allocatemem(100*10^6); KILLTIME = 600; \\ 10 minutes default(debugmem,0); default(timer,0); \\------------------------------ A ----------------------------- { print1("A:\t");gettime(); for(i=1,100,(1000+i)!/(900+i)!); print("Time = ", gettime()); } \\------------------------------ B ----------------------------- { print1("B:\t");gettime(); sum(i=1,1000,1/i); print("Time = ", gettime()); } \\------------------------------ C ----------------------------- { x = 13 * 17 * 31; y = 13 * 19 * 29; print1("C:\t");gettime(); for (i = 1, 200, gcd(x^(300+ i % 181), y^(200 + i % 181))); print("Time = ", gettime()); } \\------------------------------ D ----------------------------- { y = 'y; t = 't; print1("D:\t");gettime(); sum( i = 1, 10, i*y*t^i / (y+i*t)^i ); print("Time = ", gettime()); } \\------------------------------ E ----------------------------- { y = 'y; t = 't; print1("E:\t");gettime(); sum( i = 1, 10, i*y*t^i / (y + abs(5-i)*t)^i ); print("Time = ", gettime()); } \\------------------------------ F ----------------------------- { x = 'x; y = '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; print1("F:\t");gettime(); qqq = gcd(p, q); print("Time = ", gettime()); \\factor(qqq); } \\------------------------------ G ----------------------------- { 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; print1("G:\t");gettime(); qqq = gcd(p, q); print("Time = ", gettime()); \\ Gp print1("Gp:\t");gettime(); qqqp= gcd(p * Mod(1,181), q * Mod(1,181)); print("Time = ", gettime()); } \\------------------------------ H ----------------------------- { h80 = mathilbert(80); print1("H:\t");gettime(); matdet(h80); print("Time = ", gettime()); } \\----------------------------- I/J ----------------------------- { h40 = mathilbert(40); print1("I:\t");gettime(); hinv= h40^(-1); print("Time = ", gettime()); print1("J:\t");gettime(); h40 * hinv; print("Time = ", gettime()); } \\----------------------------- K/L ----------------------------- { h70 = mathilbert(70); print1("K:\t");gettime(); hinv= h70^(-1); print("Time = ", gettime()); print1("L:\t");gettime(); h70 * hinv; print("Time = ", gettime()); } \\------------------------------ M1 ---------------------------- { 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, 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,i,j,0); for( i=1,26, for( j=1,5, m[i, w[i, 2*j] ] = w[i, 2*j+1])); print1("M1:\t");gettime(); matdet(m); print("Time = ", gettime()); } \\------------------------------ M2 ---------------------------- { 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, 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,i,j,0); for( i=1,101, for( j=1,10, m[i, w[i, 2*j] ] = w[i, 2*j+1])); print1("M2:\t");gettime(); matdet(m); print("Time = ", gettime()); } \\------------------------------ N ----------------------------- [q1,q2,q3,q4, l1, l2, n11, n22, g, p11, p12, p21, p22, a12, a21, a22]; { 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); } Ntest() = { print1("N:\t");gettime(); subst(subst(subst(subst(res, q1, ss1), q2, ss2), q3, ss3), q4, ss4); print("Time = ", gettime()); } print("N:\tTime = KD"); /* \\ > 10 min in 2.15 { E = alarm(KILLTIME, Ntest()); if (type(E) == "t_ERROR", if (errname(E) == "e_ALARM", print("Time = KD"), print("Time = CR"))) } */ \\------------------------------ O1 ----------------------------- { 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 ]; } \\ O1 O1test()= { print1("O1:\t");gettime(); det1 = matdet(d1); print("Time = ", gettime()); det2 = matdet(d2); print("Time = ", gettime()); det3 = matdet(d3); print("Time = ", gettime()); } { O1testfailed = 0; E = alarm(3 * KILLTIME, O1test()); if (type(E) == "t_ERROR", O1testfailed = 1; if (errname(E) == "e_ALARM", print("Time = KD"), print("Time = CR"))) } \\ O2 O2test()= { print1("O2:\t");gettime(); qqq = gcd([det1, det2, det3]); print("Time = ", gettime()); } { if (O1testfailed, print("O2:\tTime = UN"); , E = alarm(KILLTIME, O2test()); if (type(E) == "t_ERROR", if (errname(E) == "e_ALARM", print("Time = KD"), print("Time = CR")))) } \\------------------------------ P ----------------------------- \\ m3 is for P. m4 is for P', the less sparse m3 { fill(n, M) = for(i=1, n^2, M[i,i] = 1); for(i=1, n^2, if (i%n == 0, M[i,n^2+1] = 1) ); for(i=1, n^2, if (i%n == 1, M[n^2+1,i] = n-(i - 1)/n)); for( i = 1, n, for( j = 1, n, if (i == j, next); for( k = 1, n-1, M[(i-1)*n + k, (j-1)*n+k+1] = n+1-j) ) ); M; } { n = 10; m3 = fill(n, matrix(n^2+1, n^2+1,i,j,0)); m4 = m3; for(i=1, n^2+1, a = m4[i,1]; for(j=1, n^2, m4[i,j] = m4[i,j+1]); m4[i,n^2+1] = a ); m4 = fill(n, m4); } { \\ P print1("P:\t");gettime(); matdet(m3); print("Time = ", gettime()); \\ P' print1("P':\t");gettime(); matdet(m4); print("Time = ", gettime()); \\ Pp print1("Pp:\t");gettime(); matdet(m3 * Mod(1,181)); print("Time = ", gettime()); \\ Pp' print1("Pp':\t");gettime(); matdet(m4 * Mod(1,181)); print("Time = ", gettime()); } \\ Q { print1("Q:\t");gettime(); charpoly(m3,,2); print("Time = ", gettime()); \\ Q' print1("Q':\t");gettime(); charpoly(m4); print("Time = ", gettime()); \\ Qp print1("Qp:\t");gettime(); charpoly(m3 * Mod(1,181),,2); print("Time = ", gettime()); \\ Qp' print1("Qp':\t");gettime(); charpoly(m4 * Mod(1,181)); print("Time = ", gettime()); } \\------------------------------ 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; 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mathnfmod(m3, matdetint(m3)); print("Time = ", gettime()); } \\ U { print1("U:\t");gettime(); matsnf(d); print("Time = ", gettime()); } \\ V { print1("V:\t");gettime(); matsnf(s); print("Time = ", gettime()); } \\ W1 { print1("W1:\t");gettime(); matsnf(m3); print("Time = ", gettime()); } \\ W2 { n = 20; m2 = fill(n, matrix(n^2+1,n^2+1,i,j,0)); print1("W2:\t");gettime(); matsnf(m2); print("Time = ", gettime()); } \\------------------------------ X ----------------------------- { x;y;z;t; /* p = (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; q = (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; T = Mod(Mod(1, 17027), (t^2+1) * Mod(1,17027)); p *= T; q *= T; */ t = ffgen(('t^2+1) * Mod(1,17027)); p = (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; q = (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; print1("X:\t");gettime(); gcd(p,q); print("Time = ", gettime()); } \\------------------------------ Y ----------------------------- { w = [ 1,0,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0,0,0; 0,1,0,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0,0; 0,0,1,0,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0; 0,0,0,1,0,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0; 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1; 0,x,0,0,0,1,0,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0,0,0; 0,0,x,0,0,0,1,0,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0,0; 0,0,0,x,0,0,0,1,0,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0; 0,0,0,0,x,0,0,0,1,0,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0; 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1; 0,x,0,0,0,0,z,0,0,0,1,0,0,0,0,0,x,0,0,0,0,t,0,0,0,0; 0,0,t,0,0,0,0,z,0,0,0,1,0,0,0,0,0,x,0,0,0,0,t,0,0,0; 0,0,0,t,0,0,0,0,z,0,0,0,1,0,0,0,0,0,x,0,0,0,0,t,0,0; 0,0,0,0,t,0,0,0,0,z,0,0,0,1,0,0,0,0,0,x,0,0,0,0,t,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,t,0,0,0,0,z,0,0,0,0,y,0,0,0,1,0,0,0,0,0,t,0,0,0,0; 0,0,t,0,0,0,0,z,0,0,0,0,y,0,0,0,1,0,0,0,0,0,t,0,0,0; 0,0,0,y,0,0,0,0,z,0,0,0,0,y,0,0,0,1,0,0,0,0,0,t,0,0; 0,0,0,0,y,0,0,0,0,z,0,0,0,0,y,0,0,0,1,0,0,0,0,0,t,0; 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1; 0,y,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,1,0,0,0,0,0; 0,0,z,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,1,0,0,0,0; 0,0,0,z,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,1,0,0,0; 0,0,0,0,z,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,1,0,0; 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1; z,0,0,0,0,z,0,0,0,0,y,0,0,0,0,x,0,0,0,0,t,0,0,0,0,0 ]; print1("Y:\t");gettime(); matdet(w * T); print("Time = ", gettime()); }