We use here the Fermat syntax of the Windows version (Mac is slightly different, see the manual). To attach the polynomial variable x the syntax is &(J = x) in Windows, but in the Mac version a special symbol replaces the J. ; A for i = 1 to 100 do (1000 + i)!/(900 + i)! od: ; ----------------------------------------------------------------------------- ; B formerly A' Sigma [ 1/i ] ; ----------------------------------------------------------------------------- ; C formerly B x := 13*17*31: y := 13*19*29: for i = 1 to 200 do GCD(x^(300 + (i | 181)), y^(200 + (i | 183))) od ; ----------------------------------------------------------------------------- ; D formerly C &(J = t); &(J = y); s := 0: for i = 1 to 10 do s := s + i*y*t^i/(y + i*t)^i od ; ----------------------------------------------------------------------------- ; E formerly D &(J = t); &(J = y); s := 0: for i = 1 to 10 do s := s + i*y*t^i/(y + |(5 - i)|*t)^i od ; ----------------------------------------------------------------------------- ; F &(J = x); &(J = y); p := (x^2 - 3*x*y + y^2)^4*(3*x - 7*y + 2)^5: q := (x^2 - 3*x*y + y^2)^3*(3*x - 7*y - 2)^6: GCD(p, q): ; ----------------------------------------------------------------------------- ; G &(J = x); &(J = y); &(J = z); p := (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 := (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): ; ----------------------------------------------------------------------------- ; Gp &(J = x); &(J = y); &(J = z); &(p = 181); p := (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 := (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): ; ----------------------------------------------------------------------------- ; H, I, J, K and L ; H Array h[80,80]; for i = 1, 80 do for j= 1, 80 do h[i,j] := 1/(i+j-1) od od; Det[h] Array h[40,40]; for i = 1, 40 do for j= 1, 40 do h[i,j] := 1/(i+j-1) od od; ; I [w] := 1/[h]; ; J [z] := [w]*[h]; Array h[70,70]; for i = 1, 70 do for j= 1, 70 do h[i,j] := 1/(i+j-1) od od; ; K [w] := 1/[h]; ; L [z] := [w]*[h]; ---------------------------------------------------- Test M1: &(J = x1); &(J = x2); &(J = x3); &(J = x4); &(J = x5); Array w[26,26] Sparse; [w] := [ [ 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] ] [ 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] ] [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] ] [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] ] [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] ] [26, [ 1, x5 ], [ 6, x4 ], [11, x3 ], [16, x2 ], [21, x1 ] ] ]; ------------------------------------------ Test M2: &(J = x1); &(J = x2); &(J = x3); &(J = x4); &(J = x5); &(J = x6); &(J = x7); &(J = x8); &(J = x9); &(J = x10); Array w[101,101] Sparse; [w] := [ [ 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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [101, [ 1, x10], [11, x9], [21, x8], [31, x7], [41, x6], [51, x5], [61, x4], [71, x3], [81, x2], [91, x1] ] ]; ------------------------------------------ Test P, Pp, Q, Qp: (convert to ordinary arrray for Q and Qp) Array v[101,101] Sparse; [v] := [ [ 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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [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] ] [101, [ 1, 10], [11, 9], [21, 8], [31, 7], [41, 6], [51, 5], [61, 4], [71, 3], [81, 2], [91, 1] ] ]; ------------------------------------------------ Test P', P'p, Q', Q'p: n := 20; Array m2[n^2+1, n^2+1] Sparse; for i=1, n^2 do m2[i,i] := 1 od; for i=1, n^2 do if i|n=0 then m2[i,n^2+1] := 1 fi od; for i=1, n^2 do if (i-1)|n=0 then m2[n^2+1,i] := n-(i - 1)/n fi od; for i=1, n do for j=1,n do if iÇj then for k = 1, n-1 do m2[(i-1)*n + k, (j-1)*n+k+1] := n+1-j od fi od od; ------------------------------------------ Test S: [d]:= [[-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 ]]; ------------------------------------------ Test W2: Get the array from the Gp file. ------------------------------------------ Test N: &(J = n11); &(J = n22); &(J = g); &(J = p11); &(J = p12); &(J = p21); &(J = p22); &(J = q1); &(J = q2); &(J = q3); &(J = q4); &(J = a12); &(J = a21); &(J = a22); ss1 := (4g)a22^3 + (((-g)a12 - 4n22 + 4n11)a21 + (7g)a12 + 4g^2 + (-4n11)n22 + 4n11)a22^2 + (((n22 - n11)a12 - 4g)a21^2 + ((-g)a12^2 + (-5g^2 + (5n11 - 7)n22 + 2n11)a12 - 4g)a21 + (3g)a12^2 + (3g^2 + (-3n11)n22 + 3n11)a12)a22 + ((g)a12)a21^3 + ((g^2 + (-n11 + 1)n22)a12^2 + (-2g)a12)a21^2 + ((-3g^2 + ( 3n11 - 3)n22)a12^2 + (-3g)a12)a21 ) / ( (((3g)a12 - 3n22)a21 + (g)a12 - n22) a22^2 + (((3n11)a12 - 3g)a21^2 + ((5g)a12^2 + (-5n22 + 4n11)a12 - 4g)a21 + (g)a12^2 + (-n22 + n11)a12 - g)a22 + ((2n11)a12^2 + (-2g)a12)a21^2 + (( 2g)a12^3 + (-2n22 + 2n11)a12^2 + (-2g)a12)a21 ; ss2 := ((4g)a12 - 4n22 + 4)a22^2 + (((-g)a12^2 + (n22 + 4n11 - 5)a12 - 4g)a21 + (3g)a12^2 + (-3n22 + 3)a12)a22 + ((-n11 + 1)a12^2 + (g)a12)a21^2 + ((3n11 - 3)a12^2 + (-3g)a12)a21 ) / ( ((2g)a12 - 2n22)a22^2 + (((g)a12^2 + (-n22 + 2n11)a12 - 2g)a21 + (2g)a12^2 + (-2n22 + 2n11)a12 - 2g)a22 + ((n11)a12^2 + (-g)a12)a21^2 + ((g)a12^3 + (-n22 + n11)a12^2 + (-g)a12)a21 ; ss3 := (4p21)a22^3 + (((-p21)a12 - 4p22 + 4p11)a21 + (7p21)a12 + (-4p11)p22 + ( 4p12)p21 + 4p11)a22^2 + (((p22 - p11)a12 - 4p12)a21^2 + ((-p21)a12^2 + (( 5p11 - 7)p22 + (-5p12)p21 + 2p11)a12 - 4p12)a21 + (3p21)a12^2 + ((-3p11) p22 + (3p12)p21 + 3p11)a12)a22 + ((p12)a12)a21^3 + (((-p11 + 1)p22 + (p12) p21)a12^2 + (-2p12)a12)a21^2 + (((3p11 - 3)p22 + (-3p12)p21)a12^2 + (-3p12) a12)a21 ) / ( (((3p21)a12 - 3p22)a21 + (p21)a12 - p22)a22^2 + (((3p11)a12 - 3p12)a21^2 + ((5p21)a12^2 + (-5p22 + 4p11)a12 - 4p12)a21 + (p21)a12^2 + (-p22 + p11)a12 - p12)a22 + ((2p11)a12^2 + (-2p12)a12)a21^2 + ((2p21)a12^3 + (-2p22 + 2p11)a12^2 + (-2p12)a12)a21 ; ss4 := ((4p21)a12 - 4p22 + 4)a22^2 + (((-p21)a12^2 + (p22 + 4p11 - 5)a12 - 4p12)a21 + (3p21)a12^2 + (-3p22 + 3)a12)a22 + ((-p11 + 1)a12^2 + (p12)a12) a21^2 + ((3p11 - 3)a12^2 + (-3p12)a12)a21 ) / ( ((2p21)a12 - 2p22)a22^2 + ( ((p21)a12^2 + (-p22 + 2p11)a12 - 2p12)a21 + (2p21)a12^2 + (-2p22 + 2p11)a12 - 2p12)a22 + ((p11)a12^2 + (-p12)a12)a21^2 + ((p21)a12^3 + (-p22 + p11)a12^2 + (-p12)a12)a21 ; res1 := (((p11)p22 + (-p12)p21)q1^2 + (((-n22 + 2n11 - 1)p11)p22 + ((n22 - 2n11 + 1)p12)p21)q1 + ((2g^2 + (-2n11 + 2)n22 + 2n11 - 2)p11)p22 + ((-2g^2 + ( 2n11 - 2)n22 - 2n11 + 2)p12)p21)q4^2 + (((((-n11)p22 + (g)p21 + (g)p12 + (-n22)p11)q1 + (-g^2 + (n11)n22 - n11)p22 + (-2g)p21 + (g)p12 + (2g^2 + (- 2n11 + 2)n22)p11)q2 + ((-n11 + 1)p22 + (g)p21 + (-2g)p12 + (2n22 - 2)p11)q1 + (-g^2 + (n11 - 1)n22 - n11 + 1)p22 + (-4g^2 + (4n11 - 4)n22 - 4n11 + 4)p11)q3 + ((((n22 - 2n11)p11 + 2n11)p22 + ((-n22 + 2n11)p12 + g) p21 + (-2g)p12 + (-n22)p11)q1 + ((-4g^2 + (4n11 - 2)n22 - 2n11)p11 + 2g^2 + (-2n11)n22 + 2n11)p22 + ((4g^2 + (-4n11 + 2)n22 + 2n11)p12 - 2g)p21 + (-2g)p12 + (2g^2 + (-2n11 + 2)n22)p11)q2 + ((-p11 - 1)p22 + (p12) p21 + 2p11)q1^2 + (((-n22 - 4n11 + 5)p11 + n22 - 1)p22 + ((n22 + 4n11 - 5)p12 + g)p21 + (4g)p12 + (4n11 - 4)p11)q1)q4 + ((-g^2 + (n11)n22)q2^2 + (g^2 + (-n11 - 1)n22 + 2n11)q2 + 2g^2 + (-2n11 + 2)n22 + 2n11 - 2)q3^2 + (((g^2 + (-n11)n22)p22 + (-2g^2 + (2n11)n22)p11 + g^2 + (-n11)n22)q2^2 + (( (2n11)p22 + (-2g)p21 + (g)p12 + (-n22)p11 + n22 - 2n11)q1 + (g^2 + (-n11 + 1)n22)p22 + (4g)p21 + (g)p12 + (4g^2 + (-4n11)n22 + 4n11)p11 - 5g^2 + ( 5n11 - 1)n22 - 4n11)q2 + ((2n11 - 2)p22 + (-2g)p21 + (-2g)p12 + (2n22 - 2)p11 - 2n22 - 2n11 + 4)q1)q3 + (((2g^2 + (-2n11)n22)p11 - 2g^2 + ( 2n11)n22)p22 + ((-2g^2 + (2n11)n22)p12)p21 + (-2g^2 + (2n11)n22)p11 + 2g^2 + (-2n11)n22)q2^2 + ((((n22 + 4n11)p11 - n22 - 4n11)p22 + ((-n22 - 4n11)p12)p21 + (-n22 - 4n11)p11 + n22 + 4n11)q1)q2 + ((-2p11 + 2)p22 + (2p12)p21 + 2p11 - 2)q1^2 ; ------------------------------------------ Tests O1 and O2: &(J=w); &(J=y); &(J=z); &(J=a1); &(J=a2); &(J=a3); &(J=a4); &(J=a5); &(J=a6); &(J=b1); &(J=b2); &(J=b3); &(J=b4); &(J=b5); &(J=b6); &(J=c1); &(J=c2); &(J=c3); &(J=c4); &(J=c5); &(J=c6); 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] := [[ 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] := [[ 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] := [[ 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 ]]; Sparse[d1]; Sparse[d2]; Sparse[d3]; &(D=100); ------------------------------------------------ Tests X and Y: &(J = t); &(P = t^2 + 1, 1: 17027, 17047, 17099, 17419, 17431, 17467, 17471, 17491, 17519, 17551, 17579, 17627, 17659, 17827, 17839, 17863, 17891, 17923, 17959, 18043, 18047, 18143, 18191, 18287, 18371, 18439, 18523, 18539, 18583, 18671, 18743, 18787, 18911, 18919, 18979, 19031, 19079, 19183, 19207, 19259, 19267, 19403, 19507, 19531, 19687, 19751, 19891, 19927, 20011, 20023, 20107, 20147, 20183, 20219, 20231, 20323, 20479, 20507, 20743, 20747, 20759, 20771, 20879, 20903, 20963: 1741, 59, 1013, 45, 677, 26, 673, 58, 277, 60, 241, 64, 173, 80, 149, 44, 137, 37, 89, 34, 73, 27, 61, 11, 53, 23); &(J = x); &(J = y); &(J = z); &(p = 17027); Function F = p4 := (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 - 3t + 1)^5; q4 := (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 + 3t - 1)^6.; Array w[26,26] Sparse; [w] := [ [ 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] ] [ 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] ] [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] ] [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] ] [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] ] [26, [ 1, z ], [ 6, z ], [11, y ], [16, x ], [21, t ] ] ];