code: def main():
      mu, nu, rho, theta, phi, sigma, tau, a, t, x, y, z, w = symbols(
          "mu, nu, rho, theta, phi, sigma, tau, a, t, x, y, z, w"
      )
  
      transform(
          "polar", Matrix([rho * cos(phi), rho * sin(phi)]), [rho, phi]
      )
  
      transform(
          "cylindrical",
          Matrix([rho * cos(phi), rho * sin(phi), z]),
          [rho, phi, z],
      )
  
      transform(
          "spherical",
          Matrix(
              [
                  rho * sin(theta) * cos(phi),
                  rho * sin(theta) * sin(phi),
                  rho * cos(theta),
              ]
          ),
          [rho, theta, phi],
          recursive=True,
      )
  
      transform(
          "rotating disk",
          Matrix(
              [
                  t,
                  x * cos(w * t) - y * sin(w * t),
                  x * sin(w * t) + y * cos(w * t),
                  z,
              ]
          ),
          [t, x, y, z],
      )
  
      transform(
          "parabolic",
          Matrix([sigma * tau, (tau**2 - sigma**2) / 2]),
          [sigma, tau],
      )
  
      transform(
          "bipolar",
          Matrix(
              [
                  a * sinh(tau) / (cosh(tau) - cos(sigma)),
                  a * sin(sigma) / (cosh(tau) - cos(sigma)),
              ]
          ),
          [sigma, tau],
      )
  
      transform(
          "elliptic",
          Matrix([a * cosh(mu) * cos(nu), a * sinh(mu) * sin(nu)]),
          [mu, nu],
      )
  
imports: from sympy import var, sin, cos, pprint, Matrix, eye, trigsimp, Eq, Function, simplify, sinh, cosh, expand, symbols
label_desc: Use image node_id 3 for calling a global function with example usage: main() without return types