Singular Manual: testPointConic

| #### D.5.11.11 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"; }

User manual for Singular version 4.4.1, 2025, generated by texi2html.