2-jet of x³: j²(0)=(0,0,0); j²(1)=(1,3,6); j²(2)=(8,12,12)

Sympy-exact verification of the 2-jet prolongation operator for the canonical cubic f(x) = x³. Derivatives: f'(x) = 3x², f''(x) = 6x. Prolongation: j²f(a) = (f(a), f'(a), f''(a)) ∈ R³. Evaluation pins: j²f(0) = (0, 0, 0) (triple root at…