# Singular          #### D.5.4.11 testPointConic

Procedure from library `paraplanecurves.lib` (see paraplanecurves_lib).

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.

Example:
 ```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"; } ```

### Misc 