Idea : work with powers of primes
Rank(A) mod 7 = 3 = rank(A)
Rankq(A) = greatest i such that q does not divide si
If all the primes appearing in the Smith form are known
Then compute the ranks modulo their powers
Rank(A) mod 3 = 1
Rank(A) mod 9 = 3
Rank(A) mod 2 = 2
Rank(A) mod 4 = 3
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