Substituting random values for all but one of the the coordinates we get a quadratic equation for the last coordinate, which in about 50 % of the cases has a kk-rational root.
i1 : kk=ZZ/(nextPrime 10^3) o1 = kk o1 : QuotientRing |
i2 : H = precomputedModelInP3xP5(kk); 1 1 o2 : Matrix (kk[w , w , w , w , z , z , z , z , z , z ]) <--- (kk[w , w , w , w , z , z , z , z , z , z ]) 0 1 2 3 0 1 2 3 4 5 0 1 2 3 0 1 2 3 4 5 |
i3 : pt=findPointInP3xP5(kk) o3 = | 107 -308 280 -176 115 -298 72 378 275 252 | 1 10 o3 : Matrix kk <--- kk |
i4 : substitute(H,pt) o4 = 0 1 1 o4 : Matrix kk <--- kk |