/run/user/1000/doc/ff2d79be/projection_sur_K

eq1: y^(2) + z^(2) + (2 * x) = 0
A = (-0.4555957327721565, -3.2460337142630706, 6.172596181883748)
alpha: x(A)
beta1: y(A)
beta2: z(A)
rho: sqrt(beta1^(2) + beta2^(2))
theta: atan2(beta2, beta1)
zh: ((-(1 / 3)) * (alpha + 1) / (((1 / 4 * sqrt(2)) * rho) + (1 / 6 * sqrt((4 / 3 * alpha^(3)) + (4 * alpha^(2)) + (9 / 2 * rho^(2)) + (4 * alpha) + 4 / 3)))^(1 / 3)) + (((1 / 4 * sqrt(2)) * rho) + (1 / 6 * sqrt((4 / 3 * alpha^(3)) + (4 * alpha^(2)) + (9 / 2 * rho^(2)) + (4 * alpha) + 4 / 3)))^(1 / 3)
alphaH: (-zh^(2))
rhoH: (sqrt(2) * zh)
beta1H: (rhoH * sin(theta))
beta2H: (rhoH * cos(theta))
AH: (alphaH, beta2H, beta1H)