> A := << 25, 15, -5; 15, 18, 0; -5, 0, 11 >>;
                              [25    15    -5]
                              [              ]
                         A := [15    18     0]
                              [              ]
                              [-5     0    11]

> B := << 18, 22, 54, 42; 22, 70, 86, 62; 54, 86, 174, 134; 42, 62, 134, 106>>;
                          [18    22     54     42]
                          [                      ]
                          [22    70     86     62]
                     B := [                      ]
                          [54    86    174    134]
                          [                      ]
                          [42    62    134    106]

> use LinearAlgebra in
>       LUDecomposition( A, method = Cholesky );
>       LUDecomposition( B, method = Cholesky );
>       evalf( % );
> end use;
                             [ 5    0    0]
                             [            ]
                             [ 3    3    0]
                             [            ]
                             [-1    1    3]

             [   1/2                                      ]
             [3 2           0            0            0   ]
             [                                            ]
             [    1/2        1/2                          ]
             [11 2       2 97                             ]
             [-------    -------         0            0   ]
             [   3          3                             ]
             [                                            ]
             [                1/2          1/2            ]
             [   1/2     30 97       2 6402               ]
             [9 2        --------    ---------        0   ]
             [              97          97                ]
             [                                            ]
             [                1/2           1/2        1/2]
             [   1/2     16 97       74 6402       8 33   ]
             [7 2        --------    ----------    -------]
             [              97          3201         33   ]

       [4.242640686        0.             0.             0.     ]
       [                                                        ]
       [5.185449728    6.565905202        0.             0.     ]
       [                                                        ]
       [12.72792206    3.046038495    1.649742248        0.     ]
       [                                                        ]
       [9.899494934    1.624553864    1.849711006    1.392621248]