#  July 9, 2008.
#
#  Q-bipartite double of first subconstituent of McLaughlin graph
#
#
#  SRG has 
#     [  1   81  30  ]        [ 1   21      90 ]
# P = [  1    9  -10 ]   Q =  [ 1   7/3  -10/3 ]
#     [  1   -3   2  ]        [ 1   -7       6 ]
d := 5;

v := [1, 30, 81, 81, 30, 1]:
verts := 224;

Q := matrix(6,6,[
1,  21,   90,   90,  21,  1,
1,   7,    6,   -6,  -7, -1,
1, 7/3,-10/3,-10/3, 7/3,  1,
1,-7/3,-10/3, 10/3, 7/3, -1,
1,  -7,    6,    6,  -7,  1,
1, -21,   90,  -90,  21, -1]);

#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
#  if we are only given the cosines (normalized column 1 of Q).

L := matrix([
[0 ,   21  ,   0    ,  0    ,   0    ,  0  ],
[1 ,    0  ,  20    ,  0    ,   0    ,  0  ],
[0 , 14/3  ,   0    , 49/3  ,   0    ,  0  ],
[0 ,    0  , 49/3   ,  0    , 14/3   ,  0  ],
[0 ,    0  ,   0    , 20    ,   0    ,  1  ],
[0 ,    0  ,   0    ,  0    ,  21    ,  0  ]
]);


 
         [0    30     0     0     0    0]
         [                              ]
         [1     0    27     0     2    0]
         [                              ]
         [0    10     0    20     0    0]
  L_1 =  [                              ]
         [0     0    20     0    10    0]
         [                              ]
         [0     2     0    27     0    1]
         [                              ]
         [0     0     0     0    30    0]
 
         [0     0    81     0     0    0]
         [                              ]
         [0    27     0    54     0    0]
         [                              ]
         [1     0    60     0    20    0]
   L_2 = [                              ]
         [0    20     0    60     0    1]
         [                              ]
         [0     0    54     0    27    0]
         [                              ]
         [0     0     0    81     0    0]
 
         [0     0     0    81     0    0]
         [                              ]
         [0     0    54     0    27    0]
         [                              ]
         [0    20     0    60     0    1]
   L_3 = [                              ]
         [1     0    60     0    20    0]
         [                              ]
         [0    27     0    54     0    0]
         [                              ]
         [0     0    81     0     0    0]
 
         [0     0     0     0    30    0]
         [                              ]
         [0     2     0    27     0    1]
         [                              ]
         [0     0    20     0    10    0]
   L_4 = [                              ]
         [0    10     0    20     0    0]
         [                              ]
         [1     0    27     0     2    0]
         [                              ]
         [0    30     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     30    81     81     30     1]
      [                                  ]
      [1     10     9     -9    -10    -1]
      [                                  ]
      [1      2    -3     -3      2     1]
 P := [                                  ]
      [1     -2    -3      3      2    -1]
      [                                  ]
      [1    -10     9      9    -10     1]
      [                                  ]
      [1    -30    81    -81     30    -1]

      [1     21      90       90      21      1]
      [                                        ]
      [1     7        6       -6      -7     -1]
      [                                        ]
      [1    7/3     -10/3    -10/3    7/3     1]
 Q := [                                        ]
      [1    -7/3    -10/3    10/3     7/3    -1]
      [                                        ]
      [1     -7       6        6      -7      1]
      [                                        ]
      [1    -21      90       -90     21     -1]
 
 
        [0     21      0       0       0      0]
        [                                      ]
        [1     0       20      0       0      0]
        [                                      ]
        [0    14/3     0      49/3     0      0]
 Ls1 =  [                                      ]
        [0     0      49/3     0      14/3    0]
        [                                      ]
        [0     0       0       20      0      1]
        [                                      ]
        [0     0       0       0       21     0]
 
       [0     0       90        0       0      0]
       [                                        ]
       [0     20       0       70       0      0]
       [                                        ]
       [1     0      218/3      0      49/3    0]
 Ls2 = [                                        ]
       [0    49/3      0      218/3     0      1]
       [                                        ]
       [0     0       70        0       20     0]
       [                                        ]
       [0     0        0       90       0      0]
 
       [0     0        0       90       0      0]
       [                                        ]
       [0     0       70        0       20     0]
       [                                        ]
       [0    49/3      0      218/3     0      1]
 Ls3 = [                                        ]
       [1     0      218/3      0      49/3    0]
       [                                        ]
       [0     20       0       70       0      0]
       [                                        ]
       [0     0       90        0       0      0]
 
        [0     0       0       0       21     0]
        [                                      ]
        [0     0       0       20      0      1]
        [                                      ]
        [0     0      49/3     0      14/3    0]
 Ls4 =  [                                      ]
        [0    14/3     0      49/3     0      0]
        [                                      ]
        [1     0       20      0       0      0]
        [                                      ]
        [0     21      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]