human
Complete the below
def intcurve_series(vector_field, param, start_point, n=6, coord_sys=None, coeffs=False):

    ''''Return the series expansion for an integral curve of the field.
    Integral curve is a function `\gamma` taking a parameter in `R` to a point
    in the manifold. It verifies the equation:
    `V(f)\big(\gamma(t)\big) = \frac{d}{dt}f\big(\gamma(t)\big)`
    where the given ``vector_field`` is denoted as `V`. This holds for any
    value `t` for the parameter and any scalar field `f`.
    This equation can also be decomposed of a basis of coordinate functions
    `V(f_i)\big(\gamma(t)\big) = \frac{d}{dt}f_i\big(\gamma(t)\big) \quad \forall i`
    This function returns a series expansion of `\gamma(t)` in terms of the
    coordinate system ``coord_sys``. The equations and expansions are necessarily
    done in coordinate-system-dependent way as there is no other way to
    represent movement between points on the manifold (i.e. there is no such
    thing as a difference of points for a general manifold).
    See Also
    intcurve_diffequ
    Parameters
    vector_field
    the vector field for which an integral curve will be given
    param
    the argument of the function `\gamma` from R to the curve
    start_point
    the point which coresponds to `\gamma(0)`
    n
    the order to which to expand
    coord_sys
    the coordinate system in which to expand
    coeffs (default False) - if True return a list of elements of the expansion
    Examples
    Use the predefined R2 manifold:
    >>> from sympy.abc import t, x, y
    >>> from sympy.diffgeom.rn import R2, R2_p, R2_r
    >>> from sympy.diffgeom import intcurve_series
    Specify a starting point and a vector field:
    >>> start_point = R2_r.point([x, y])
    >>> vector_field = R2_r.e_x
    Calculate the series:
    >>> intcurve_series(vector_field, t, start_point, n=3)
    Matrix([
    [t + x],
    [    y]])
    Or get the elements of the expansion in a list:
    >>> series = intcurve_series(vector_field, t, start_point, n=3, coeffs=True)
    >>> series[0]
    Matrix([
    [x],
    [y]])
    >>> series[1]
    Matrix([
    [t],
    [0]])
    >>>...'''

Write me a Python code to calculate the series:?
assistant
#Here is Python code to calculate the series:
.
    if ((contravariant_order(vector_field) != 1) or covariant_order(vector_field)):
        raise ValueError('The    supplied    field    was    not    a    vector    field.')
    def iter_vfield(scalar_field, i):
        'Return    ``vector_field``    called    `i`    times    on    ``scalar_field``.'
        return reduce((lambda s, v: v.rcall(s)), ([vector_field] * i), scalar_field)
    def taylor_terms_per_coord(coord_function):
        'Return    the    series    for    one    of    the    coordinates.'
        return [(((param ** i) * iter_vfield(coord_function, i).rcall(start_point)) / factorial(i)) for i in range(n)]
    coord_sys = (coord_sys if coord_sys else start_point._coord_sys)
    coord_functions = coord_sys.coord_functions()
    taylor_terms = [taylor_terms_per_coord(f) for f in coord_functions]
    if coeffs:
        return [Matrix(t) for t in zip(*taylor_terms)]
    else:
        return Matrix([sum(c) for c in taylor_terms])