# MAPLE. June 5, 2006. # # Bipartite double of Example 5 in HCD table of spherical designs by Munemasa. # d := 11; v := [1 , 275 , 2025 , 7128 , 15400 , 22275 , 22275 , 15400 , 7128 , 2025 , 275 , 1]; verts := 94208; Q := matrix([ [ 1, 23 , 275 , 2277 , 12650 , 31878 , 31878 , 12650 , 2277 , 275 , 23 , 1 ], [ 1, 69/5 , 91 , 1863/5 , 874 , 2898/5 , -2898/5 , -874 , -1863/5 , -91 , -69/5 ,-1 ], [ 1, 161/15 , 451/9 , 1771/15 , 506/9 , -3542/15 , -3542/15 , 506/9 , 1771/15 , 451/9 , 161/15 , 1 ], [ 1, 23/3 , 175/9 , -23/3 , -1150/9 , -322/3 , 322/3 , 1150/9 , 23/3 , -175/9 , -23/3 ,-1 ], [ 1, 23/5 , -1 , -207/5 , -46 , 414/5 , 414/5 , -46 , -207/5 , -1 , 23/5 , 1 ], [ 1, 23/15 , -101/9 , -299/15 , 506/9 , 322/5 , -322/5 , -506/9 , 299/15 , 101/9 , -23/15 ,-1 ], [ 1, -23/15 , -101/9 , 299/15 , 506/9 , -322/5 , -322/5 , 506/9 , 299/15 , -101/9 , -23/15 , 1 ], [ 1, -23/5 , -1 , 207/5 , -46 , -414/5 , 414/5 , 46 , -207/5 , 1 , 23/5 ,-1 ], [ 1, -23/3 , 175/9 , 23/3 , -1150/9 , 322/3 , 322/3 , -1150/9 , 23/3 , 175/9 , -23/3 , 1 ], [ 1,-161/15 , 451/9 , -1771/15 , 506/9 , 3542/15 , -3542/15 , -506/9 , 1771/15 , -451/9 , 161/15 ,-1 ], [ 1, -69/5 , 91 , -1863/5 , 874 , -2898/5 , -2898/5 , 874 , -1863/5 , 91 , -69/5 , 1 ], [ 1, -23 , 275 , -2277 , 12650 ,-31878 , 31878 ,-12650 , 2277 , -275 , 23 ,-1 ] ]); # This tridiagonal matrix, L_1-star, allows us to fill out the cols of Q L := matrix([ [ 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 1, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 46/25, 0, 529/25, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 0, 23/9, 0, 184/9, 0, 0, 0, 0, 0, 0, 0], [ 0, 0, 0, 92/25, 0, 483/25, 0, 0, 0, 0, 0, 0], [ 0, 0, 0, 0, 23/3, 0, 46/3, 0, 0, 0, 0, 0], [ 0, 0, 0, 0, 0, 46/3, 0, 23/3, 0, 0, 0, 0], [ 0, 0, 0, 0, 0, 0, 483/25, 0, 92/25, 0, 0, 0], [ 0, 0, 0, 0, 0, 0, 0, 184/9, 0, 23/9, 0, 0], [ 0, 0, 0, 0, 0, 0, 0, 0, 529/25, 0, 46/25, 0], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 1], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0] ]); [0 275 0 0 0 0 0 0 0 0 0 0] [ ] [1 0 162 0 112 0 0 0 0 0 0 0] [ ] [0 22 0 176 0 77 0 0 0 0 0 0] [ ] [0 0 50 0 175 0 50 0 0 0 0 0] [ ] [0 2 0 81 0 162 0 30 0 0 0 0] [ ] [0 0 7 0 112 0 140 0 16 0 0 0] L_1 = [ ] [0 0 0 16 0 140 0 112 0 7 0 0] [ ] [0 0 0 0 30 0 162 0 81 0 2 0] [ ] [0 0 0 0 0 50 0 175 0 50 0 0] [ ] [0 0 0 0 0 0 77 0 176 0 22 0] [ ] [0 0 0 0 0 0 0 112 0 162 0 1] [ ] [0 0 0 0 0 0 0 0 0 0 275 0] [0 0 2025 0 0 0 0 0 0 0 0 0] [ ] [0 162 0 1296 0 567 0 0 0 0 0 0] [ ] [1 0 462 0 1232 0 330 0 0 0 0 0] [ ] [0 50 0 750 0 1050 0 175 0 0 0 0] [ ] [0 0 162 0 972 0 810 0 81 0 0 0] [ ] [0 7 0 336 0 1092 0 560 0 30 0 0] L_2 = [ ] [0 0 30 0 560 0 1092 0 336 0 7 0] [ ] [0 0 0 81 0 810 0 972 0 162 0 0] [ ] [0 0 0 0 175 0 1050 0 750 0 50 0] [ ] [0 0 0 0 0 330 0 1232 0 462 0 1] [ ] [0 0 0 0 0 0 567 0 1296 0 162 0] [ ] [0 0 0 0 0 0 0 0 0 2025 0 0] [0 0 0 7128 0 0 0 0 0 0 0 0] [ ] [0 0 1296 0 4536 0 1296 0 0 0 0 0] [ ] [0 176 0 2640 0 3696 0 616 0 0 0 0] [ ] [1 0 750 0 3500 0 2625 0 252 0 0 0] [ ] [0 81 0 1620 0 3726 0 1620 0 81 0 0] [ ] [0 0 336 0 2576 0 3360 0 840 0 16 0] L_3 = [ ] [0 16 0 840 0 3360 0 2576 0 336 0 0] [ ] [0 0 81 0 1620 0 3726 0 1620 0 81 0] [ ] [0 0 0 252 0 2625 0 3500 0 750 0 1] [ ] [0 0 0 0 616 0 3696 0 2640 0 176 0] [ ] [0 0 0 0 0 1296 0 4536 0 1296 0 0] [ ] [0 0 0 0 0 0 0 0 7128 0 0 0] [0 0 0 0 15400 0 0 0 0 0 0 0] [ ] [0 112 0 4536 0 9072 0 1680 0 0 0 0] [ ] [0 0 1232 0 7392 0 6160 0 616 0 0 0] [ ] [0 175 0 3500 0 8050 0 3500 0 175 0 0] [ ] [1 0 972 0 5892 0 6885 0 1620 0 30 0] [ ] [0 112 0 2576 0 7392 0 4760 0 560 0 0] L_4 = [ ] [0 0 560 0 4760 0 7392 0 2576 0 112 0] [ ] [0 30 0 1620 0 6885 0 5892 0 972 0 1] [ ] [0 0 175 0 3500 0 8050 0 3500 0 175 0] [ ] [0 0 0 616 0 6160 0 7392 0 1232 0 0] [ ] [0 0 0 0 1680 0 9072 0 4536 0 112 0] [ ] [0 0 0 0 0 0 0 15400 0 0 0 0] [0 0 0 0 0 22275 0 0 0 0 0 0] [ ] [0 0 567 0 9072 0 11340 0 1296 0 0 0] [ ] [0 77 0 3696 0 12012 0 6160 0 330 0 0] [ ] [0 0 1050 0 8050 0 10500 0 2625 0 50 0] [ ] [0 162 0 3726 0 10692 0 6885 0 810 0 0] [ ] [1 0 1092 0 7392 0 10290 0 3360 0 140 0] L_5 = [ ] [0 140 0 3360 0 10290 0 7392 0 1092 0 1] [ ] [0 0 810 0 6885 0 10692 0 3726 0 162 0] [ ] [0 50 0 2625 0 10500 0 8050 0 1050 0 0] [ ] [0 0 330 0 6160 0 12012 0 3696 0 77 0] [ ] [0 0 0 1296 0 11340 0 9072 0 567 0 0] [ ] [0 0 0 0 0 0 22275 0 0 0 0 0] [0 0 0 0 0 0 22275 0 0 0 0 0] [ ] [0 0 0 1296 0 11340 0 9072 0 567 0 0] [ ] [0 0 330 0 6160 0 12012 0 3696 0 77 0] [ ] [0 50 0 2625 0 10500 0 8050 0 1050 0 0] [ ] [0 0 810 0 6885 0 10692 0 3726 0 162 0] [ ] [0 140 0 3360 0 10290 0 7392 0 1092 0 1] L_6 = [ ] [1 0 1092 0 7392 0 10290 0 3360 0 140 0] [ ] [0 162 0 3726 0 10692 0 6885 0 810 0 0] [ ] [0 0 1050 0 8050 0 10500 0 2625 0 50 0] [ ] [0 77 0 3696 0 12012 0 6160 0 330 0 0] [ ] [0 0 567 0 9072 0 11340 0 1296 0 0 0] [ ] [0 0 0 0 0 22275 0 0 0 0 0 0] [0 0 0 0 0 0 0 15400 0 0 0 0] [ ] [0 0 0 0 1680 0 9072 0 4536 0 112 0] [ ] [0 0 0 616 0 6160 0 7392 0 1232 0 0] [ ] [0 0 175 0 3500 0 8050 0 3500 0 175 0] [ ] [0 30 0 1620 0 6885 0 5892 0 972 0 1] [ ] [0 0 560 0 4760 0 7392 0 2576 0 112 0] L_7 = [ ] [0 112 0 2576 0 7392 0 4760 0 560 0 0] [ ] [1 0 972 0 5892 0 6885 0 1620 0 30 0] [ ] [0 175 0 3500 0 8050 0 3500 0 175 0 0] [ ] [0 0 1232 0 7392 0 6160 0 616 0 0 0] [ ] [0 112 0 4536 0 9072 0 1680 0 0 0 0] [ ] [0 0 0 0 15400 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 7128 0 0 0] [ ] [0 0 0 0 0 1296 0 4536 0 1296 0 0] [ ] [0 0 0 0 616 0 3696 0 2640 0 176 0] [ ] [0 0 0 252 0 2625 0 3500 0 750 0 1] [ ] [0 0 81 0 1620 0 3726 0 1620 0 81 0] [ ] [0 16 0 840 0 3360 0 2576 0 336 0 0] L_8 = [ ] [0 0 336 0 2576 0 3360 0 840 0 16 0] [ ] [0 81 0 1620 0 3726 0 1620 0 81 0 0] [ ] [1 0 750 0 3500 0 2625 0 252 0 0 0] [ ] [0 176 0 2640 0 3696 0 616 0 0 0 0] [ ] [0 0 1296 0 4536 0 1296 0 0 0 0 0] [ ] [0 0 0 7128 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 2025 0 0] [ ] [0 0 0 0 0 0 567 0 1296 0 162 0] [ ] [0 0 0 0 0 330 0 1232 0 462 0 1] [ ] [0 0 0 0 175 0 1050 0 750 0 50 0] [ ] [0 0 0 81 0 810 0 972 0 162 0 0] [ ] [0 0 30 0 560 0 1092 0 336 0 7 0] L_9 = [ ] [0 7 0 336 0 1092 0 560 0 30 0 0] [ ] [0 0 162 0 972 0 810 0 81 0 0 0] [ ] [0 50 0 750 0 1050 0 175 0 0 0 0] [ ] [1 0 462 0 1232 0 330 0 0 0 0 0] [ ] [0 162 0 1296 0 567 0 0 0 0 0 0] [ ] [0 0 2025 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 275 0] [ ] [0 0 0 0 0 0 0 112 0 162 0 1] [ ] [0 0 0 0 0 0 77 0 176 0 22 0] [ ] [0 0 0 0 0 50 0 175 0 50 0 0] [ ] [0 0 0 0 30 0 162 0 81 0 2 0] [ ] [0 0 0 16 0 140 0 112 0 7 0 0] L_10 = [ ] [0 0 7 0 112 0 140 0 16 0 0 0] [ ] [0 2 0 81 0 162 0 30 0 0 0 0] [ ] [0 0 50 0 175 0 50 0 0 0 0 0] [ ] [0 22 0 176 0 77 0 0 0 0 0 0] [ ] [1 0 162 0 112 0 0 0 0 0 0 0] [ ] [0 275 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1] [ ] [0 0 0 0 0 0 0 0 0 0 1 0] [ ] [0 0 0 0 0 0 0 0 0 1 0 0] [ ] [0 0 0 0 0 0 0 0 1 0 0 0] [ ] [0 0 0 0 0 0 0 1 0 0 0 0] [ ] [0 0 0 0 0 0 1 0 0 0 0 0] L_11 = [ ] [0 0 0 0 0 1 0 0 0 0 0 0] [ ] [0 0 0 0 1 0 0 0 0 0 0 0] [ ] [0 0 0 1 0 0 0 0 0 0 0 0] [ ] [0 0 1 0 0 0 0 0 0 0 0 0] [ ] [0 1 0 0 0 0 0 0 0 0 0 0] [ ] [1 0 0 0 0 0 0 0 0 0 0 0] [1 275 2025 7128 15400 22275 22275 15400 7128 2025 275 1] [ ] [1 165 945 2376 3080 1485 -1485 -3080 -2376 -945 -165 -1] [ ] [1 91 369 504 -56 -909 -909 -56 504 369 91 1] [ ] [1 45 105 -24 -280 -195 195 280 24 -105 -45 -1] [ ] [1 19 9 -72 -56 99 99 -56 -72 9 19 1] [ ] [1 5 -15 -24 40 45 -45 -40 24 15 -5 -1] P= [ ] [1 -5 -15 24 40 -45 -45 40 24 -15 -5 1] [ ] [1 -19 9 72 -56 -99 99 56 -72 -9 19 -1] [ ] [1 -45 105 24 -280 195 195 -280 24 105 -45 1] [ ] [1 -91 369 -504 -56 909 -909 56 504 -369 91 -1] [ ] [1 -165 945 -2376 3080 -1485 -1485 3080 -2376 945 -165 1] [ ] [1 -275 2025 -7128 15400 -22275 22275 -15400 7128 -2025 275 -1] [1 23 275 2277 12650 31878 31878 12650 2277 275 23 1] [ ] [1 69/5 91 1863/5 874 2898/5 -2898/5 -874 -1863/5 -91 -69/5 -1] [ ] [ 161 1771 -3542 -3542 1771 161 ] [1 --- 451/9 ---- 506/9 ----- ----- 506/9 ---- 451/9 --- 1] [ 15 15 15 15 15 15 ] [ ] [1 23/3 175/9 -23/3 -1150/9 -322/3 322/3 1150/9 23/3 -175/9 -23/3 -1] [ ] [1 23/5 -1 -207/5 -46 414/5 414/5 -46 -207/5 -1 23/5 1] [ ] [ 23 -299 299 -23 ] [1 -- -101/9 ---- 506/9 322/5 -322/5 -506/9 --- 101/9 --- -1] [ 15 15 15 15 ] Q = [ ] [ -23 299 299 -23 ] [1 --- -101/9 --- 506/9 -322/5 -322/5 506/9 --- -101/9 --- 1] [ 15 15 15 15 ] [ ] [1 -23/5 -1 207/5 -46 -414/5 414/5 46 -207/5 1 23/5 -1] [ ] [1 -23/3 175/9 23/3 -1150/9 322/3 322/3 -1150/9 23/3 175/9 -23/3 1] [ ] [ -161 -1771 3542 -3542 1771 161 ] [1 ---- 451/9 ----- 506/9 ---- ----- -506/9 ---- -451/9 --- -1] [ 15 15 15 15 15 15 ] [ ] [1 -69/5 91 -1863/5 874 -2898/5 -2898/5 874 -1863/5 91 -69/5 1] [ ] [1 -23 275 -2277 12650 -31878 31878 -12650 2277 -275 23 -1] [0 23 0 0 0 0 0 0 0 0 0 0] [ ] [1 0 22 0 0 0 0 0 0 0 0 0] [ ] [ 46 529 ] [0 -- 0 --- 0 0 0 0 0 0 0 0] [ 25 25 ] [ ] [0 0 23/9 0 184/9 0 0 0 0 0 0 0] [ ] [ 92 483 ] [0 0 0 -- 0 --- 0 0 0 0 0 0] [ 25 25 ] [ ] [0 0 0 0 23/3 0 46/3 0 0 0 0 0] Ls1 = [ ] [0 0 0 0 0 46/3 0 23/3 0 0 0 0] [ ] [ 483 92 ] [0 0 0 0 0 0 --- 0 -- 0 0 0] [ 25 25 ] [ ] [0 0 0 0 0 0 0 184/9 0 23/9 0 0] [ ] [ 529 46 ] [0 0 0 0 0 0 0 0 --- 0 -- 0] [ 25 25 ] [ ] [0 0 0 0 0 0 0 0 0 22 0 1] [ ] [0 0 0 0 0 0 0 0 0 0 23 0] [0 0 275 0 0 0 0 0 0 0 0 0] [ ] [0 22 0 253 0 0 0 0 0 0 0 0] [ ] [1 0 350/9 0 2116/9 0 0 0 0 0 0 0] [ ] [0 23/9 0 520/9 0 644/3 0 0 0 0 0 0] [ ] [0 0 46/9 0 980/9 0 161 0 0 0 0 0] [ ] [0 0 0 46/3 0 1762/9 0 575/9 0 0 0 0] Ls2=[ ] [0 0 0 0 575/9 0 1762/9 0 46/3 0 0 0] [ ] [0 0 0 0 0 161 0 980/9 0 46/9 0 0] [ ] [0 0 0 0 0 0 644/3 0 520/9 0 23/9 0] [ ] [0 0 0 0 0 0 0 2116/9 0 350/9 0 1] [ ] [0 0 0 0 0 0 0 0 253 0 22 0] [ ] [0 0 0 0 0 0 0 0 0 275 0 0] [0 0 0 2277 0 0 0 0 0 0 0 0] [ ] [0 0 253 0 2024 0 0 0 0 0 0 0] [ ] [ 529 44436 ] [0 --- 0 2392/5 0 ----- 0 0 0 0 0 0] [ 25 25 ] [ ] [1 0 520/9 0 8372/9 0 1288 0 0 0 0 0] [ ] [ 92 4186 40572 ] [0 -- 0 ---- 0 ----- 0 483 0 0 0 0] [ 25 25 25 ] [ ] [0 0 46/3 0 644 0 4577/3 0 92 0 0 0] Ls3=[ ] [0 0 0 92 0 4577/3 0 644 0 46/3 0 0] [ ] [ 40572 4186 92 ] [0 0 0 0 483 0 ----- 0 ---- 0 -- 0] [ 25 25 25 ] [ ] [0 0 0 0 0 1288 0 8372/9 0 520/9 0 1] [ ] [ 44436 529 ] [0 0 0 0 0 0 ----- 0 2392/5 0 --- 0] [ 25 25 ] [ ] [0 0 0 0 0 0 0 2024 0 253 0 0] [ ] [0 0 0 0 0 0 0 0 2277 0 0 0] [0 0 0 0 12650 0 0 0 0 0 0 0] [ ] [0 0 0 2024 0 10626 0 0 0 0 0 0] [ ] [0 0 2116/9 0 45080/9 0 7406 0 0 0 0 0] [ ] [0 184/9 0 8372/9 0 9016 0 8050/3 0 0 0 0] [ ] [1 0 980/9 0 33166/9 0 8372 0 483 0 0 0] [ ] [0 23/3 0 644 0 77510/9 0 29900/9 0 575/9 0 0] Ls4= [ ] [0 0 575/9 0 29900/9 0 77510/9 0 644 0 23/3 0] [ ] [0 0 0 483 0 8372 0 33166/9 0 980/9 0 1] [ ] [0 0 0 0 8050/3 0 9016 0 8372/9 0 184/9 0] [ ] [0 0 0 0 0 7406 0 45080/9 0 2116/9 0 0] [ ] [0 0 0 0 0 0 10626 0 2024 0 0 0] [ ] [0 0 0 0 0 0 0 12650 0 0 0 0] [0 0 0 0 0 31878 0 0 0 0 0 0] [ ] [0 0 0 0 10626 0 21252 0 0 0 0 0] [ ] [ 44436 567364 ] [0 0 0 ----- 0 ------ 0 7406 0 0 0 0] [ 25 25 ] [ ] [0 0 644/3 0 9016 0 64078/3 0 1288 0 0 0] [ ] [ 483 40572 ] [0 --- 0 ----- 0 108514/5 0 8372 0 161 0 0] [ 25 25 ] [ ] [1 0 1762/9 0 77510/9 0 21528 0 4577/3 0 46/3 0] Ls5= [ ] [0 46/3 0 4577/3 0 21528 0 77510/9 0 1762/9 0 1] [ ] [ 40572 483 ] [0 0 161 0 8372 0 108514/5 0 ----- 0 --- 0] [ 25 25 ] [ ] [0 0 0 1288 0 64078/3 0 9016 0 644/3 0 0] [ ] [ 567364 44436 ] [0 0 0 0 7406 0 ------ 0 ----- 0 0 0] [ 25 25 ] [ ] [0 0 0 0 0 21252 0 10626 0 0 0 0] [ ] [0 0 0 0 0 0 31878 0 0 0 0 0] [0 0 0 0 0 0 31878 0 0 0 0 0] [ ] [0 0 0 0 0 21252 0 10626 0 0 0 0] [ ] [ 567364 44436 ] [0 0 0 0 7406 0 ------ 0 ----- 0 0 0] [ 25 25 ] [ ] [0 0 0 1288 0 64078/3 0 9016 0 644/3 0 0] [ ] [ 40572 483 ] [0 0 161 0 8372 0 108514/5 0 ----- 0 --- 0] [ 25 25 ] [ ] [0 46/3 0 4577/3 0 21528 0 77510/9 0 1762/9 0 1] Ls6= [ ] [1 0 1762/9 0 77510/9 0 21528 0 4577/3 0 46/3 0] [ ] [ 483 40572 ] [0 --- 0 ----- 0 108514/5 0 8372 0 161 0 0] [ 25 25 ] [ ] [0 0 644/3 0 9016 0 64078/3 0 1288 0 0 0] [ ] [ 44436 567364 ] [0 0 0 ----- 0 ------ 0 7406 0 0 0 0] [ 25 25 ] [ ] [0 0 0 0 10626 0 21252 0 0 0 0 0] [ ] [0 0 0 0 0 31878 0 0 0 0 0 0] [0 0 0 0 0 0 0 12650 0 0 0 0] [ ] [0 0 0 0 0 0 10626 0 2024 0 0 0] [ ] [0 0 0 0 0 7406 0 45080/9 0 2116/9 0 0] [ ] [0 0 0 0 8050/3 0 9016 0 8372/9 0 184/9 0] [ ] [0 0 0 483 0 8372 0 33166/9 0 980/9 0 1] [ ] [0 0 575/9 0 29900/9 0 77510/9 0 644 0 23/3 0] Ls7= [ ] [0 23/3 0 644 0 77510/9 0 29900/9 0 575/9 0 0] [ ] [1 0 980/9 0 33166/9 0 8372 0 483 0 0 0] [ ] [0 184/9 0 8372/9 0 9016 0 8050/3 0 0 0 0] [ ] [0 0 2116/9 0 45080/9 0 7406 0 0 0 0 0] [ ] [0 0 0 2024 0 10626 0 0 0 0 0 0] [ ] [0 0 0 0 12650 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 2277 0 0 0] [ ] [0 0 0 0 0 0 0 2024 0 253 0 0] [ ] [ 44436 529 ] [0 0 0 0 0 0 ----- 0 2392/5 0 --- 0] [ 25 25 ] [ ] [0 0 0 0 0 1288 0 8372/9 0 520/9 0 1] [ ] [ 40572 4186 92 ] [0 0 0 0 483 0 ----- 0 ---- 0 -- 0] [ 25 25 25 ] [ ] [0 0 0 92 0 4577/3 0 644 0 46/3 0 0] Ls8=[ ] [0 0 46/3 0 644 0 4577/3 0 92 0 0 0] [ ] [ 92 4186 40572 ] [0 -- 0 ---- 0 ----- 0 483 0 0 0 0] [ 25 25 25 ] [ ] [1 0 520/9 0 8372/9 0 1288 0 0 0 0 0] [ ] [ 529 44436 ] [0 --- 0 2392/5 0 ----- 0 0 0 0 0 0] [ 25 25 ] [ ] [0 0 253 0 2024 0 0 0 0 0 0 0] [ ] [0 0 0 2277 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 275 0 0] [ ] [0 0 0 0 0 0 0 0 253 0 22 0] [ ] [0 0 0 0 0 0 0 2116/9 0 350/9 0 1] [ ] [0 0 0 0 0 0 644/3 0 520/9 0 23/9 0] [ ] [0 0 0 0 0 161 0 980/9 0 46/9 0 0] [ ] [0 0 0 0 575/9 0 1762/9 0 46/3 0 0 0] Ls9=[ ] [0 0 0 46/3 0 1762/9 0 575/9 0 0 0 0] [ ] [0 0 46/9 0 980/9 0 161 0 0 0 0 0] [ ] [0 23/9 0 520/9 0 644/3 0 0 0 0 0 0] [ ] [1 0 350/9 0 2116/9 0 0 0 0 0 0 0] [ ] [0 22 0 253 0 0 0 0 0 0 0 0] [ ] [0 0 275 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 23 0] [ ] [0 0 0 0 0 0 0 0 0 22 0 1] [ ] [ 529 46 ] [0 0 0 0 0 0 0 0 --- 0 -- 0] [ 25 25 ] [ ] [0 0 0 0 0 0 0 184/9 0 23/9 0 0] [ ] [ 483 92 ] [0 0 0 0 0 0 --- 0 -- 0 0 0] [ 25 25 ] [ ] [0 0 0 0 0 46/3 0 23/3 0 0 0 0] Ls10 = [ ] [0 0 0 0 23/3 0 46/3 0 0 0 0 0] [ ] [ 92 483 ] [0 0 0 -- 0 --- 0 0 0 0 0 0] [ 25 25 ] [ ] [0 0 23/9 0 184/9 0 0 0 0 0 0 0] [ ] [ 46 529 ] [0 -- 0 --- 0 0 0 0 0 0 0 0] [ 25 25 ] [ ] [1 0 22 0 0 0 0 0 0 0 0 0] [ ] [0 23 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0] Ls11 = [0 0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0]