polar-laplacian-3d.egi

--
-- This file has been auto-generated by egison-translator.
--

def x := r * sin θ * cos φ

def y := r * sin θ * sin φ

def z := r * cos θ

def uR := ∂/∂ (u x y z) r

uR

def uRR := ∂/∂ (∂/∂ (u x y z) r) r

uRR

def uΘ := ∂/∂ (u x y z) θ

uΘ

def uΘΘ := ∂/∂ (∂/∂ (u x y z) θ) θ

uΘΘ

def uΦ := ∂/∂ (u x y z) φ

uΦ

def uΦΦ := ∂/∂ (∂/∂ (u x y z) φ) φ

uΦΦ

uRR + 2 / r * uR + 1 / r ^ 2 * uΘΘ + cos θ / (r ^ 2 * sin θ) * uΘ +
1 / (r * sin θ) ^ 2 * uΦΦ