# MAPLE.   May 28, 2006.
# 
# Example 2 in HCD table of spherical designs by Munemasa.
d := 4;

v := [1,  891,  2816,  891,  1];
verts := 4600;


Q := matrix([
[1 ,   23   ,   275  ,  2277  ,   2024 ],
[1 ,  23/3  ,  175/9 ,  -23/3 ,  -184/9],
[1 ,    0   ,  -25/2 ,    0   ,   23/2 ],
[1 ,  -23/3 ,  175/9 ,  23/3  ,  -184/9],
[1 ,   -23  ,   275  ,  -2277 ,   2024 ]
 ]);


#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
L := matrix([
[0 ,  23  ,  0  ,    0  ,    0  ],
[1 ,  0   ,  22 ,    0  ,    0  ],
[0 , 46/25,  0  ,529/25 ,    0  ],
[0 ,  0   , 23/9,    0  ,  184/9],
[0 ,  0   ,  0  ,   23  ,    0  ]
]);


       [0    891      0      0    0]
       [                           ]
       [1    336    512     42    0]
       [                           ]
L_1 =  [0    162    567    162    0]
       [                           ]
       [0     42    512    336    1]
       [                           ]
       [0      0      0    891    0]

      [0      0    2816      0    0]
      [                            ]
      [0    512    1792    512    0]
      [                            ]
L_2 = [1    567    1680    567    1]
      [                            ]
      [0    512    1792    512    0]
      [                            ]
      [0      0    2816      0    0]

       [0      0      0    891    0]
       [                           ]
       [0     42    512    336    1]
       [                           ]
L_3  = [0    162    567    162    0]
       [                           ]
       [1    336    512     42    0]
       [                           ]
       [0    891      0      0    0]


       [0    0    0    0    1]
       [                     ]
       [0    0    0    1    0]
       [                     ]
       [0    0    1    0    0]
L_4 =  [                     ]
       [0    1    0    0    0]
       [                     ]
       [1    0    0    0    0]


      [1    891    2816     891     1]
      [                              ]
      [1    297       0    -297    -1]
      [                              ]
P  =  [1     63    -128      63     1]
      [                              ]
      [1     -3       0       3    -1]
      [                              ]
      [1     -9      16      -9     1]

      [1     23       275     2277      2024 ]
      [                                      ]
      [1    23/3     175/9    -23/3    -184/9]
      [                                      ]
Q =   [1      0      -25/2      0       23/2 ]
      [                                      ]
      [1    -23/3    175/9    23/3     -184/9]
      [                                      ]
      [1     -23      275     -2277     2024 ]




       [0    23     0       0       0  ]
       [                               ]
       [1    0      22      0       0  ]
       [                               ]
Ls1 =  [     46            529         ]
       [0    --     0      ---      0  ]
       [     25            25          ]
       [                               ]
       [0    0     23/9     0     184/9]
       [                               ]
       [0    0      0      23       0  ]


      [0     0       275       0         0   ]
      [                                      ]
      [0     22       0       253        0   ]
      [                                      ]
Ls2 = [1     0      350/9      0       2116/9]
      [                                      ]
      [0    23/9      0      2452/9      0   ]
      [                                      ]
      [              575                4375 ]
      [0     0       ---       0        ---- ]
      [              18                  18  ]
   
   
      [0     0       0       2277        0   ]
      [                                      ]
      [0     0      253        0       2024  ]
      [                                      ]
      [     529              56396           ]
Ls3 = [0    ---      0       -----       0   ]
      [     25                25             ]
      [                                      ]
      [1     0     2452/9      0      18032/9]
      [                                      ]
      [0    23       0       2254        0   ]
   
   
     [0      0        0          0        2024  ]
     [                                          ]
     [0      0        0        2024         0   ]
     [                                          ]
Ls4 =[0      0      2116/9       0       16100/9]
     [                                          ]
     [0    184/9      0       18032/9       0   ]
     [                                          ]
     [               4375                 32039 ]
     [1      0       ----        0        ----- ]
     [                18                   18   ]