with(linalg): readlib(showtime): on; # ----------------------------------------------------------------------------- # A for i from 1 to 100 do (1000 + i)!/(900 + i)! od: # ----------------------------------------------------------------------------- # B formerly A' s := 0: for i from 1 to 1000 do s := s + 1/i od: s := 's': # ----------------------------------------------------------------------------- # C formerly B x := 13*17*31: y := 13*19*29: for i from 1 to 200 do gcd(x^(300 + (i mod 181)), y^(200 + (i mod 183))) od: x := 'x': y := 'y': # ----------------------------------------------------------------------------- # D formerly C s := 0: for i from 1 to 10 do s := s + i*y*t^i/(y + i*t)^i od: s := 's': # ----------------------------------------------------------------------------- # E formerly D s := 0: for i from 1 to 10 do s := s + i*y*t^i/(y + abs(5 - i)*t)^i od: s := 's': # ----------------------------------------------------------------------------- # F p := expand((x^2 - 3*x*y + y^2)^4*(3*x - 7*y + 2)^5): q := expand((x^2 - 3*x*y + y^2)^3*(3*x - 7*y - 2)^6): gcd(p, q): factor(%); p := 'p': q := 'q': # ----------------------------------------------------------------------------- # G p := expand((7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^5): q := expand((7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6): gcd(p, q): factor(%); p := 'p': q := 'q': # ----------------------------------------------------------------------------- # Gp p := expand((7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^5) mod 181: q := expand((7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6) mod 181: Gcd(p, q) mod 181: Factor(%) mod 181; p := 'p': q := 'q': # ----------------------------------------------------------------------------- # H, I, J, K and L # H h80 := hilbert(80): det(h80): h80 := 'h80': h40 := hilbert(40): # I hinv := inverse(h40): # J evalm(h40 &* hinv): h40 := 'h40': hinv := 'hinv': h70 := hilbert(70): # K hinv := inverse(h70): # L evalm(h70 &* hinv): h70 := 'h70': hinv := 'hinv': # ----------------------------------------------------------------------------- # M1 w := matrix( [ [ 1, 1, 1, 7, x4 , 12, x3 , 17, x2 , 22, x1 ], [ 2, 2, 1, 8, x4 , 13, x3 , 18, x2 , 23, x1 ], [ 3, 3, 1, 9, x4 , 14, x3 , 19, x2 , 24, x1 ], [ 4, 4, 1, 10, x4 , 15, x3 , 20, x2 , 25, x1 ], [ 5, 5, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [ 6, 2, x5 , 6, 1, 12, x3 , 17, x2 , 22, x1 ], [ 7, 3, x5 , 7, 1, 13, x3 , 18, x2 , 23, x1 ], [ 8, 4, x5 , 8, 1, 14, x3 , 19, x2 , 24, x1 ], [ 9, 5, x5 , 9, 1, 15, x3 , 20, x2 , 25, x1 ], [10, 10, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [11, 2, x5 , 7, x4 , 11, 1, 17, x2 , 22, x1 ], [12, 3, x5 , 8, x4 , 12, 1, 18, x2 , 23, x1 ], [13, 4, x5 , 9, x4 , 13, 1, 19, x2 , 24, x1 ], [14, 5, x5 , 10, x4 , 14, 1, 20, x2 , 25, x1 ], [15, 15, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [16, 2, x5 , 7, x4 , 12, x3 , 16, 1, 22, x1 ], [17, 3, x5 , 8, x4 , 13, x3 , 17, 1, 23, x1 ], [18, 4, x5 , 9, x4 , 14, x3 , 18, 1, 24, x1 ], [19, 5, x5 , 10, x4 , 15, x3 , 19, 1, 25, x1 ], [20, 20, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [21, 2, x5 , 7, x4 , 12, x3 , 17, x2 , 21, 1], [22, 3, x5 , 8, x4 , 13, x3 , 18, x2 , 22, 1], [23, 4, x5 , 9, x4 , 14, x3 , 19, x2 , 23, 1], [24, 5, x5 , 10, x4 , 15, x3 , 20, x2 , 24, 1], [25, 25, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [26, 1, x5 , 6, x4 , 11, x3 , 16, x2 , 21, x1 ] ]): m := matrix(26, 26, 0): fill := proc() global m, w; local i, j; for i from 1 to 26 do for j from 1 to 5 do m[i, w[i, 2*j]] := w[i, 2*j+1] od od end: fill(): det(m): w := 'w': m := 'm': # ----------------------------------------------------------------------------- # M2 w := matrix([ [ 1, 1, 1, 12, x9, 22, x8, 32, x7, 42, x6, 52, x5, 62, x4, 72, x3, 82, x2, 92, x1], [ 2, 2, 1, 13, x9, 23, x8, 33, x7, 43, x6, 53, x5, 63, x4, 73, x3, 83, x2, 93, x1], [ 3, 3, 1, 14, x9, 24, x8, 34, x7, 44, x6, 54, x5, 64, x4, 74, x3, 84, x2, 94, x1], [ 4, 4, 1, 15, x9, 25, x8, 35, x7, 45, x6, 55, x5, 65, x4, 75, x3, 85, x2, 95, x1], [ 5, 5, 1, 16, x9, 26, x8, 36, x7, 46, x6, 56, x5, 66, x4, 76, x3, 86, x2, 96, x1], [ 6, 6, 1, 17, x9, 27, x8, 37, x7, 47, x6, 57, x5, 67, x4, 77, x3, 87, x2, 97, x1], [ 7, 7, 1, 18, x9, 28, x8, 38, x7, 48, x6, 58, x5, 68, x4, 78, x3, 88, x2, 98, x1], [ 8, 8, 1, 19, x9, 29, x8, 39, x7, 49, x6, 59, x5, 69, x4, 79, x3, 89, x2, 99, x1], [ 9, 9, 1, 20, x9, 30, x8, 40, x7, 50, x6, 60, x5, 70, x4, 80, x3, 90, x2, 100, x1], [10, 10, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [11, 2, x10, 11, 1, 22, x8, 32, x7, 42, x6, 52, x5, 62, x4, 72, x3, 82, x2, 92, x1], [12, 3, x10, 12, 1, 23, x8, 33, x7, 43, x6, 53, x5, 63, x4, 73, x3, 83, x2, 93, x1], [13, 4, x10, 13, 1, 24, x8, 34, x7, 44, x6, 54, x5, 64, x4, 74, x3, 84, x2, 94, x1], [14, 5, x10, 14, 1, 25, x8, 35, x7, 45, x6, 55, x5, 65, x4, 75, x3, 85, x2, 95, x1], [15, 6, x10, 15, 1, 26, x8, 36, x7, 46, x6, 56, x5, 66, x4, 76, x3, 86, x2, 96, x1], [16, 7, x10, 16, 1, 27, x8, 37, x7, 47, x6, 57, x5, 67, x4, 77, x3, 87, x2, 97, x1], [17, 8, x10, 17, 1, 28, x8, 38, x7, 48, x6, 58, x5, 68, x4, 78, x3, 88, x2, 98, x1], [18, 9, x10, 18, 1, 29, x8, 39, x7, 49, x6, 59, x5, 69, x4, 79, x3, 89, x2, 99, x1], [19, 10, x10, 19, 1, 30, x8, 40, x7, 50, x6, 60, x5, 70, x4, 80, x3, 90, x2, 100, x1], [20, 20, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [21, 2, x10, 12, x9, 21, 1, 32, x7, 42, x6, 52, x5, 62, x4, 72, x3, 82, x2, 92, x1], [22, 3, x10, 13, x9, 22, 1, 33, x7, 43, x6, 53, x5, 63, x4, 73, x3, 83, x2, 93, x1], [23, 4, x10, 14, x9, 23, 1, 34, x7, 44, x6, 54, x5, 64, x4, 74, x3, 84, x2, 94, x1], [24, 5, x10, 15, x9, 24, 1, 35, x7, 45, x6, 55, x5, 65, x4, 75, x3, 85, x2, 95, x1], [25, 6, x10, 16, x9, 25, 1, 36, x7, 46, x6, 56, x5, 66, x4, 76, x3, 86, x2, 96, x1], [26, 7, x10, 17, x9, 26, 1, 37, x7, 47, x6, 57, x5, 67, x4, 77, x3, 87, x2, 97, x1], [27, 8, x10, 18, x9, 27, 1, 38, x7, 48, x6, 58, x5, 68, x4, 78, x3, 88, x2, 98, x1], [28, 9, x10, 19, x9, 28, 1, 39, x7, 49, x6, 59, x5, 69, x4, 79, x3, 89, x2, 99, x1], [29, 10, x10, 20, x9, 29, 1, 40, x7, 50, x6, 60, x5, 70, x4, 80, x3, 90, x2, 100, x1], [30, 30, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [31, 2, x10, 12, x9, 22, x8, 31, 1, 42, x6, 52, x5, 62, x4, 72, x3, 82, x2, 92, x1], [32, 3, x10, 13, x9, 23, x8, 32, 1, 43, x6, 53, x5, 63, x4, 73, x3, 83, x2, 93, x1], [33, 4, x10, 14, x9, 24, x8, 33, 1, 44, x6, 54, x5, 64, x4, 74, x3, 84, x2, 94, x1], [34, 5, x10, 15, x9, 25, x8, 34, 1, 45, x6, 55, x5, 65, x4, 75, x3, 85, x2, 95, x1], [35, 6, x10, 16, x9, 26, x8, 35, 1, 46, x6, 56, x5, 66, x4, 76, x3, 86, x2, 96, x1], [36, 7, x10, 17, x9, 27, x8, 36, 1, 47, x6, 57, x5, 67, x4, 77, x3, 87, x2, 97, x1], [37, 8, x10, 18, x9, 28, x8, 37, 1, 48, x6, 58, x5, 68, x4, 78, x3, 88, x2, 98, x1], [38, 9, x10, 19, x9, 29, x8, 38, 1, 49, x6, 59, x5, 69, x4, 79, x3, 89, x2, 99, x1], [39, 10, x10, 20, x9, 30, x8, 39, 1, 50, x6, 60, x5, 70, x4, 80, x3, 90, x2, 100, x1], [40, 40, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [41, 2, x10, 12, x9, 22, x8, 32, x7, 41, 1, 52, x5, 62, x4, 72, x3, 82, x2, 92, x1], [42, 3, x10, 13, x9, 23, x8, 33, x7, 42, 1, 53, x5, 63, x4, 73, x3, 83, x2, 93, x1], [43, 4, x10, 14, x9, 24, x8, 34, x7, 43, 1, 54, x5, 64, x4, 74, x3, 84, x2, 94, x1], [44, 5, x10, 15, x9, 25, x8, 35, x7, 44, 1, 55, x5, 65, x4, 75, x3, 85, x2, 95, x1], [45, 6, x10, 16, x9, 26, x8, 36, x7, 45, 1, 56, x5, 66, x4, 76, x3, 86, x2, 96, x1], [46, 7, x10, 17, x9, 27, x8, 37, x7, 46, 1, 57, x5, 67, x4, 77, x3, 87, x2, 97, x1], [47, 8, x10, 18, x9, 28, x8, 38, x7, 47, 1, 58, x5, 68, x4, 78, x3, 88, x2, 98, x1], [48, 9, x10, 19, x9, 29, x8, 39, x7, 48, 1, 59, x5, 69, x4, 79, x3, 89, x2, 99, x1], [49, 10, x10, 20, x9, 30, x8, 40, x7, 49, 1, 60, x5, 70, x4, 80, x3, 90, x2, 100, x1], [50, 50, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [51, 2, x10, 12, x9, 22, x8, 32, x7, 42, x6, 51, 1, 62, x4, 72, x3, 82, x2, 92, x1], [52, 3, x10, 13, x9, 23, x8, 33, x7, 43, x6, 52, 1, 63, x4, 73, x3, 83, x2, 93, x1], [53, 4, x10, 14, x9, 24, x8, 34, x7, 44, x6, 53, 1, 64, x4, 74, x3, 84, x2, 94, x1], [54, 5, x10, 15, x9, 25, x8, 35, x7, 45, x6, 54, 1, 65, x4, 75, x3, 85, x2, 95, x1], [55, 6, x10, 16, x9, 26, x8, 36, x7, 46, x6, 55, 1, 66, x4, 76, x3, 86, x2, 96, x1], [56, 7, x10, 17, x9, 27, x8, 37, x7, 47, x6, 56, 1, 67, x4, 77, x3, 87, x2, 97, x1], [57, 8, x10, 18, x9, 28, x8, 38, x7, 48, x6, 57, 1, 68, x4, 78, x3, 88, x2, 98, x1], [58, 9, x10, 19, x9, 29, x8, 39, x7, 49, x6, 58, 1, 69, x4, 79, x3, 89, x2, 99, x1], [59, 10, x10, 20, x9, 30, x8, 40, x7, 50, x6, 59, 1, 70, x4, 80, x3, 90, x2, 100, x1], [60, 60, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [61, 2, x10, 12, x9, 22, x8, 32, x7, 42, x6, 52, x5, 61, 1, 72, x3, 82, x2, 92, x1], [62, 3, x10, 13, x9, 23, x8, 33, x7, 43, x6, 53, x5, 62, 1, 73, x3, 83, x2, 93, x1], [63, 4, x10, 14, x9, 24, x8, 34, x7, 44, x6, 54, x5, 63, 1, 74, x3, 84, x2, 94, x1], [64, 5, x10, 15, x9, 25, x8, 35, x7, 45, x6, 55, x5, 64, 1, 75, x3, 85, x2, 95, x1], [65, 6, x10, 16, x9, 26, x8, 36, x7, 46, x6, 56, x5, 65, 1, 76, x3, 86, x2, 96, x1], [66, 7, x10, 17, x9, 27, x8, 37, x7, 47, x6, 57, x5, 66, 1, 77, x3, 87, x2, 97, x1], [67, 8, x10, 18, x9, 28, x8, 38, x7, 48, x6, 58, x5, 67, 1, 78, x3, 88, x2, 98, x1], [68, 9, x10, 19, x9, 29, x8, 39, x7, 49, x6, 59, x5, 68, 1, 79, x3, 89, x2, 99, x1], [69, 10, x10, 20, x9, 30, x8, 40, x7, 50, x6, 60, x5, 69, 1, 80, x3, 90, x2, 100, x1], [70, 70, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [71, 2, x10, 12, x9, 22, x8, 32, x7, 42, x6, 52, x5, 62, x4, 71, 1, 82, x2, 92, x1], [72, 3, x10, 13, x9, 23, x8, 33, x7, 43, x6, 53, x5, 63, x4, 72, 1, 83, x2, 93, x1], [73, 4, x10, 14, x9, 24, x8, 34, x7, 44, x6, 54, x5, 64, x4, 73, 1, 84, x2, 94, x1], [74, 5, x10, 15, x9, 25, x8, 35, x7, 45, x6, 55, x5, 65, x4, 74, 1, 85, x2, 95, x1], [75, 6, x10, 16, x9, 26, x8, 36, x7, 46, x6, 56, x5, 66, x4, 75, 1, 86, x2, 96, x1], [76, 7, x10, 17, x9, 27, x8, 37, x7, 47, x6, 57, x5, 67, x4, 76, 1, 87, x2, 97, x1], [77, 8, x10, 18, x9, 28, x8, 38, x7, 48, x6, 58, x5, 68, x4, 77, 1, 88, x2, 98, x1], [78, 9, x10, 19, x9, 29, x8, 39, x7, 49, x6, 59, x5, 69, x4, 78, 1, 89, x2, 99, x1], [79, 10, x10, 20, x9, 30, x8, 40, x7, 50, x6, 60, x5, 70, x4, 79, 1, 90, x2, 100, x1], [80, 80, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [81, 2, x10, 12, x9, 22, x8, 32, x7, 42, x6, 52, x5, 62, x4, 72, x3, 81, 1, 92, x1], [82, 3, x10, 13, x9, 23, x8, 33, x7, 43, x6, 53, x5, 63, x4, 73, x3, 82, 1, 93, x1], [83, 4, x10, 14, x9, 24, x8, 34, x7, 44, x6, 54, x5, 64, x4, 74, x3, 83, 1, 94, x1], [84, 5, x10, 15, x9, 25, x8, 35, x7, 45, x6, 55, x5, 65, x4, 75, x3, 84, 1, 95, x1], [85, 6, x10, 16, x9, 26, x8, 36, x7, 46, x6, 56, x5, 66, x4, 76, x3, 85, 1, 96, x1], [86, 7, x10, 17, x9, 27, x8, 37, x7, 47, x6, 57, x5, 67, x4, 77, x3, 86, 1, 97, x1], [87, 8, x10, 18, x9, 28, x8, 38, x7, 48, x6, 58, x5, 68, x4, 78, x3, 87, 1, 98, x1], [88, 9, x10, 19, x9, 29, x8, 39, x7, 49, x6, 59, x5, 69, x4, 79, x3, 88, 1, 99, x1], [89, 10, x10, 20, x9, 30, x8, 40, x7, 50, x6, 60, x5, 70, x4, 80, x3, 89, 1, 100, x1], [90, 90, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [91, 2, x10, 12, x9, 22, x8, 32, x7, 42, x6, 52, x5, 62, x4, 72, x3, 82, x2, 91, 1], [92, 3, x10, 13, x9, 23, x8, 33, x7, 43, x6, 53, x5, 63, x4, 73, x3, 83, x2, 92, 1], [93, 4, x10, 14, x9, 24, x8, 34, x7, 44, x6, 54, x5, 64, x4, 74, x3, 84, x2, 93, 1], [94, 5, x10, 15, x9, 25, x8, 35, x7, 45, x6, 55, x5, 65, x4, 75, x3, 85, x2, 94, 1], [95, 6, x10, 16, x9, 26, x8, 36, x7, 46, x6, 56, x5, 66, x4, 76, x3, 86, x2, 95, 1], [96, 7, x10, 17, x9, 27, x8, 37, x7, 47, x6, 57, x5, 67, x4, 77, x3, 87, x2, 96, 1], [97, 8, x10, 18, x9, 28, x8, 38, x7, 48, x6, 58, x5, 68, x4, 78, x3, 88, x2, 97, 1], [98, 9, x10, 19, x9, 29, x8, 39, x7, 49, x6, 59, x5, 69, x4, 79, x3, 89, x2, 98, 1], [99, 10, x10, 20, x9, 30, x8, 40, x7, 50, x6, 60, x5, 70, x4, 80, x3, 90, x2, 99, 1], [100, 100, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [101, 1, x10, 11, x9, 21, x8, 31, x7, 41, x6, 51, x5, 61, x4, 71, x3, 81, x2, 91, x1] ] ): m := matrix(101, 101, 0): fill := proc() global m, w; local i, j; for i from 1 to 101 do for j from 1 to 10 do m[i, w[i, 2*j]] := w[i, 2*j+1] od od end: fill(): det(m): w := 'w': m := 'm': # ----------------------------------------------------------------------------- # N res := p11*p22*q1^2*q4^2-p12*p21*q1^2*q4^2-n22*p11*p22*q1*q4^2+2*n11*p11*p22*q1*q4^2- p11*p22*q1*q4^2+n22*p12*p21*q1*q4^2-2*n11*p12*p21*q1*q4^2+p12*p21*q1*q4^2+2*g^2* p11*p22*q4^2-2*n11*n22*p11*p22*q4^2+2*n22*p11*p22*q4^2+2*n11*p11*p22*q4^2-2*p11*p22* q4^2-2*g^2*p12*p21*q4^2+2*n11*n22*p12*p21*q4^2-2*n22*p12*p21*q4^2-2*n11*p12*p21*q4^2+ 2*p12*p21*q4^2-n11*p22*q1*q2*q3*q4+g*p21*q1*q2*q3*q4+g*p12*q1*q2*q3*q4-n22*p11* q1*q2*q3*q4-g^2*p22*q2*q3*q4+n11*n22*p22*q2*q3*q4-n11*p22*q2*q3*q4-2*g*p21*q2*q3* q4+g*p12*q2*q3*q4+2*g^2*p11*q2*q3*q4-2*n11*n22*p11*q2*q3*q4+2*n22*p11*q2*q3*q4-n11* p22*q1*q3*q4+p22*q1*q3*q4+g*p21*q1*q3*q4-2*g*p12*q1*q3*q4+2*n22*p11*q1*q3*q4-2*p11* q1*q3*q4-g^2*p22*q3*q4+n11*n22*p22*q3*q4-n22*p22*q3*q4-n11*p22*q3*q4+p22*q3*q4- 4*g^2*p11*q3*q4+4*n11*n22*p11*q3*q4-4*n22*p11*q3*q4-4*n11*p11*q3*q4+4*p11*q3*q4+ n22*p11*p22*q1*q2*q4-2*n11*p11*p22*q1*q2*q4+2*n11*p22*q1*q2*q4-n22*p12*p21*q1*q2* q4+2*n11*p12*p21*q1*q2*q4+g*p21*q1*q2*q4-2*g*p12*q1*q2*q4-n22*p11*q1*q2*q4-4*g^2* p11*p22*q2*q4+4*n11*n22*p11*p22*q2*q4-2*n22*p11*p22*q2*q4-2*n11*p11*p22*q2*q4+2*g^2* p22*q2*q4-2*n11*n22*p22*q2*q4+2*n11*p22*q2*q4+4*g^2*p12*p21*q2*q4-4*n11*n22*p12*p21* q2*q4+2*n22*p12*p21*q2*q4+2*n11*p12*p21*q2*q4-2*g*p21*q2*q4-2*g*p12*q2*q4+2*g^2*p11* q2*q4-2*n11*n22*p11*q2*q4+2*n22*p11*q2*q4-p11*p22*q1^2*q4-p22*q1^2*q4+p12*p21*q1^2* q4+2*p11*q1^2*q4-n22*p11*p22*q1*q4-4*n11*p11*p22*q1*q4+5*p11*p22*q1*q4+n22*p22*q1* q4-p22*q1*q4+n22*p12*p21*q1*q4+4*n11*p12*p21*q1*q4-5*p12*p21*q1*q4+g*p21*q1*q4+ 4*g*p12*q1*q4+4*n11*p11*q1*q4-4*p11*q1*q4-g^2*q2^2*q3^2+n11*n22*q2^2*q3^2+g^2* q2*q3^2-n11*n22*q2*q3^2-n22*q2*q3^2+2*n11*q2*q3^2+2*g^2*q3^2-2*n11*n22*q3^2+2*n22* q3^2+2*n11*q3^2-2*q3^2+g^2*p22*q2^2*q3-n11*n22*p22*q2^2*q3-2*g^2*p11*q2^2*q3+2*n11* n22*p11*q2^2*q3+g^2*q2^2*q3-n11*n22*q2^2*q3+2*n11*p22*q1*q2*q3-2*g*p21*q1*q2*q3+ g*p12*q1*q2*q3-n22*p11*q1*q2*q3+n22*q1*q2*q3-2*n11*q1*q2*q3+g^2*p22*q2*q3-n11* n22*p22*q2*q3+n22*p22*q2*q3+4*g*p21*q2*q3+g*p12*q2*q3+4*g^2*p11*q2*q3-4*n11*n22* p11*q2*q3+4*n11*p11*q2*q3-5*g^2*q2*q3+5*n11*n22*q2*q3-n22*q2*q3-4*n11*q2*q3+2*n11* p22*q1*q3-2*p22*q1*q3-2*g*p21*q1*q3-2*g*p12*q1*q3+2*n22*p11*q1*q3-2*p11*q1*q3-2*n22* q1*q3-2*n11*q1*q3+4*q1*q3+2*g^2*p11*p22*q2^2-2*n11*n22*p11*p22*q2^2-2*g^2*p22*q2^2+ 2*n11*n22*p22*q2^2-2*g^2*p12*p21*q2^2+2*n11*n22*p12*p21*q2^2-2*g^2*p11*q2^2+2*n11* n22*p11*q2^2+2*g^2*q2^2-2*n11*n22*q2^2+n22*p11*p22*q1*q2+4*n11*p11*p22*q1*q2-n22* p22*q1*q2-4*n11*p22*q1*q2-n22*p12*p21*q1*q2-4*n11*p12*p21*q1*q2-n22*p11*q1*q2-4* n11*p11*q1*q2+n22*q1*q2+4*n11*q1*q2-2*p11*p22*q1^2+2*p22*q1^2+2*p12*p21*q1^2+2*p11* q1^2-2*q1^2: ss1 := (4*g*a22^3-g*a12*a21*a22^2-4*n22*a21*a22^2+4*n11*a21*a22^2+7*g*a12*a22^2+4*g^2*a22^2- 4*n11*n22*a22^2+4*n11*a22^2+n22*a12*a21^2*a22-n11*a12*a21^2*a22-4*g*a21^2*a22- g*a12^2*a21*a22-5*g^2*a12*a21*a22+5*n11*n22*a12*a21*a22-7*n22*a12*a21*a22+2*n11*a12* a21*a22-4*g*a21*a22+3*g*a12^2*a22+3*g^2*a12*a22-3*n11*n22*a12*a22+3*n11*a12*a22+g* a12*a21^3+g^2*a12^2*a21^2-n11*n22*a12^2*a21^2+n22*a12^2*a21^2-2*g*a12*a21^2-3*g^2* a12^2*a21+3*n11*n22*a12^2*a21-3*n22*a12^2*a21-3*g*a12*a21)/(3*g*a12*a21*a22^2-3*n22* a21*a22^2+g*a12*a22^2-n22*a22^2+3*n11*a12*a21^2*a22-3*g*a21^2*a22+5*g*a12^2*a21* a22-5*n22*a12*a21*a22+4*n11*a12*a21*a22-4*g*a21*a22+g*a12^2*a22-n22*a12*a22+n11* a12*a22-g*a22+2*n11*a12^2*a21^2-2*g*a12*a21^2+2*g*a12^3*a21-2*n22*a12^2*a21+2*n11* a12^2*a21-2*g*a12*a21): ss2 := (4*g*a12*a22^2-4*n22*a22^2+4*a22^2-g*a12^2*a21*a22+n22*a12*a21*a22+4*n11*a12*a21* a22-5*a12*a21*a22-4*g*a21*a22+3*g*a12^2*a22-3*n22*a12*a22+3*a12*a22-n11*a12^2*a21^2+ a12^2*a21^2+g*a12*a21^2+3*n11*a12^2*a21-3*a12^2*a21-3*g*a12*a21)/(2*g*a12*a22^2- 2*n22*a22^2+g*a12^2*a21*a22-n22*a12*a21*a22+2*n11*a12*a21*a22-2*g*a21*a22+2*g*a12^2* a22-2*n22*a12*a22+2*n11*a12*a22-2*g*a22+n11*a12^2*a21^2-g*a12*a21^2+g*a12^3*a21- n22*a12^2*a21+n11*a12^2*a21-g*a12*a21): ss3 := (4*p21*a22^3-p21*a12*a21*a22^2-4*p22*a21*a22^2+4*p11*a21*a22^2+7*p21*a12*a22^2-4* p11*p22*a22^2+4*p12*p21*a22^2+4*p11*a22^2+p22*a12*a21^2*a22-p11*a12*a21^2*a22-4* p12*a21^2*a22-p21*a12^2*a21*a22+5*p11*p22*a12*a21*a22-7*p22*a12*a21*a22-5*p12*p21* a12*a21*a22+2*p11*a12*a21*a22-4*p12*a21*a22+3*p21*a12^2*a22-3*p11*p22*a12*a22+3*p12* p21*a12*a22+3*p11*a12*a22+p12*a12*a21^3-p11*p22*a12^2*a21^2+p22*a12^2*a21^2+p12* p21*a12^2*a21^2-2*p12*a12*a21^2+3*p11*p22*a12^2*a21-3*p22*a12^2*a21-3*p12*p21*a12^2* a21-3*p12*a12*a21)/(3*p21*a12*a21*a22^2-3*p22*a21*a22^2+p21*a12*a22^2-p22*a22^2+ 3*p11*a12*a21^2*a22-3*p12*a21^2*a22+5*p21*a12^2*a21*a22-5*p22*a12*a21*a22+4*p11*a12* a21*a22-4*p12*a21*a22+p21*a12^2*a22-p22*a12*a22+p11*a12*a22-p12*a22+2*p11*a12^2* a21^2-2*p12*a12*a21^2+2*p21*a12^3*a21-2*p22*a12^2*a21+2*p11*a12^2*a21-2*p12*a12*a21): ss4 := (4*p21*a12*a22^2-4*p22*a22^2+4*a22^2-p21*a12^2*a21*a22+p22*a12*a21*a22+4*p11*a12* a21*a22-5*a12*a21*a22-4*p12*a21*a22+3*p21*a12^2*a22-3*p22*a12*a22+3*a12*a22-p11*a12^2* a21^2+a12^2*a21^2+p12*a12*a21^2+3*p11*a12^2*a21-3*a12^2*a21-3*p12*a12*a21)/(2*p21* a12*a22^2-2*p22*a22^2+p21*a12^2*a21*a22-p22*a12*a21*a22+2*p11*a12*a21*a22-2*p12* a21*a22+2*p21*a12^2*a22-2*p22*a12*a22+2*p11*a12*a22-2*p12*a22+p11*a12^2*a21^2-p12* a12*a21^2+p21*a12^3*a21-p22*a12^2*a21+p11*a12^2*a21-p12*a12*a21): q1 := ss1: q2 := ss2: q3 := ss3: q4 := ss4: res; normal(%); simplify(%); res := 'res': ss1 := 'ss1': ss2 := 'ss2': ss3 := 'ss3': ss4 := 'ss4': q1 := 'q1': q2 := 'q2': q3 := 'q3': q4 := 'q4': # ----------------------------------------------------------------------------- # O1 and O2 f := a6*y^2 + a5*y*z + a4*y*w + a3*z^2 + a2*z*w + a1*w^2: g := b6*y^2 + b5*y*z + b4*y*w + b3*z^2 + b2*z*w + b1*w^2: h := c6*y^2 + c5*y*z + c4*y*w + c3*z^2 + c2*z*w + c1*w^2: d1 := matrix([ [ a6, a5, a4, a3, a2, a1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0], [0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0], [0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0], [0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0], [0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1], [0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0], [0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0], [0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0], [0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1], [0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1], [0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0], [0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0 ] ]): d2 := matrix([[ b6, b5, b4, b3, b2, b1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0], [0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0], [0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0], [0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0], [0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1], [0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0], [0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0], [0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0], [0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1], [0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1], [0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0], [0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0 ] ]): d3 := matrix([ [ c6, c5, c4, c3, c2, c1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0], [0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0], [0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0], [0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0], [0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1], [0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0], [0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0], [0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0], [0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1], [0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1], [0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0], [0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0 ] ]): # O1 det1 := det(d1): det2 := det(d2): det3 := det(d3): # O2 gcd(gcd(det1, det2), det3): factor(%); f := 'f': g := 'g': h := 'h': d1 := 'd1': d2 := 'd2': d3 := 'd3': det1 := 'det1': det2 := 'det2': det3 := 'det3': # ----------------------------------------------------------------------------- # P, Pp, P', P'p, Q, Qp, Q', Q'p, T and W1 d := matrix([[-517,-540,-90,-353,-1086,-1315,-187,168,-317,-1426,-754,-83,542,-215,538,-1471,-885,-925,373,1344], [ 1210,-716,-1241,-444,50,168,1162,-233,1325,185,769,519,1187,760,1332,849,-795,-956,-956,461], [ -500,1003,-1447,-180,678,-195,446,1447,-342,141,-779,294,879,-119,86,-888,746,911,1209,-85], [ 294,-967,1224,842,1120,803,584,-325,-1257,-1497,50,-343,1088,-293,1491,-841,421,-880,-678,-758], [ -793,-193,290,-1254,14,-713,-1359,-1255,1424,517,785,1157,-640,-873,851,611,669,1450,105,918], [ -1369,515,289,1231,-1206,-991,1342,899,851,-1355,505,-1462,268,376,414,1099,-1297,97,-565,751], [ 178,548,1170,-744,130,-1238,111,-447,-788,-285,374,-293,-424,-1364,-394,899,-1031,-524,403,-436], [ 557,-414,-130,311,-1346,-1439,-293,1341,420,-775,-999,-1457,-1183,-819,303,-661,407,177,-327,820], [ 539,-64,-613,1164,-827,931,1361,1050,1260,362,-977,-634,1105,-1172,653,-658,-1426,-264,507,-272], [ 392,253,92,895,-487,619,1286,-124,-743,-904,824,180,511,-57,1362,642,-14,782,386,-396], [ -685,-934,483,-659,-13,-232,861,1076,-950,-671,1414,-769,260,28,232,-1037,636,-1180,1116,1310], [ 1319,-276,-936,-1149,873,196,-1488,-626,-150,-1172,-1319,-92,-1163,659,345,1036,-265,-587,-959,-986], [ -81,1015,1062,-1162,907,-555,-51,712,-706,277,-300,1061,-1067,449,-1453,-1296,3,1034,-238,383], [ 1150,-460,-1073,-907,255,-1407,-872,-1433,-282,705,925,-263,1367,740,40,1425,88,-418,-86,1175], [ -1491,791,-1476,1150,-496,-809,-781,98,715,1372,157,-397,1460,732,576,1265,-133,1083,-945,95], [-1302,1271,-371,66,-468,484,-217,175,-1254,1274,267,-609,-1161,-1497,-607,-104,-1418,-444,-1403,1259], [ -1015,1351,893,557,-631,1172,1308,-1196,996,104,972,346,-810,198,-690,52,-1137,1373,-708,662], [ 627,-266,-478,1109,-874,1399,735,874,-46,-802,962,1494,1193,-742,524,969,-668,-758,-1346,1207], [ -705,1356,-123,-100,-1343,-603,-756,-643,-637,61,879,15,-1009,244,89,-51,-257,-1289,511,-1093], [ 599,1079,-976,1486,852,-685,-378,-386,1333,814,1483,-1171,-383,845,729,244,304,533,810,-724 ]]): w := matrix([ [ 1, 1, 1, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [ 2, 2, 1, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [ 3, 3, 1, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [ 4, 4, 1, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [ 5, 5, 1, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [ 6, 6, 1, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [ 7, 7, 1, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [ 8, 8, 1, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [ 9, 9, 1, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [10, 10, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [11, 2, 10, 11, 1, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [12, 3, 10, 12, 1, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [13, 4, 10, 13, 1, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [14, 5, 10, 14, 1, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [15, 6, 10, 15, 1, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [16, 7, 10, 16, 1, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [17, 8, 10, 17, 1, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [18, 9, 10, 18, 1, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [19, 10, 10, 19, 1, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [20, 20, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [21, 2, 10, 12, 9, 21, 1, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [22, 3, 10, 13, 9, 22, 1, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [23, 4, 10, 14, 9, 23, 1, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [24, 5, 10, 15, 9, 24, 1, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [25, 6, 10, 16, 9, 25, 1, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [26, 7, 10, 17, 9, 26, 1, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [27, 8, 10, 18, 9, 27, 1, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [28, 9, 10, 19, 9, 28, 1, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [29, 10, 10, 20, 9, 29, 1, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [30, 30, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [31, 2, 10, 12, 9, 22, 8, 31, 1, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [32, 3, 10, 13, 9, 23, 8, 32, 1, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [33, 4, 10, 14, 9, 24, 8, 33, 1, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [34, 5, 10, 15, 9, 25, 8, 34, 1, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [35, 6, 10, 16, 9, 26, 8, 35, 1, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [36, 7, 10, 17, 9, 27, 8, 36, 1, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [37, 8, 10, 18, 9, 28, 8, 37, 1, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [38, 9, 10, 19, 9, 29, 8, 38, 1, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [39, 10, 10, 20, 9, 30, 8, 39, 1, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [40, 40, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [41, 2, 10, 12, 9, 22, 8, 32, 7, 41, 1, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ], [42, 3, 10, 13, 9, 23, 8, 33, 7, 42, 1, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ], [43, 4, 10, 14, 9, 24, 8, 34, 7, 43, 1, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ], [44, 5, 10, 15, 9, 25, 8, 35, 7, 44, 1, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ], [45, 6, 10, 16, 9, 26, 8, 36, 7, 45, 1, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ], [46, 7, 10, 17, 9, 27, 8, 37, 7, 46, 1, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ], [47, 8, 10, 18, 9, 28, 8, 38, 7, 47, 1, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ], [48, 9, 10, 19, 9, 29, 8, 39, 7, 48, 1, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ], [49, 10, 10, 20, 9, 30, 8, 40, 7, 49, 1, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ], [50, 50, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [51, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 51, 1, 62, 4, 72, 3, 82, 2, 92, 1 ], [52, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 52, 1, 63, 4, 73, 3, 83, 2, 93, 1 ], [53, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 53, 1, 64, 4, 74, 3, 84, 2, 94, 1 ], [54, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 54, 1, 65, 4, 75, 3, 85, 2, 95, 1 ], [55, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 55, 1, 66, 4, 76, 3, 86, 2, 96, 1 ], [56, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 56, 1, 67, 4, 77, 3, 87, 2, 97, 1 ], [57, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 57, 1, 68, 4, 78, 3, 88, 2, 98, 1 ], [58, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 58, 1, 69, 4, 79, 3, 89, 2, 99, 1 ], [59, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 59, 1, 70, 4, 80, 3, 90, 2, 100, 1 ], [60, 60, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [61, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 61, 1, 72, 3, 82, 2, 92, 1 ], [62, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 62, 1, 73, 3, 83, 2, 93, 1 ], [63, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 63, 1, 74, 3, 84, 2, 94, 1 ], [64, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 64, 1, 75, 3, 85, 2, 95, 1 ], [65, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 65, 1, 76, 3, 86, 2, 96, 1 ], [66, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 66, 1, 77, 3, 87, 2, 97, 1 ], [67, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 67, 1, 78, 3, 88, 2, 98, 1 ], [68, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 68, 1, 79, 3, 89, 2, 99, 1 ], [69, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 69, 1, 80, 3, 90, 2, 100, 1 ], [70, 70, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [71, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 71, 1, 82, 2, 92, 1 ], [72, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 72, 1, 83, 2, 93, 1 ], [73, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 73, 1, 84, 2, 94, 1 ], [74, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 74, 1, 85, 2, 95, 1 ], [75, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 75, 1, 86, 2, 96, 1 ], [76, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 76, 1, 87, 2, 97, 1 ], [77, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 77, 1, 88, 2, 98, 1 ], [78, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 78, 1, 89, 2, 99, 1 ], [79, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 79, 1, 90, 2, 100, 1 ], [80, 80, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [81, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 81, 1, 92, 1 ], [82, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 82, 1, 93, 1 ], [83, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 83, 1, 94, 1 ], [84, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 84, 1, 95, 1 ], [85, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 85, 1, 96, 1 ], [86, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 86, 1, 97, 1 ], [87, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 87, 1, 98, 1 ], [88, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 88, 1, 99, 1 ], [89, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 89, 1, 100, 1 ], [90, 90, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [91, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 91, 1 ], [92, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 92, 1 ], [93, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 93, 1 ], [94, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 94, 1 ], [95, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 95, 1 ], [96, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 96, 1 ], [97, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 97, 1 ], [98, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 98, 1 ], [99, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 99, 1 ], [100, 100, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ], [101, 1, 10, 11, 9, 21, 8, 31, 7, 41, 6, 51, 5, 61, 4, 71, 3, 81, 2, 91, 1 ] ] ): m := matrix(101, 101, 0): fill := proc() global m, w; local i, j; for i from 1 to 101 do for j from 1 to 10 do m[i, w[i, 2*j]] := w[i, 2*j+1] od od end: fill(): # P det(m): # Q charpoly(m, lambda): # T ihermite(m): # W1 ismith(m): mm := matrix(101, 101, (i, j) -> m[i, j] mod 181): # Pp Det(mm) mod 181: # Qp charpoly(mm, lambda) mod 181: m2 := matrix(101, 101, (i, j) -> m[i, j]): fill2 := proc() global m2; local a, i, j; for i from 1 to 101 do a := m2[i, 1]; for j from 1 to 100 do m2[i, j] := m2[i, j+1] od; m2[i, 101] := a od end: fill3 := proc() global m, m2; local i, j; for i from 1 to 101 do for j from 1 to 101 do if m[i, j] <> 0 then m2[i, j] := m[i, j] fi od od end: fill2(): fill3(): # P' det(m2): # Q' charpoly(m2, lambda): mm2 := matrix(101, 101, (i, j) -> m2[i, j] mod 181): # P'p Det(mm2) mod 181: # Q'p charpoly(mm2, lambda) mod 181: d := 'd': w := 'w': m := 'm': mm := 'mm': m2 := 'm2': mm2 := 'mm2': # ----------------------------------------------------------------------------- # S and U d := matrix([[-517,-540,-90,-353,-1086,-1315,-187,168,-317,-1426,-754,-83,542,-215,538,-1471,-885,-925,373,1344], [ 1210,-716,-1241,-444,50,168,1162,-233,1325,185,769,519,1187,760,1332,849,-795,-956,-956,461], [ -500,1003,-1447,-180,678,-195,446,1447,-342,141,-779,294,879,-119,86,-888,746,911,1209,-85], [ 294,-967,1224,842,1120,803,584,-325,-1257,-1497,50,-343,1088,-293,1491,-841,421,-880,-678,-758], [ -793,-193,290,-1254,14,-713,-1359,-1255,1424,517,785,1157,-640,-873,851,611,669,1450,105,918], [ -1369,515,289,1231,-1206,-991,1342,899,851,-1355,505,-1462,268,376,414,1099,-1297,97,-565,751], [ 178,548,1170,-744,130,-1238,111,-447,-788,-285,374,-293,-424,-1364,-394,899,-1031,-524,403,-436], [ 557,-414,-130,311,-1346,-1439,-293,1341,420,-775,-999,-1457,-1183,-819,303,-661,407,177,-327,820], [ 539,-64,-613,1164,-827,931,1361,1050,1260,362,-977,-634,1105,-1172,653,-658,-1426,-264,507,-272], [ 392,253,92,895,-487,619,1286,-124,-743,-904,824,180,511,-57,1362,642,-14,782,386,-396], [ -685,-934,483,-659,-13,-232,861,1076,-950,-671,1414,-769,260,28,232,-1037,636,-1180,1116,1310], [ 1319,-276,-936,-1149,873,196,-1488,-626,-150,-1172,-1319,-92,-1163,659,345,1036,-265,-587,-959,-986], [ -81,1015,1062,-1162,907,-555,-51,712,-706,277,-300,1061,-1067,449,-1453,-1296,3,1034,-238,383], [ 1150,-460,-1073,-907,255,-1407,-872,-1433,-282,705,925,-263,1367,740,40,1425,88,-418,-86,1175], [ -1491,791,-1476,1150,-496,-809,-781,98,715,1372,157,-397,1460,732,576,1265,-133,1083,-945,95], [-1302,1271,-371,66,-468,484,-217,175,-1254,1274,267,-609,-1161,-1497,-607,-104,-1418,-444,-1403,1259], [ -1015,1351,893,557,-631,1172,1308,-1196,996,104,972,346,-810,198,-690,52,-1137,1373,-708,662], [ 627,-266,-478,1109,-874,1399,735,874,-46,-802,962,1494,1193,-742,524,969,-668,-758,-1346,1207], [ -705,1356,-123,-100,-1343,-603,-756,-643,-637,61,879,15,-1009,244,89,-51,-257,-1289,511,-1093], [ 599,1079,-976,1486,852,-685,-378,-386,1333,814,1483,-1171,-383,845,729,244,304,533,810,-724 ]]): # S ihermite(d): # U ismith(d): d := 'd': # ----------------------------------------------------------------------------- # V z:=matrix([[-271,3050530,-91160,38029376,1055567244,63951178,124789174,170725207,4044,-85971,-48175890,-38362416,-49920,257920,169561,-3176995,-3598707917,-10143059,545091351,99792,-63663280,720,69990947,16103771108,50083241,-47547320,-47512696,-9227925,27813563,63397407,-2381,0,-47589601,-266269036,63730092,0,5374463054,-3011287,467631761,-81916066,15847356,-940211231,-13331724,-947172331,951195982,-4,-20465309,266303389,179984610,-27889228,0,-141306,0,47620312,6339290,-3760844920,237736450,-5367924084,-5705683,-316964281],[ 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20: m2 := matrix(n^2+1, n^2+1, 0): for i from 1 to n^2 do m2[i, i] := 1 od: for i from 1 to n^2 do if i mod n = 0 then m2[i, n^2+1] := 1 fi od: for i from 1 to n^2 do if (i - 1) mod n = 0 then m2[n^2+1, i] := n - (i - 1)/n fi od: for i from 1 to n do for j from 1 to n do if i <> j then for k from 1 to n-1 do m2[(i-1)*n+k, (j-1)*n+k+1] := n + 1 - j od fi od od: ismith(m2): j := 'j': k := 'k': m2 := 'm2': # ----------------------------------------------------------------------------- # X and Y t:= RootOf(_Z^2 + 1): # X p4 := expand((7*t*y*x^2*z^2 - 3*t + t*x*y*z + 11*(x + 1 + t)*y^2 + 5*z + t + 1)^4 *(3*t*x - 7*t*y + 2*z - 3*t + 1)^5) mod 17027: q4 := expand((7*t*y*x^2*z^2 - 3*t + t*x*y*z + 11*(x + 1 + t)*y^2 + 5*z + t + 1)^3 *(3*t*x - 7*t*y + 2*z + 3*t - 1)^6) mod 17027: Gcd(p4, q4) mod 17027: Factor(%) mod 17027; p4 := 'p4': q4 := 'q4': # Y w := matrix([ [ 1, 1, 1, 7, z , 12, y , 17, x , 22, t ], [ 2, 2, 1, 8, z , 13, y , 18, x , 23, t ], [ 3, 3, 1, 9, z , 14, y , 19, x , 24, t ], [ 4, 4, 1, 10, z , 15, y , 20, x , 25, t ], [ 5, 5, 1, 26, 1, 1, 0, 1, 0, 1, 0 ], [ 6, 2, x , 6, 1, 12, y , 17, x , 22, t ], [ 7, 3, x , 7, 1, 13, y , 18, x , 23, t ], [ 8, 4, x , 8, 1, 14, y , 19, x , 24, t ], [ 9, 5, x , 9, 1, 15, y , 20, x , 25, t ], [10, 10, 1, 26, 1, 1, 0, 1, 0, 1, 0], [11, 2, x , 7, z , 11, 1, 17, x , 22, t ], [12, 3, t , 8, z , 12, 1, 18, x , 23, t ], [13, 4, t , 9, z , 13, 1, 19, x , 24, t ], [14, 5, t , 10, z , 14, 1, 20, x , 25, t ], [15, 15, 1, 26, 1, 1, 0, 1, 0, 1, 0], [16, 2, t , 7, z , 12, y , 16, 1, 22, t ], [17, 3, t , 8, z , 13, y , 17, 1, 23, t ], [18, 4, y , 9, z , 14, y , 18, 1, 24, t ], [19, 5, y , 10, z , 15, y , 19, 1, 25, t ], [20, 20, 1, 26, 1, 1, 0, 1, 0, 1, 0], [21, 2, y , 7, z , 12, y , 17, x , 21, 1], [22, 3, z , 8, z , 13, y , 18, x , 22, 1], [23, 4, z , 9, z , 14, y , 19, x , 23, 1], [24, 5, z , 10, z , 15, y , 20, x , 24, 1], [25, 25, 1, 26, 1, 1, 0, 1, 0, 1, 0], [26, 1, z , 6, z , 11, y , 16, x , 21, t ]]): m := matrix(26, 26, 0): fill := proc() global m, w; local i, j; for i from 1 to 26 do for j from 1 to 5 do m[i, w[i, 2*j]] := w[i, 2*j+1] od od end: fill(): Det(m) mod 17027: simplify(%); m := 'm': w := 'w': t := 't': # ---------- Quit ---------- quit