Singular

D.5.1.11 testPointConic

Usage:

testPointConic(p, r); p poly, r ring

Assume:

assumes that p is a homogeneous quadratic polynomial in the first three ring variables of the current basering;
Assumes that there is a (1x3) matrix named 'point' in r with entries from the ground field of r.

Return:

returns 1 iff the point named 'point', residing in r, lies on the conic given by p; 0 otherwise

Note:

This method temporarily changes the basering to r. Afterwards, the basering will be the same as before.

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);
if (testPointConic(p, S) == 1)
==> conic: x2-4xy+2y2+3xz+17yz+5z2
==> point: (-1/4a), (-1/4a+1/4), 0
==> minpoly: (a2-2)
{ "point lies on conic"; }
==> point lies on conic
else
{ "point does not lie on conic"; }