# MAPLE.   May 29, 2006.
# 
# Example 6 in HCD table of spherical designs by Munemasa.
d := 3;

v := [1 , 462,  1232,  330 ];
verts := 2025;


Q := matrix([
[1 ,   22 ,   252 ,   1750],
[1 ,   7  ,162/11 ,-250/11],
[1 ,  -1/2,-261/22, 125/11],
[1 ,   -8 ,252/11 ,-175/11]]);


#  This tridiagonal  matrix, L_1-star,  allows us to fill out the cols of Q
L := matrix([
[0 ,   22 ,   0  ,   0 ],
[1 ,   0  ,   21 ,   0 ],
[0 ,  11/6, 27/22,625/33],
[0 ,   0  , 30/11,212/11]]);



for h from 2 to d
 do
    for i from 1 to d+1 do Q[i,h+1] := solve( Q[i,2]*Q[i,h] = L[h-1,h]*Q[i,h-1]+L[h+1,h]*x); od;
 od:


     [0    462      0      0]
     [                      ]
     [1    185    256     20]
L_1= [                      ]
     [0     96    291     75]
     [                      ]
     [0     28    280    154]


     [0      0    1232      0]
     [                       ]
     [0    256     776    200]
L_2= [                       ]
     [1    291     730    210]
     [                       ]
     [0    280     784    168]


     [0      0      0    330]
     [                      ]
     [0     20    200    110]
L_3= [                      ]
     [0     75    210     45]
     [                      ]
     [1    154    168      7]


       [1    462    1232     330]
       [                        ]
       [1    147     -28    -120]
  P := [                        ]
       [1     27     -58      30]
       [                        ]
       [1     -6       8      -3]



      [1     22     252     1750]
      [                         ]
      [             162     -250]
      [1     7      ---     ----]
      [             11       11 ]
      [                         ]
 Q := [             -261    125 ]
      [1    -1/2    ----    --- ]
      [              22     11  ]
      [                         ]
      [             252     -175]
      [1     -8     ---     ----]
      [             11       11 ]


     [0     22     0      0 ]
     [                      ]
     [1     0      21     0 ]
Ls1= [                      ]
     [             27    625]
     [0    11/6    --    ---]
     [             22    33 ]
     [                      ]
     [             30    212]
     [0     0      --    ---]
     [             11    11 ]


    [0    0     252       0  ]
    [                        ]
    [           1701    26250]
    [0    21    ----    -----]
    [           121      121 ]
Ls2=[                        ]
    [     27    9195    25625]
    [1    --    ----    -----]
    [     22    242      121 ]
    [                        ]
    [     30    3690    26472]
    [0    --    ----    -----]
    [     11    121      121 ]


    [0     0       0       1750 ]
    [                           ]
    [            26250    185500]
    [0     0     -----    ------]
    [             121      121  ]
Ls3=[                           ]
    [     625    25625    551500]
    [0    ---    -----    ------]
    [     33      121      363  ]
    [                           ]
    [     212    26472    182825]
    [1    ---    -----    ------]
    [     11      121      121  ]