How to compute Lie derivative?

[Narheem]

Hi;

Could anyone help me to compute the lie derivative of the function h:R^3-->R with respect to the vector-valued function f:R^5-->R^3 below?

f(x,y,L,u,v) = [x + u;
               y + v;
               L]

and 

h(x,y,L) = sqrt((y-x)^2 + (L)^2)

Thank you in advance.

import sympy as sym

x, y, L, u , v = sym.symbols('x y L u v')
X = sym.Matrix([[x],[y], [L], [u], [v]])

# f(x,y,L,u,v) : R^5-->R^3
f = sym.Matrix([[ x + u], [ y + v ], [L]])

# h(x,y,L) : R^3-->R^1
h = sym.Matrix([[ sym.sqrt(L**2 + (y - x)**2) ]])

# L1hf : first-order lie derivative of h wrt f
L1hf = sym.diffgeom.LieDerivative(f,h) # ???

Enter code here...

[Francesco Bonazzi]

You have to declare variables as sympy.diffgeom objects.

[Narheem]

Thank you for reply.
I'm a python newbie; could you tell me how i can do that? Could you provide a piece of code, please?