# MAPLE.   May 29, 2006.
# 
# Example 9 in HCD table of spherical designs by Munemasa.
d := 4;

v := [1 , 750,  3500,  2625, 252 ];
verts := 7128;


Q := matrix([
[1 ,  22  ,     252 ,  1750,    5103 ],
[1 , 44/5 ,  756/25 ,    28, -1701/25],
[1 , 11/5 , -234/25 ,   -23 ,  729/25],
[1 , -22/5,   -36/25,    34,  -729/25],
[1 ,  -11 ,      54 ,  -125,     81  ]
 ]);



#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
L := matrix(d+1,d+1,[
[0 ,   22 ,    0  ,    0  ,    0  ],
[1 ,   0  ,   21  ,    0  ,    0  ],
[0 ,  11/6,    0  ,  121/6,    0  ],
[0 ,   0 ,363/125 ,   8/5 ,2187/125],
[0 ,   0 ,     0  ,    6  ,    16 ]
]);


     [0    750      0      0      0]
     [                             ]
     [1    224    448     77      0]
     [                             ]
L_1 =[0     96    417    228      9]
     [                             ]
     [0     22    304    376     48]
     [                             ]
     [0      0    125    500    125]


     [0      0    3500       0      0]
     [                               ]
     [0    448    1946    1064     42]
     [                               ]
L_2 =[1    417    1729    1236    117]
     [                               ]
     [0    304    1648    1392    156]
     [                               ]
     [0    125    1625    1625    125]


     [0      0       0    2625      0]
     [                               ]
     [0     77    1064    1316    168]
     [                               ]
L_3 =[0    228    1236    1044    117]
     [                               ]
     [1    376    1392     808     48]
     [                               ]
     [0    500    1625     500      0]


      [0      0      0      0    252]
      [                             ]
      [0      0     42    168     42]
      [                             ]
L_4 = [0      9    117    117      9]
      [                             ]
      [0     48    156     48      0]
      [                             ]
      [1    125    125      0      1]



      [1    750    3500    2625     252]
      [                                ]
      [1    300     350    -525    -126]
      [                                ]
P  =  [1     90    -130     -15      54]
      [                                ]
      [1     12     -46      51     -18]
      [                                ]
      [1    -10      20     -15       4]

      [1     22      252     1750    5103 ]
      [                                   ]
      [              756             -1701]
      [1    44/5     ---       28    -----]
      [              25               25  ]
      [                                   ]
      [              -234             729 ]
Q  =  [1    11/5     ----     -23     --- ]
      [               25              25  ]
      [                                   ]
      [              -36             -729 ]
      [1    -22/5    ---       34    ---- ]
      [              25               25  ]
      [                                   ]
      [1     -11      54     -125     81  ]




      [0     22      0       0       0  ]
      [                                 ]
      [1     0      21       0       0  ]
      [                                 ]
Ls1 = [0    11/6     0     121/6     0  ]
      [                                 ]
      [             363             2187]
      [0     0      ---     8/5     ----]
      [             125             125 ]
      [                                 ]
      [0     0       0       6       16 ]


    [0     0     252       0        0   ]
    [                                   ]
    [0    21      0       231       0   ]
    [                                   ]
    [            5118             24057 ]
Ls2=[1     0     ----    88/5     ----- ]
    [            125               125  ]
    [                                   ]
    [     363    1584             104976]
    [0    ---    ----    393/5    ------]
    [     125    625               625  ]
    [                                   ]
    [            1188             23112 ]
    [0     0     ----    288/5    ----- ]
    [            125               125  ]


    [0      0        0       1750       0   ]
    [                                       ]
    [                        1400     15309 ]
    [0      0       231      ----     ----- ]
    [                         11       11   ]
    [                                       ]
Ls3=[0    121/6    88/5     3275/6    5832/5]
    [                                       ]
    [                        4360     69984 ]
    [1     8/5     393/5     ----     ----- ]
    [                         11       55   ]
    [                                       ]
    [                        4800     68752 ]
    [0      6      288/5     ----     ----- ]
    [                         11       55   ]
 
 
    [0     0        0         0         5103  ]
    [                                         ]
    [                       15309      40824  ]
    [0     0        0       -----      -----  ]
    [                        11         11    ]
    [                                         ]
    [             24057                468018 ]
Ls4=[0     0      -----     5832/5     ------ ]
    [              125                  125   ]
    [                                         ]
    [     2187    104976    69984     25060104]
    [0    ----    ------    -----     --------]
    [     125      625       55         6875  ]
    [                                         ]
    [             23112     68752     5020218 ]
    [1     16     -----     -----     ------- ]
    [              125       55        1375   ]