# 
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2004
#
# file:  lu
#
# LDU factorization
#
with(LinearAlgebra):
A := Matrix([[5,35,-20,65],[35,244,-143,461],
             [-20,-143,73,-232],[65,461,-232,856]]);
LUDecomposition(A);
(P,L,U) := LUDecomposition(A);
P.L.U;
(P,L,U) := LUDecomposition(A,method=Cholesky);

# another example

with(LinearAlgebra):
A := Matrix([[6,-2,2,4],[12,-8,6,10],
             [3,-13,9,3],[-6,4,1,-18]]);
LUDecomposition(A);
(P,L,U) := LUDecomposition(A);
P.L.U;