Linear Algebra and the C Language/a046

__NOTOC__ The coefficients of a conic with the left inverse (Pseudo-Inverse). I use Pinv_Rn_mR(); to calculate the coefficients of a conic. Presentation : Find the coefficients a, b, c, d, e of the conic, ax**2 + by**2 + cx + dy + e = 0 which crosses these four points (x[1],y[1]) (x[2],y[2]) (x[3],y[3]) (x[4],y[4]) Using the four points we obtain the matrix. (a)x**2 (b)y**2 (c)x (d)y (e) = 0 x[1]**2 y[1]**2 x[1] y[1] 1 0 x[2]**2 y[2]**2 x[2] y[2] 1 0 x[3]**2 y[3]**2 x[3] y[3] 1 0 x[4]**2 y[4]**2 x[4] y[4] 1 0 This system has four lines and five unknowns (a, b, c, d, e). It is a homogeneous system, so it has an infinite number of solutions. To find a solution, I chose to set a = 1. We therefore have five rows and five unknowns. 1 0 0 0 0 1 x[1]**2 y[1]**2 x[1] y[1] 1 0 x[2]**2 y[2]**2 x[2] y[2] 1 0 x[3]**2 y[3]**2 x[3] y[3] 1 0 x[4]**2 y[4]**2 x[4] y[4] 1 0 All that remains is to solve the system. c00a.c ..... ..... ax**2 + by**2 + cx + dy + e = 0 c00b.c c00c.c c00d.c