#10519: analytic combinatorics: new code for computing asymptotics for
multivariate
generating functions
-----------------------------+----------------------------------------------
Reporter: araichev | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6.2
Component: combinatorics | Keywords: analytic combinatorics,
multivariate generating functions, asymptotics
Author: Alex Raichev | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by slabbe):
> Question for you experienced Sage developers: how can i better package
my code?
Hi, I am currently at Sage Days 28. Right now, there is a discussion about
Analytic combinatorics in Sage and your code was mentionned in the
discussion.
I am not an expert of the domain, but I am coding oriented object Python
since
some time now. So below are just some of my thoughts to, I hope, help you
turn
your set of functions into an oriented object structure.
How to structure a bunch of functions into classes? How to find which
objects
(python classes) you need? Here is the trick I personaly use. Consider
each of
your functions as a question you ask. Then, ask yourself to who are you
asking
each of your questions? Answers often gives you a good hint about the
objects
you need to implement. EXAMPLE. Suppose I code the function
``determinant``.
Question : ``To who do I ask the determinant?``. Answer: ``To a matrix``.
Hence, ``matrix`` might be a good object (a python class) to implement.
You are the best person to answer to these questions. You might have 30
functions in you file, but only two or three different answers to the
above
question. Regroup the similar functions together: they will become the
methods
of a same class.
The sage file you uploaded starts with :
{{{
> 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.
}}}
Reading only these lines, I imagine the following structure:
{{{
#!python
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
...
}}}
It also looks like you need some robustness somehow. But I need to know
more
information about what means
> that asymptotics in the direction of `\alpha` (a tuple of positive
integers)
> are controlled by smooth or multiple points.
to decide whether this is checked at the creation of the object or before
returning the asymptotics. But these hypothesis should be checked
somewhere.
Hope this helps.
Cheers,
Sébastien Labbé, Montréal, (but currently at Sage Days 28, Orsay, France)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10519#comment:4>
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