r"""
[...]

This code relates to analytic combinatorics.
More specifically, it is a collection of functions designed
to compute asymptotics of Maclaurin coefficients of certain classes of
multivariate generating functions.

The main function asymptotics() returns the first `N` terms of
the asymptotic expansion of the Maclaurin coefficients `F_{n\alpha}`
of the multivariate meromorphic function `F=G/H` as `n\to\infty`.
It assumes that `F` is holomorphic in a neighborhood of the origin,
that `H` is a polynomial, and that asymptotics in the direction of
`\alpha` (a tuple of positive integers) are controlled by smooth
or multiple points.

[...]
"""

class HolomorphicMultivariateMeromorphicFunction(object):

    # Constructor of the object
    def __init__(self, F, G):
        #stores important information on the object as attributes of self
        self._F = F
        self._G = G

    def maclaurin_coefficients(self, n, alpha):
        r"""
        Return the maclaurin coefficients of self.

        INPUT:

        - ``alpha`` - tuple of positive integers

        OUTPUT:

        a python list of the first terms

        OR

        maybe an object of a class you implement if there exists pertinent
        questions to ask to it.
        """
        #Do some computations based (I guess) on self._F and self._G
        intermediate_result1 = self.some_intermediate_computations_1()
        #Do more computations
        return something

    def asymptotics(self, N, alpha):
        r"""
        Returns the asymptotics of Maclaurin coefficients.
        """
        #Do some computations based (I guess) on self._F and self._G
        intermediate_result2 = self.some_intermediate_computations_2()
        intermediate_result3 = self.some_intermediate_computations_3()
        return something

    #put here all the others functions needed to compute the asymptotics
    def some_intermediate_computations_1(self):
        pass
    def some_intermediate_computations_2(self):
        pass
    def some_intermediate_computations_3(self):
        pass

    ...