# MAPLE.   June 3, 2006.
# 
# Block scheme of the small Witt design.
#
# extended Q-bipartite double exists.
d := 3;

v := [1 , 15 ,  30 ,  20 ]:
verts := 66;


Q := matrix([
[1 ,   10   ,   44   ,   11  ],
[1 ,   8/3  , -22/15 ,  -11/5],
[1 ,   -1   ,  -22/5 ,  22/5 ],
[1 ,  -14/3 ,  88/15 ,  -11/5]
]);



#  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 ,   10  ,   0    ,  0  ],
[1 ,  1/27 , 242/27 ,  0  ],
[0 , 55/27 , 778/135, 11/5],
[0 ,   0   ,  44/5  , 6/5 ]
]);



        [0    30     0     0]
        [                   ]
        [1    15    10     4]
L_1  =  [                   ]
        [0    15     6     9]
        [                   ]
        [0     8    12    10]

        [0     0    20    0]
        [                  ]
        [0    10     4    6]
L_2  =  [                  ]
        [1     6    10    3]
        [                  ]
        [0    12     4    4]

        [0     0    0    15]
        [                  ]
        [0     4    6     5]
L_3  =  [                  ]
        [0     9    3     3]
        [                  ]
        [1    10    4     0]



     [1    30    20    15]
     [                   ]
     [1     8    -2    -7]
P  = [                   ]
     [1    -1    -2     2]
     [                   ]
     [1    -6     8    -3]


     [1     10       44       11  ]
     [                            ]
     [               -22          ]
     [1     8/3      ---     -11/5]
     [               15           ]
Q := [                            ]
     [1     -1      -22/5    22/5 ]
     [                            ]
     [               88           ]
     [1    -14/3     --      -11/5]
     [               15           ]



     [0     10      0       0  ]
     [                         ]
     [             242         ]
     [1    1/27    ---      0  ]
     [             27          ]
Ls1= [                         ]
     [      55     778         ]
     [0     --     ---     11/5]
     [      27     135         ]
     [                         ]
     [0     0      44/5    6/5 ]


     [0     0       44       0 ]
     [                         ]
     [     242     17116    242]
     [0    ---     -----    ---]
     [     27       675     25 ]
Ls2= [                         ]
     [     778     20086    187]
     [1    ---     -----    ---]
     [     135      675     25 ]
     [                         ]
     [              748     132]
     [0    44/5     ---     ---]
     [              25      25 ]


     [0     0       0     11]
     [                      ]
     [             242    33]
     [0     0      ---    --]
     [             25     25]
Ls3= [                      ]
     [             187    33]
     [0    11/5    ---    --]
     [             25     25]
     [                      ]
     [             132    88]
     [1    6/5     ---    --]
     [             25     25]