%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/JGD_CAG/CAG_mat72
% name: JGD_CAG/CAG_mat72
% [CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada]
% id: 1943
% date: 2008
% author: M. Monagan
% ed: J.-G. Dumas
% fields: name title A id date author ed kind notes
% kind: combinatorial problem
%-------------------------------------------------------------------------------
% notes:
% CAG matrix set from Michael Monagan, Simon Fraser Univ., Canada        
% From Jean-Guillaume Dumas' Sparse Integer Matrix Collection,           
% http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html              
%                                                                        
% Strongly Connected Graph Components and Computing                      
% Characteristic Polynomials of Integer Matrices in Maple,               
% Simon Lo, Michael Monagan, Allan Wittkopf                              
% {sclo,mmonagan,wittkopf} at cecm.sfu.ca                                
% Centre for Experimental and Constructive Mathematics,                  
% Department of Mathematics, Simon Fraser University,                    
% Burnaby, B.C., V5A 1S6, Canada.                                        
%                                                                        
% abstract:                                                              
% Let A be an n x 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.                                                 
%                                                                        
% http://www.cecm.sfu.ca/~monaganm/papers/CP8.pdf                        
%                                                                        
% Filename in JGD collection: CAG/mat72.sms                              
%-------------------------------------------------------------------------------
