# MAPLE.  June 4, 2006.
#
# 3-class primitive cometric association scheme
# defined on blocks of the 4-(47,11,48) design from the quadratic residue
# code.  (See MacWilliams and Sloane p494).
d := 3;
v := [ 1, 462, 2475, 1386 ];
verts := 4324;


Q := matrix([
[ 1 ,      46 ,     1034 ,     3243 ],
[ 1 ,  437/33 ,  1175/21 , -5405/77 ],  
[ 1 ,  230/99 , -1034/45 ,  1081/55 ],
[ 1 , -851/99 ,  1363/63 , -1081/77 ]
]);


# Tridiagonal matrix L = L1-star can be used to obtain Q (and
# then all parameters) from just the cosines.
L := matrix([
[0 ,           46 ,             0 ,          0 ],
[1 ,    2875/1782 ,    77315/1782 ,          0 ],       
[0 ,  37835/19602 ,  183563/12474 ,  24863/847 ],
[0 ,            0 ,      2162/231 ,   8464/231 ]    
]):






         [0    462      0      0]
         [                      ]
         [1    110    300     51]
  L_1  = [                      ]
         [0     56    280    126]
         [                      ]
         [0     17    225    220]

         [0      0    2475      0]
         [                       ]
         [0    300    1500    675]
  L_2  = [                       ]
         [1    280    1410    784]
         [                       ]
         [0    225    1400    850]

         [0      0      0    1386]
         [                       ]
         [0     51    675     660]
   L_3 = [                       ]
         [0    126    784     476]
         [                       ]
         [1    220    850     315]




       [1    462    2475    1386]
       [                        ]
       [1    133     125    -259]
P  =   [                        ]
       [1     25     -55      29]
       [                        ]
       [1    -10      15      -6]

       [1     46     1034     3243 ]
       [                           ]
       [     437     1175     -5405]
       [1    ---     ----     -----]
       [     33       21       77  ]
       [                           ]
  Q := [     230     -1034    1081 ]
       [1    ---     -----    ---- ]
       [     99       45       55  ]
       [                           ]
       [     -851    1363     -1081]
       [1    ----    ----     -----]
       [      99      63       77  ]



       [0     46        0         0  ]
       [                             ]
       [     2875     77315          ]
       [1    ----     -----       0  ]
       [     1782     1782           ]
       [                             ]
Ls1 =  [     37835    183563    24863]
       [0    -----    ------    -----]
       [     19602    12474      847 ]
       [                             ]
       [               2162     8464 ]
       [0      0       ----     ---- ]
       [               231      231  ]

       [0      0         1034         0   ]
       [                                  ]
       [     77315      375107      50807 ]
       [0    -----      ------      ----- ]
       [     1782        1134        77   ]
       [                                  ]
Ls2  = [     183563    10390243    2038766]
       [1    ------    --------    -------]
       [     12474      39690       2695  ]
       [                                  ]
       [      2162      177284     6334096]
       [0     ----      ------     -------]
       [      231        735        8085  ]

       [0      0         0         3243  ]
       [                                 ]
       [               50807      198904 ]
       [0      0       -----      ------ ]
       [                77          77   ]
       [                                 ]
Ls3  = [     24863    2038766    72842104]
       [0    -----    -------    --------]
       [      847      2695       29645  ]
       [                                 ]
       [     8464     6334096    6527078 ]
       [1    ----     -------    ------- ]
       [     231       8085       2695   ]