 LIB "paraplanecurves.lib";
ring R = 0, (x,y,z), dp;
system("random", 4711);
poly p = x^2 + 2*y^2 + 5*z^2  4*x*y + 3*x*z + 17*y*z;
def S = rationalPointConic(p); // quadratic field extension,
// minpoly = a^2  2
testPointConic(p, S);
==> conic: x24xy+2y2+3xz+17yz+5z2
==> point: (1/4a), (1/4a+1/4), 0
==> minpoly: (a22)
==> 1
setring R;
p = x^2  1857669520 * y^2 + 86709575222179747132487270400 * z^2;
S = rationalPointConic(p); // same as current basering,
// no extension needed
testPointConic(p, S);
==> conic: x21857669520y2+86709575222179747132487270400z2
==> point: 819398304609269135405871919690911280, 4998995645707055256041604614\
16220, 73117135886813712113057
==> 1
