# MAPLE.   April 4, 2010
# 
# Open parameter set from Van Dam thesis
#
d := 3;

v := [1 ,  28 ,  42 ,  28 ]:
verts := 99;


Q := matrix([
[1 ,  14 ,   63  ,   21  ],
[1 ,   5 ,  -9/4 ,  -15/4],
[1 ,  -1 ,  -9/2 ,   9/2 ],
[1 ,  -4 ,  27/4 ,  -15/4]
]);



#  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 ,     14    ,     0      ,    0    ],
[1 ,   35/11   ,  108/11    ,    0    ],
[0 ,   24/11   ,  355/44    ,  15/4   ],
[0 ,      0    ,   45/4     ,  11/4   ]
]);


      [0    28     0     0]
      [                   ]
      [1    12    12     3]
L_1 = [                   ]
      [0     8    10    10]
      [                   ]
      [0     3    15    10]

      [0     0    42     0]
      [                   ]
      [0    12    15    15]
L_2 = [                   ]
      [1    10    21    10]
      [                   ]
      [0    15    15    12]

      [0     0     0    28]
      [                   ]
      [0     3    15    10]
L_3 = [                   ]
      [0    10    10     8]
      [                   ]
      [1    10    12     5]


     [1    28    42    28]
     [                   ]
     [1    10    -3    -8]
P := [                   ]
     [1    -1    -3     3]
     [                   ]
     [1    -5     9    -5]


    [1    14     63      21  ]
    [                        ]
    [1     5    -9/4    -15/4]
Q = [                        ]
    [1    -1    -9/2     9/2 ]
    [                        ]
    [1    -4    27/4    -15/4]

      [0    14     0       0  ]
      [                       ]
      [     35    108         ]
      [1    --    ---      0  ]
      [     11    11          ]
Ls1 = [                       ]
      [     24    355         ]
      [0    --    ---     15/4]
      [     11    44          ]
      [                       ]
      [0    0     45/4    11/4]

     [0     0       63        0  ]
     [                           ]
     [     108     3195          ]
     [0    ---     ----     135/8]
     [     11       88           ]
Ls2= [                           ]
     [     355     3591          ]
     [1    ---     ----     105/8]
     [     44       88           ]
     [                           ]
     [0    45/4    315/8    99/8 ]

     [0     0        0       21 ]
     [                          ]
     [0     0      135/8    33/8]
Ls3= [                          ]
     [0    15/4    105/8    33/8]
     [                          ]
     [1    11/4    99/8     39/8]