#  July 9, 2008.
#
#  Q-bipartite double of 2nd subconstituent of McLaughlin graph
#
#
#  SRG has 
#     [  1   105  56  ]        [ 1   21     140 ]
# P = [  1    15  -16 ]   Q =  [ 1    3      -4 ]
#     [  1   -3   2   ]        [ 1   -6       5 ]
d := 5;

v := [1, 56, 105, 105, 56, 1]:
verts := 324;

Q := matrix(6,6,[
[1  ,  21  , 140  ,  140  , 21  ,  1],
[1  ,   6  ,   5  ,   -5  , -6  , -1],
[1  ,   3  ,  -4  ,   -4  ,  3  ,  1],
[1  ,  -3  ,  -4  ,  , 4  ,  3  , -1],
[1  ,  -6  ,   5  ,  , 5  , -6  ,  1],
[1  , -21  , 140  , -140  , 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 ,  3  ,   0  , 18  ,   0  ,  0  ],
[0 ,  0  ,  18  ,  0  ,   3  ,  0  ],
[0 ,  0  ,   0  , 20  ,   0  ,  1  ],
[0 ,  0  ,   0  ,  0  ,  21  ,  0  ]
]);



      [0    56     0     0     0    0]
      [                              ]
      [1     0    45     0    10    0]
      [                              ]
      [0    24     0    32     0    0]
L_1 = [                              ]
      [0     0    32     0    24    0]
      [                              ]
      [0    10     0    45     0    1]
      [                              ]
      [0     0     0     0    56    0]

      [0     0    105      0     0    0]
      [                                ]
      [0    45      0     60     0    0]
      [                                ]
      [1     0     72      0    32    0]
L_2 = [                                ]
      [0    32      0     72     0    1]
      [                                ]
      [0     0     60      0    45    0]
      [                                ]
      [0     0      0    105     0    0]

      [0     0      0    105     0    0]
      [                                ]
      [0     0     60      0    45    0]
      [                                ]
      [0    32      0     72     0    1]
L_3 = [                                ]
      [1     0     72      0    32    0]
      [                                ]
      [0    45      0     60     0    0]
      [                                ]
      [0     0    105      0     0    0]

      [0     0     0     0    56    0]
      [                              ]
      [0    10     0    45     0    1]
      [                              ]
      [0     0    32     0    24    0]
L_4 = [                              ]
      [0    24     0    32     0    0]
      [                              ]
      [1     0    45     0    10    0]
      [                              ]
      [0    56     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     56    105     105     56     1]
      [                                    ]
      [1     16     15     -15    -16    -1]
      [                                    ]
      [1      2     -3      -3      2     1]
 P := [                                    ]
      [1     -2     -3       3      2    -1]
      [                                    ]
      [1    -16     15      15    -16     1]
      [                                    ]
      [1    -56    105    -105     56    -1]


       [1     21    140     140    21     1]
       [                                   ]
       [1      6      5      -5    -6    -1]
       [                                   ]
       [1      3     -4      -4     3     1]
  Q := [                                   ]
       [1     -3     -4       4     3    -1]
       [                                   ]
       [1     -6      5       5    -6     1]
       [                                   ]
       [1    -21    140    -140    21    -1]


      [0    21     0     0     0    0]
      [                              ]
      [1     0    20     0     0    0]
      [                              ]
      [0     3     0    18     0    0]
Ls1 = [                              ]
      [0     0    18     0     3    0]
      [                              ]
      [0     0     0    20     0    1]
      [                              ]
      [0     0     0     0    21    0]

      [0     0    140      0     0    0]
      [                                ]
      [0    20      0    120     0    0]
      [                                ]
      [1     0    121      0    18    0]
Ls2 = [                                ]
      [0    18      0    121     0    1]
      [                                ]
      [0     0    120      0    20    0]
      [                                ]
      [0     0      0    140     0    0]

      [0     0      0    140     0    0]
      [                                ]
      [0     0    120      0    20    0]
      [                                ]
      [0    18      0    121     0    1]
Ls3 = [                                ]
      [1     0    121      0    18    0]
      [                                ]
      [0    20      0    120     0    0]
      [                                ]
      [0     0    140      0     0    0]

      [0     0     0     0    21    0]
      [                              ]
      [0     0     0    20     0    1]
      [                              ]
      [0     0    18     0     3    0]
Ls4 = [                              ]
      [0     3     0    18     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]