
def main():
    from sympy import symbols, sqrt, diff

    r, x, k = symbols('r x k')
    a, b, c = symbols('a b c')
    delta, zeta, mu = symbols('delta zeta mu')
    b               = -(k**2+x**2+r**2)
    a               = k**2
    c               = x**2
    delta           = b**2 - 4 * a*c
    zeta           = sqrt( (- b + sqrt(delta)) / (2*a) )
    mu = x/(k*zeta)

    dmudx   = diff(mu,x)
    dzetadx = diff(zeta,x)
    dmudr   = diff(mu,r)
    dzetadr = diff(zeta,r)


    print('delta')
    print(delta)
    print('Mu')
    print(mu)
    print('zeta')
    print(zeta)

    print('dmu_dx=')
    print(dmudx)
    print('dzeta_dx=')
    print(dzetadx)

    print('dmu_dr=')
    print(dmudr)
    print('dzeta_dr=')
    print(dzetadr)

    print('test')
    print(diff(sqrt(x),x))
