i1 : (ZZ[a_0, a_1, a_2])[x_0, x_1]; F=a_0*x_0^2+a_1*x_0*x_1+a_2*x_1^2 2 2 o2 = a x + a x x + a x 0 0 1 0 1 2 1 o2 : ZZ[a , a , a ][x , x ] 0 1 2 0 1 |
i3 : time Discriminant F -- used 0.0112861 seconds 2 o3 = - a + 4a a 1 0 2 o3 : ZZ[a , a , a ] 0 1 2 |
i4 : (ZZ[a_0, a_1, a_2, a_3])[x_0, x_1]; F=a_0*x_0^3+a_1*x_0^2*x_1+a_2*x_0*x_1^2+a_3*x_1^3 3 2 2 3 o5 = a x + a x x + a x x + a x 0 0 1 0 1 2 0 1 3 1 o5 : ZZ[a , a , a , a ][x , x ] 0 1 2 3 0 1 |
i6 : time Discriminant F -- used 0.0125578 seconds 2 2 3 3 2 2 o6 = - 3a a + 12a a + 12a a - 54a a a a + 81a a 1 2 0 2 1 3 0 1 2 3 0 3 o6 : ZZ[a , a , a , a ] 0 1 2 3 |
i7 : R=ZZ/331[x_0..x_3]; |
i8 : F=x_0^4+x_1^4+x_2^4+x_3^4 4 4 4 4 o8 = x + x + x + x 0 1 2 3 o8 : R |
i9 : G=x_0^4-x_0*x_1^3-x_2^4+x_2*x_3^3 4 3 4 3 o9 = x - x x - x + x x 0 0 1 2 2 3 o9 : R |
i10 : R'=ZZ/331[t_0,t_1][x_0..x_3]; |
i11 : pencil=t_0*sub(F,R')+t_1*sub(G,R') 4 3 4 4 3 4 o11 = (t + t )x - t x x + t x + (t - t )x + t x x + t x 0 1 0 1 0 1 0 1 0 1 2 1 2 3 0 3 o11 : R' |
i12 : time D=Discriminant pencil -- used 2.94415 seconds 108 106 2 102 6 100 8 98 10 96 12 o12 = - 62t + 19t t + 160t t + 91t t + 129t t + 117t t + 0 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 94 14 92 16 90 18 88 20 86 22 84 24 161t t + 124t t - 82t t - 21t t - 49t t - 123t t + 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 82 26 80 28 78 30 76 32 74 34 72 36 5t t - 4t t + 75t t + 103t t + 47t t + 108t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 70 38 68 40 66 42 64 44 62 46 60 48 62t t - 97t t - 131t t + 71t t - 68t t - 144t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 58 50 56 52 54 54 52 56 50 58 48 60 163t t + 10t t - 35t t + 105t t + 7t t + 10t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 46 62 44 64 42 66 40 68 38 70 36 72 3t t + 76t t - 152t t - 81t t + 106t t - 11t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 34 74 32 76 30 78 28 80 26 82 24 84 13t t + 17t t + 18t t + 88t t + 9t t + 58t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 22 86 20 88 18 90 16 92 14 94 12 96 73t t + 113t t - 154t t - 102t t - 161t t + 33t t - 0 1 0 1 0 1 0 1 0 1 0 1 ----------------------------------------------------------------------- 10 98 8 100 6 102 4 104 2 106 108 130t t - 21t t + 157t t + 105t t + 82t t + 69t 0 1 0 1 0 1 0 1 0 1 1 ZZ o12 : ---[t , t ] 331 0 1 |
i13 : factor D 9 9 9 9 18 18 2 2 9 2 2 9 o13 = (128t - t ) (128t + t ) (11t - t ) (11t + t ) (t - t ) (t + t ) (39t - 139t t + t ) (39t + 139t t + t ) (69) 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 o13 : Expression of class Product |