def test_LDLdecomposition():
A = Matrix(((25,15,-5), (15,18,0), (-5,0,11)))
L, D = A.LDLdecomposition()
assert L * D * L.T == A
assert L.is_lower()
assert L == Matrix([[1, 0, 0], [ S(3)/5, 1, 0], [S(-1)/5, S(1)/3, 1]])
assert D.is_diagonal()
assert D == Matrix([[25, 0, 0], [0, 9, 0], [0, 0, 9]])
