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

翻译：我们用Faddeev-LeVerrier 算法来计算典型的多数值,以适应对称矩阵的Pfaffian计算法。这产生一个非常简单、容易实施和平行计算成本的计算算法 $O(n ⁇ beta+1}) 美元, 美元是矩阵的大小, 美元(n ⁇ beta}) 美元是乘以 $n\times n$- maters, $\beta\ in[2,2.37286] 的费用。我们将其性能与其他算法的性能进行比较, 并展示如何使用计算机代数来计算里曼多元的Euler形式。