if <math>t> 1</math>.

We wish to have <math>a_{t,j_t}\neq0</math>; if this is the case this step is complete, otherwise there is by assumption some <math>k</math> with <math>a_{k,j_t} \neq 0</math>, and we can exchange rows <math>t</math> and <math>k</math>, thereby obtaining <math>a_{t,j_t}\neq0</math>.

Our chosen pivot is now at position <math>(t, j_t)</math>.