Strongly Connected Graph Components and Computing Characteristic Polynomials of Integer Matrices in Maple

Let A be an n× n matrix of integers. We present details of our Maple implementation of a simple modular method for computing the characteristic polynomial of A. We consider several different representations for the computation modulo primes, in particular, the use of double precision floats. The algorithm used in Maple releases 7–10 is the Berkowitz algorithm. We present some timings comparing the two algorithms on a sequence of matrices arising from an application in combinatorics of Jocelyn Quaintance. These matrices have a hidden block structure. Once identified, we can further reduce the computing time dramatically. This work has been incorporated into Maple 11’s LinearAlgebra package.