manifold_check_latex.py 文件源码

def Simple_manifold_with_scalar_function_derivative():
    Print_Function()
    coords = (x, y, z) = symbols('x y z')
    basis = (e1, e2, e3, grad) = MV.setup('e_1 e_2 e_3', metric='[1,1,1]', coords=coords)
    # Define surface
    mfvar = (u, v) = symbols('u v')
    X = u*e1 + v*e2 + (u**2 + v**2)*e3
    print('\\f{X}{u,v} =', X)
    MF = Manifold(X, mfvar)
    (eu, ev) = MF.Basis()
    # Define field on the surface.
    g = (v + 1)*log(u)

    print('\\f{g}{u,v} =', g)

    # Method 1: Using old Manifold routines.
    VectorDerivative = (MF.rbasis[0]/MF.E_sq)*diff(g, u) + (MF.rbasis[1]/MF.E_sq)*diff(g, v)
    print('\\eval{\\nabla g}{u=1,v=0} =', VectorDerivative.subs({u: 1, v: 0}))

    # Method 2: Using new Manifold routines.
    dg = MF.Grad(g)
    print('\\eval{\\f{Grad}{g}}{u=1,v=0} =', dg.subs({u: 1, v: 0}))
    dg = MF.grad*g
    print('\\eval{\\nabla g}{u=1,v=0} =', dg.subs({u: 1, v: 0}))
    return