Local Smith Form at p : via elimination

• Not efficient to compute in Z(p) ? elimination mod pe

For k = 1 to e

| Gauß-Bareiss with pivot invertible mod pe-k+1

| When no more invertible element

| Return actual rank as rank mod pk

| Divide every remaining non-zero coefficient by p

If rank mod pe = integer rank then stop

Else try with bigger e

• Try first with pe close to word size

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