The probabilistic early termination does not take much time here, the charpoly stabilizes at about 85% of the primes required to reach the Hadamard bound. Testing with a few random matrices, I often get stabilization at about 80% (+/-10%), in this situation I think it's best to wait a little more and return a deterministic answer. The sitation is different for determinants in the generic situation where the last invariant factor is big. For the matrix of this thread, the lif is however small, and certifying the determinant does not cost much, like for the charpoly (I get the det in 1.7s and the charpoly in 3.1s with giac 1.2.2-89 vs 0.9s and 6.8s for sage 6.9). This matrix is also special because it has a double eigenvalue 155789435562191565856, the minimal polynomial has degree 171-1.
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