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We review the Preparata-Sarwate algorithm, a simple $O(n^{3.5})$ method forcomputing the characteristic polynomial, determinant and adjugate of an $n\times n$ matrix using only ring operations together with exact divisions bysmall integers. The algorithm is a baby-step giant-step version of the morewell-known Faddeev-Leverrier algorithm. We make a few comments about thealgorithm and evaluate its performance empirically.

On a fast and nearly division-free algorithm for the characteristic polynomial