# MAPLE.   May 30, 2006.
# 
# Example 18 in HCD table of spherical designs by Munemasa.
#
# This is the Q-bipartite double cover of  SRG(275,112; 30,56)
# in Example 10.
d := 5;

v := [1 , 112 , 162 , 162 , 112 , 1 ];
verts := 550;


Q := matrix([
[1 ,   22   ,   252   ,  252  ,   22   ,   1],
[1 ,  11/2  ,   9/2   , -9/2  ,  -11/2 ,  -1],
[1 ,  11/3  ,  -14/3  , -14/3 ,  11/3  ,   1],
[1 ,  -11/3 ,  -14/3  , 14/3  ,  11/3  ,  -1],
[1 ,  -11/2 ,   9/2   ,  9/2  ,  -11/2 ,   1],
[1 ,   -22  ,   252   , -252  ,   22   ,  -1]
 ]);



#  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   ,  0],
[1  ,  0    ,  21  ,     0   ,   0   ,  0],
[0  , 11/6  ,   0  ,   121/6 ,   0   ,  0],
[0  ,  0    , 121/6,     0   ,  11/6 ,  0],
[0  ,  0    ,   0  ,    21   ,   0   ,  1],
[0  ,  0    ,   0  ,     0   ,   22  ,  0]
]);


       [0    112     0     0      0    0]
       [                                ]
       [1      0    81     0     30    0]
L_1  = [                                ]
       [0     56     0    56      0    0]
       [                                ]
       [0      0    56     0     56    0]
       [                                ]
       [0     30     0    81      0    1]
       [                                ]
       [0      0     0     0    112    0]


       [0     0    162      0     0    0]
       [                                ]
       [0    81      0     81     0    0]
       [                                ]
       [1     0    105      0    56    0]
L_2  = [                                ]
       [0    56      0    105     0    1]
       [                                ]
       [0     0     81      0    81    0]
       [                                ]
       [0     0      0    162     0    0]


       [0     0      0    162     0    0]
       [                                ]
       [0     0     81      0    81    0]
       [                                ]
       [0    56      0    105     0    1]
L_3 =  [                                ]
       [1     0    105      0    56    0]
       [                                ]
       [0    81      0     81     0    0]
       [                                ]
       [0     0    162      0     0    0]


       [0      0     0     0    112    0]
       [                                ]
       [0     30     0    81      0    1]
       [                                ]
       [0      0    56     0     56    0]
L_4 =  [                                ]
       [0     56     0    56      0    0]
       [                                ]
       [1      0    81     0     30    0]
       [                                ]
       [0    112     0     0      0    0]


       [0    0    0    0    0    1]
       [                          ]
       [0    0    0    0    1    0]
       [                          ]
       [0    0    0    1    0    0]
L_5 =  [                          ]
       [0    0    1    0    0    0]
       [                          ]
       [0    1    0    0    0    0]
       [                          ]
       [1    0    0    0    0    0]


     [1     112    162     162    112     1]
     [                                     ]
     [1      28     27     -27    -28    -1]
     [                                     ]
     [1       2     -3      -3      2     1]
P =  [                                     ]
     [1      -2     -3       3      2    -1]
     [                                     ]
     [1     -28     27      27    -28     1]
     [                                     ]
     [1    -112    162    -162    112    -1]

     [1     22       252      252      22       1]
     [                                           ]
     [1    11/2      9/2     -9/2     -11/2    -1]
     [                                           ]
     [1    11/3     -14/3    -14/3    11/3      1]
Q =  [                                           ]
     [1    -11/3    -14/3    14/3     11/3     -1]
     [                                           ]
     [1    -11/2     9/2      9/2     -11/2     1]
     [                                           ]
     [1     -22      252     -252      22      -1]




      [0     22       0        0       0      0]
      [                                        ]
      [1     0       21        0       0      0]
      [                                        ]
      [0    11/6      0      121/6     0      0]
Ls1 = [                                        ]
      [0     0      121/6      0      11/6    0]
      [                                        ]
      [0     0        0       21       0      1]
      [                                        ]
      [0     0        0        0       22     0]

      [0      0       252        0         0      0]
      [                                            ]
      [0     21        0        231        0      0]
      [                                            ]
      [1      0      1385/6      0       121/6    0]
Ls2 = [                                            ]
      [0    121/6      0       1385/6      0      1]
      [                                            ]
      [0      0       231        0        21      0]
      [                                            ]
      [0      0        0        252        0      0]

      [0      0        0        252        0      0]
      [                                            ]
      [0      0       231        0        21      0]
      [                                            ]
      [0    121/6      0       1385/6      0      1]
Ls3 = [                                            ]
      [1      0      1385/6      0       121/6    0]
      [                                            ]
      [0     21        0        231        0      0]
      [                                            ]
      [0      0       252        0         0      0]

      [0     0        0        0       22     0]
      [                                        ]
      [0     0        0       21       0      1]
      [                                        ]
      [0     0      121/6      0      11/6    0]
Ls4 = [                                        ]
      [0    11/6      0      121/6     0      0]
      [                                        ]
      [1     0       21        0       0      0]
      [                                        ]
      [0     22       0        0       0      0]

      [0    0    0    0    0    1]
      [                          ]
      [0    0    0    0    1    0]
      [                          ]
      [0    0    0    1    0    0]
Ls5 = [                          ]
      [0    0    1    0    0    0]
      [                          ]
      [0    1    0    0    0    0]
      [                          ]
      [1    0    0    0    0    0]