#  MAPLE.  May 30, 2006.
#
#  Q-bipartite quotient of the Leech lattice scheme.
with(linalg):
verts := 98280;
v := [ 1,  4600 ,   47104  ,  46575];

Q := matrix([
[1 ,  299 ,   17250 ,  80730],
[1 ,   65 ,    285  ,  -351 ],
[1 ,  13/2, -1875/16,1755/16],
[1 ,  -13 ,    90   ,   -78 ]]);


# Tridiagonal matrix L1-star.
L := matrix([
[0 ,   299   ,   0     ,    0    ],
[1 ,  286/7  , 1800/7  ,    0    ],
[0 ,   156/35, 1859/28 , 4563/20 ] ,
[0 ,    0    , 195/4   ,   1001/4]
]);





        [0    4600       0       0]
        [                         ]
        [1     892    2816     891]
L_1  =  [                         ]
        [0     275    2300    2025]
        [                         ]
        [0      88    2048    2464]


       [0       0    47104        0]
       [                           ]
       [0    2816    23552    20736]
L_2 =  [                           ]
       [1    2300    22528    22275]
       [                           ]
       [0    2048    22528    22528]


       [0       0        0    46575]
       [                           ]
       [0     891    20736    24948]
L_3 =  [                           ]
       [0    2025    22275    22275]
       [                           ]
       [1    2464    22528    21582]


     [1    4600    47104    46575]
     [                           ]
     [1    1000     1024    -2025]
P := [                           ]
     [1      76     -320      243]
     [                           ]
     [1     -20       64      -45]


     [1    299     17250    80730]
     [                           ]
     [1     65      285     -351 ]
     [                           ]
Q := [             -1875    1755 ]
     [1    13/2    -----    ---- ]
     [              16       16  ]
     [                           ]
     [1    -13      90       -78 ]


        [0     299       0         0   ]
        [                              ]
        [1    286/7    1800/7      0   ]
        [                              ]
 Ls1 =  [      156      1859      4563 ]
        [0     ---      ----      ---- ]
        [      35        28        20  ]
        [                              ]
        [0      0      195/4     1001/4]


       [0      0       17250        0   ]
       [                                ]
       [               53625            ]
       [0    1800/7    -----     26325/2]
       [                14              ]
       [                                ]
Ls2 =  [      1859     686745    451737 ]
       [1     ----     ------    ------ ]
       [       28       224        32   ]
       [                                ]
       [               96525     453915 ]
       [0    195/4     -----     ------ ]
       [                32         32   ]


      [0      0          0        80730  ]
      [                                  ]
      [0      0       26325/2    135135/2]
      [                                  ]
Ls3=  [      4563     451737     10621611]
      [0     ----     ------     --------]
      [       20        32         160   ]
      [                                  ]
      [               453915     2121405 ]
      [1    1001/4    ------     ------- ]
      [                 32         32    ]