Abstract : We analyze the precision of the characteristic polynomial of an n×n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O˜(n^omega)) for χ(A) to have precision exactly O(p^N). We also give a O˜(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).
