The Faddeev-LeVerrier algorithm and the Pfaffian

We adapt the Faddeev-LeVerrier algorithm for computation of characteristic polynomials to Pfaffian a skew-symmetric matrix. This yields very simple, easy implement and parallelize computational cost O(n?+1) where n is size matrix O(n?) multiplying n×n-matrices, ??[2,2.37286). compare its performance that other algorithms show how it can be used compute Euler form Riemannian manifold using computer algebra.