def METHOD_NAME(self, x):
    """
    Returns the image of ``x`` by the antipode
    This default implementation coerces to the default
    realization, computes the antipode there, and coerces the
    result back.
    EXAMPLES::
        sage: # needs sage.combinat sage.modules
        sage: N = NonCommutativeSymmetricFunctions(QQ)
        sage: R = N.ribbon()
        sage: R.antipode_by_coercion.__module__
        'sage.categories.hopf_algebras'
        sage: R.antipode_by_coercion(R[1,3,1])
        -R[2, 1, 2]
    """
    R = self.realization_of().a_realization()
    return self(R(x).antipode())