i1 : K = ZZ/33331; ringP5 = K[x_0..x_5]; |
i3 : -- Farkas-Verra surface S = ideal(x_0*x_2*x_3-2*x_1*x_2*x_3-x_1*x_3^2-x_2*x_3^2-x_0*x_1*x_4+2*x_1^2*x_4-x_1*x_2*x_4+x_2^2*x_4+2*x_0*x_3*x_4-x_1*x_3*x_4-x_1*x_4^2+x_1*x_3*x_5, x_1^2*x_3-4*x_1*x_2*x_3-x_0*x_3^2-3*x_1*x_3^2-2*x_2*x_3^2+2*x_0^2*x_4-9*x_0*x_1*x_4+11*x_1^2*x_4-x_0*x_2*x_4-2*x_1*x_2*x_4+2*x_2^2*x_4+12*x_0*x_3*x_4-7*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-6*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+2*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2, x_0*x_1*x_3-7*x_1*x_2*x_3-3*x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+x_3^3+3*x_0^2*x_4-14*x_0*x_1*x_4+17*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+19*x_0*x_3*x_4-9*x_1*x_3*x_4-x_2*x_3*x_4-6*x_3^2*x_4+x_0*x_4^2-9*x_1*x_4^2+6*x_2*x_4^2-3*x_3*x_4^2-3*x_4^3-2*x_0*x_1*x_5+2*x_1^2*x_5+4*x_1*x_2*x_5+5*x_0*x_3*x_5+4*x_1*x_3*x_5-2*x_3^2*x_5-2*x_0*x_4*x_5-7*x_1*x_4*x_5+5*x_2*x_4*x_5+3*x_3*x_4*x_5-2*x_1*x_5^2, x_0^2*x_3-12*x_1*x_2*x_3-6*x_0*x_3^2-6*x_1*x_3^2-5*x_2*x_3^2+2*x_3^3+5*x_0^2*x_4-24*x_0*x_1*x_4+29*x_1^2*x_4-x_0*x_2*x_4-5*x_1*x_2*x_4+5*x_2^2*x_4+32*x_0*x_3*x_4-14*x_1*x_3*x_4-2*x_2*x_3*x_4-10*x_3^2*x_4+x_0*x_4^2-15*x_1*x_4^2+10*x_2*x_4^2-5*x_3*x_4^2-5*x_4^3-3*x_0*x_1*x_5+3*x_1^2*x_5+6*x_1*x_2*x_5+8*x_0*x_3*x_5+7*x_1*x_3*x_5-3*x_3^2*x_5-3*x_0*x_4*x_5-11*x_1*x_4*x_5+8*x_2*x_4*x_5+5*x_3*x_4*x_5-3*x_1*x_5^2, x_1*x_2^2+6*x_1*x_2*x_3+2*x_0*x_3^2+3*x_1*x_3^2+2*x_2*x_3^2-x_3^3-3*x_0^2*x_4+12*x_0*x_1*x_4-14*x_1^2*x_4-2*x_2^2*x_4-15*x_0*x_3*x_4+6*x_1*x_3*x_4+x_2*x_3*x_4+5*x_3^2*x_4+x_0*x_4^2+8*x_1*x_4^2-5*x_2*x_4^2+2*x_3*x_4^2+2*x_4^3+x_0*x_1*x_5-2*x_1^2*x_5-4*x_1*x_2*x_5-4*x_0*x_3*x_5-3*x_1*x_3*x_5+2*x_3^2*x_5+2*x_0*x_4*x_5+7*x_1*x_4*x_5-4*x_2*x_4*x_5-2*x_3*x_4*x_5+2*x_1*x_5^2, x_0*x_2^2+10*x_1*x_2*x_3+3*x_0*x_3^2+5*x_1*x_3^2+4*x_2*x_3^2-x_3^3-5*x_0^2*x_4+19*x_0*x_1*x_4-22*x_1^2*x_4-x_0*x_2*x_4+3*x_1*x_2*x_4-4*x_2^2*x_4-24*x_0*x_3*x_4+9*x_1*x_3*x_4+x_2*x_3*x_4+8*x_3^2*x_4+2*x_0*x_4^2+11*x_1*x_4^2-7*x_2*x_4^2+4*x_3*x_4^2+3*x_4^3+2*x_0*x_1*x_5-4*x_1^2*x_5-7*x_1*x_2*x_5-7*x_0*x_3*x_5-5*x_1*x_3*x_5-x_2*x_3*x_5+3*x_3^2*x_5+4*x_0*x_4*x_5+12*x_1*x_4*x_5-7*x_2*x_4*x_5-3*x_3*x_4*x_5+4*x_1*x_5^2, x_1^2*x_2+17*x_1*x_2*x_3+6*x_0*x_3^2+9*x_1*x_3^2+7*x_2*x_3^2-2*x_3^3-9*x_0^2*x_4+36*x_0*x_1*x_4-44*x_1^2*x_4+3*x_0*x_2*x_4+5*x_1*x_2*x_4-7*x_2^2*x_4-47*x_0*x_3*x_4+21*x_1*x_3*x_4+2*x_2*x_3*x_4+16*x_3^2*x_4+24*x_1*x_4^2-16*x_2*x_4^2+7*x_3*x_4^2+7*x_4^3+3*x_0*x_1*x_5-6*x_1^2*x_5-9*x_1*x_2*x_5-12*x_0*x_3*x_5-8*x_1*x_3*x_5+5*x_3^2*x_5+5*x_0*x_4*x_5+19*x_1*x_4*x_5-12*x_2*x_4*x_5-7*x_3*x_4*x_5+5*x_1*x_5^2, x_0*x_1*x_2+29*x_1*x_2*x_3+11*x_0*x_3^2+15*x_1*x_3^2+12*x_2*x_3^2-4*x_3^3-16*x_0^2*x_4+62*x_0*x_1*x_4-74*x_1^2*x_4+5*x_0*x_2*x_4+9*x_1*x_2*x_4-12*x_2^2*x_4-80*x_0*x_3*x_4+35*x_1*x_3*x_4+4*x_2*x_3*x_4+27*x_3^2*x_4+40*x_1*x_4^2-27*x_2*x_4^2+12*x_3*x_4^2+12*x_4^3+5*x_0*x_1*x_5-10*x_1^2*x_5-16*x_1*x_2*x_5-21*x_0*x_3*x_5-14*x_1*x_3*x_5+9*x_3^2*x_5+9*x_0*x_4*x_5+33*x_1*x_4*x_5-21*x_2*x_4*x_5-12*x_3*x_4*x_5+9*x_1*x_5^2, x_0^2*x_2+49*x_1*x_2*x_3+19*x_0*x_3^2+25*x_1*x_3^2+20*x_2*x_3^2-7*x_3^3-28*x_0^2*x_4+106*x_0*x_1*x_4-124*x_1^2*x_4+8*x_0*x_2*x_4+16*x_1*x_2*x_4-20*x_2^2*x_4-134*x_0*x_3*x_4+58*x_1*x_3*x_4+7*x_2*x_3*x_4+45*x_3^2*x_4+66*x_1*x_4^2-45*x_2*x_4^2+20*x_3*x_4^2+20*x_4^3+9*x_0*x_1*x_5-18*x_1^2*x_5-28*x_1*x_2*x_5-37*x_0*x_3*x_5-23*x_1*x_3*x_5+16*x_3^2*x_5+16*x_0*x_4*x_5+57*x_1*x_4*x_5-36*x_2*x_4*x_5-20*x_3*x_4*x_5+16*x_1*x_5^2, x_1^3+47*x_1*x_2*x_3+18*x_0*x_3^2+23*x_1*x_3^2+19*x_2*x_3^2-7*x_3^3-24*x_0^2*x_4+97*x_0*x_1*x_4-117*x_1^2*x_4+8*x_0*x_2*x_4+16*x_1*x_2*x_4-19*x_2^2*x_4-127*x_0*x_3*x_4+54*x_1*x_3*x_4+7*x_2*x_3*x_4+42*x_3^2*x_4-x_0*x_4^2+62*x_1*x_4^2-42*x_2*x_4^2+19*x_3*x_4^2+19*x_4^3+9*x_0*x_1*x_5-16*x_1^2*x_5-25*x_1*x_2*x_5-33*x_0*x_3*x_5-23*x_1*x_3*x_5+14*x_3^2*x_5+14*x_0*x_4*x_5+51*x_1*x_4*x_5-33*x_2*x_4*x_5-19*x_3*x_4*x_5+14*x_1*x_5^2, x_0*x_1^2+79*x_1*x_2*x_3+29*x_0*x_3^2+40*x_1*x_3^2+32*x_2*x_3^2-11*x_3^3-41*x_0^2*x_4+164*x_0*x_1*x_4-196*x_1^2*x_4+14*x_0*x_2*x_4+26*x_1*x_2*x_4-32*x_2^2*x_4-214*x_0*x_3*x_4+92*x_1*x_3*x_4+11*x_2*x_3*x_4+71*x_3^2*x_4-2*x_0*x_4^2+105*x_1*x_4^2-71*x_2*x_4^2+32*x_3*x_4^2+32*x_4^3+14*x_0*x_1*x_5-26*x_1^2*x_5-41*x_1*x_2*x_5-55*x_0*x_3*x_5-38*x_1*x_3*x_5+23*x_3^2*x_5+23*x_0*x_4*x_5+85*x_1*x_4*x_5-55*x_2*x_4*x_5-32*x_3*x_4*x_5+23*x_1*x_5^2, x_0^2*x_1+133*x_1*x_2*x_3+48*x_0*x_3^2+68*x_1*x_3^2+54*x_2*x_3^2-18*x_3^3-70*x_0^2*x_4+278*x_0*x_1*x_4-330*x_1^2*x_4+24*x_0*x_2*x_4+44*x_1*x_2*x_4-54*x_2^2*x_4-361*x_0*x_3*x_4+156*x_1*x_3*x_4+18*x_2*x_3*x_4+120*x_3^2*x_4-4*x_0*x_4^2+177*x_1*x_4^2-120*x_2*x_4^2+54*x_3*x_4^2+54*x_4^3+23*x_0*x_1*x_5-44*x_1^2*x_5-69*x_1*x_2*x_5-93*x_0*x_3*x_5-63*x_1*x_3*x_5+39*x_3^2*x_5+39*x_0*x_4*x_5+144*x_1*x_4*x_5-93*x_2*x_4*x_5-54*x_3*x_4*x_5+39*x_1*x_5^2, x_0^3+224*x_1*x_2*x_3+80*x_0*x_3^2+115*x_1*x_3^2+91*x_2*x_3^2-30*x_3^3-119*x_0^2*x_4+470*x_0*x_1*x_4-555*x_1^2*x_4+41*x_0*x_2*x_4+75*x_1*x_2*x_4-91*x_2^2*x_4-608*x_0*x_3*x_4+263*x_1*x_3*x_4+30*x_2*x_3*x_4+202*x_3^2*x_4-8*x_0*x_4^2+297*x_1*x_4^2-202*x_2*x_4^2+91*x_3*x_4^2+91*x_4^3+39*x_0*x_1*x_5-76*x_1^2*x_5-118*x_1*x_2*x_5-158*x_0*x_3*x_5-105*x_1*x_3*x_5+67*x_3^2*x_5+68*x_0*x_4*x_5+245*x_1*x_4*x_5-158*x_2*x_4*x_5-91*x_3*x_4*x_5+67*x_1*x_5^2); o3 : Ideal of ringP5 |
i4 : time X = specialCubicFourfold(S,NumNodes=>3) -- used 3.58445 seconds o4 = -- special cubic fourfold -- ambient projective space: Proj(K[x , x , x , x , x , x ]) 0 1 2 3 4 5 surface: { 2 2 2 2 2 x x x - 2x x x - x x - x x - x x x + 2x x - x x x + x x + 2x x x - x x x - x x + x x x , 0 2 3 1 2 3 1 3 2 3 0 1 4 1 4 1 2 4 2 4 0 3 4 1 3 4 1 4 1 3 5 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 x x - 4x x x - x x - 3x x - 2x x + 2x x - 9x x x + 11x x - x x x - 2x x x + 2x x + 12x x x - 7x x x - 4x x + x x - 6x x + 4x x - 2x x - 2x - x x x + x x + 2x x x + 3x x x + 2x x x - x x - x x x - 4x x x + 3x x x + 2x x x - x x , 1 3 1 2 3 0 3 1 3 2 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x x - 7x x x - 3x x - 4x x - 3x x + x + 3x x - 14x x x + 17x x - x x x - 3x x x + 3x x + 19x x x - 9x x x - x x x - 6x x + x x - 9x x + 6x x - 3x x - 3x - 2x x x + 2x x + 4x x x + 5x x x + 4x x x - 2x x - 2x x x - 7x x x + 5x x x + 3x x x - 2x x , 0 1 3 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x - 12x x x - 6x x - 6x x - 5x x + 2x + 5x x - 24x x x + 29x x - x x x - 5x x x + 5x x + 32x x x - 14x x x - 2x x x - 10x x + x x - 15x x + 10x x - 5x x - 5x - 3x x x + 3x x + 6x x x + 8x x x + 7x x x - 3x x - 3x x x - 11x x x + 8x x x + 5x x x - 3x x , 0 3 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x + 6x x x + 2x x + 3x x + 2x x - x - 3x x + 12x x x - 14x x - 2x x - 15x x x + 6x x x + x x x + 5x x + x x + 8x x - 5x x + 2x x + 2x + x x x - 2x x - 4x x x - 4x x x - 3x x x + 2x x + 2x x x + 7x x x - 4x x x - 2x x x + 2x x , 1 2 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x + 10x x x + 3x x + 5x x + 4x x - x - 5x x + 19x x x - 22x x - x x x + 3x x x - 4x x - 24x x x + 9x x x + x x x + 8x x + 2x x + 11x x - 7x x + 4x x + 3x + 2x x x - 4x x - 7x x x - 7x x x - 5x x x - x x x + 3x x + 4x x x + 12x x x - 7x x x - 3x x x + 4x x , 0 2 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 2 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 x x + 17x x x + 6x x + 9x x + 7x x - 2x - 9x x + 36x x x - 44x x + 3x x x + 5x x x - 7x x - 47x x x + 21x x x + 2x x x + 16x x + 24x x - 16x x + 7x x + 7x + 3x x x - 6x x - 9x x x - 12x x x - 8x x x + 5x x + 5x x x + 19x x x - 12x x x - 7x x x + 5x x , 1 2 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 x x x + 29x x x + 11x x + 15x x + 12x x - 4x - 16x x + 62x x x - 74x x + 5x x x + 9x x x - 12x x - 80x x x + 35x x x + 4x x x + 27x x + 40x x - 27x x + 12x x + 12x + 5x x x - 10x x - 16x x x - 21x x x - 14x x x + 9x x + 9x x x + 33x x x - 21x x x - 12x x x + 9x x , 0 1 2 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 x x + 49x x x + 19x x + 25x x + 20x x - 7x - 28x x + 106x x x - 124x x + 8x x x + 16x x x - 20x x - 134x x x + 58x x x + 7x x x + 45x x + 66x x - 45x x + 20x x + 20x + 9x x x - 18x x - 28x x x - 37x x x - 23x x x + 16x x + 16x x x + 57x x x - 36x x x - 20x x x + 16x x , 0 2 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 3 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x + 47x x x + 18x x + 23x x + 19x x - 7x - 24x x + 97x x x - 117x x + 8x x x + 16x x x - 19x x - 127x x x + 54x x x + 7x x x + 42x x - x x + 62x x - 42x x + 19x x + 19x + 9x x x - 16x x - 25x x x - 33x x x - 23x x x + 14x x + 14x x x + 51x x x - 33x x x - 19x x x + 14x x , 1 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x + 79x x x + 29x x + 40x x + 32x x - 11x - 41x x + 164x x x - 196x x + 14x x x + 26x x x - 32x x - 214x x x + 92x x x + 11x x x + 71x x - 2x x + 105x x - 71x x + 32x x + 32x + 14x x x - 26x x - 41x x x - 55x x x - 38x x x + 23x x + 23x x x + 85x x x - 55x x x - 32x x x + 23x x , 0 1 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x x + 133x x x + 48x x + 68x x + 54x x - 18x - 70x x + 278x x x - 330x x + 24x x x + 44x x x - 54x x - 361x x x + 156x x x + 18x x x + 120x x - 4x x + 177x x - 120x x + 54x x + 54x + 23x x x - 44x x - 69x x x - 93x x x - 63x x x + 39x x + 39x x x + 144x x x - 93x x x - 54x x x + 39x x , 0 1 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 3 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 x + 224x x x + 80x x + 115x x + 91x x - 30x - 119x x + 470x x x - 555x x + 41x x x + 75x x x - 91x x - 608x x x + 263x x x + 30x x x + 202x x - 8x x + 297x x - 202x x + 91x x + 91x + 39x x x - 76x x - 118x x x - 158x x x - 105x x x + 67x x + 68x x x + 245x x x - 158x x x - 91x x x + 67x x 0 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 } fourfold: { 3 2 2 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 - 670x + 5864x x - 10808x x - 7531x + 5071x x - 9579x x x + 8444x x + 16659x x + 8570x x - 6635x x + 3783x x x - 6898x x - 456x x x + 2587x x x - 10336x x - 3250x x - 1163x x + 4037x - 16218x x + 14703x x x - 13275x x + 12795x x x - 3876x x x + 1163x x - 2719x x x + 15994x x x - 4037x x x + 3357x x + 9858x x - 16194x x + 13302x x - 1619x x + 15053x + 7183x x x + 11912x x - 14902x x x + 9930x x x + 13524x x x - 16659x x x - 13382x x + 2607x x x + 11530x x x + 15001x x x - 15053x x x + 3277x x 0 0 1 0 1 1 0 2 0 1 2 1 2 0 2 1 2 0 3 0 1 3 1 3 0 2 3 1 2 3 0 3 1 3 2 3 3 0 4 0 1 4 1 4 0 2 4 1 2 4 2 4 0 3 4 1 3 4 2 3 4 3 4 0 4 1 4 2 4 3 4 4 0 1 5 1 5 1 2 5 0 3 5 1 3 5 2 3 5 3 5 0 4 5 1 4 5 2 4 5 3 4 5 1 5 } o4 : SpecialCubicFourfold (Cubic fourfold containing a surface of degree 7 and sectional genus 0) |
i5 : time discriminant X -- used 0.104496 seconds o5 = 26 |
i6 : time f = detectCongruence X; S: surface of degree 7 in PP^5 cut out by 13 hypersurfaces of degree 3 phi: cubic rational map from PP^5 to PP^12 Z=phi(P^5) multidegre(phi): {1, 3, 9, 20, 30, 29} number lines containing in Z and passing through the point phi(p): 8 number 2-secant lines to S passing through p: 7 number 5-secant conics to S passing through p: 1 -- used 2.77142 seconds |
i7 : p = point ring X -- random point on P^5 o7 = ideal (x + 6834x , x + 5647x , x + 11151x , x + 11773x , x + 4 5 3 5 2 5 1 5 0 ------------------------------------------------------------------------ 11690x ) 5 o7 : Ideal of ringP5 |
i8 : time C = f p -- 5-secant conic to S -- used 0.167655 seconds o8 = ideal (x + 6637x + 3535x - 13870x , x - 9264x + 1715x + 15433x , 2 3 4 5 1 3 4 5 ------------------------------------------------------------------------ 2 2 x + 13697x + 9151x + 6376x , x + 10518x x + 15681x + 6431x x - 0 3 4 5 3 3 4 4 3 5 ------------------------------------------------------------------------ 2 15567x x - 4954x ) 4 5 5 o8 : Ideal of ringP5 |
i9 : codim C == 4 and degree C == 2 and codim(C+S) == 5 and degree(C+S) == 5 and isSubset(C,p) o9 = true |