#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-5.4
Component: combinatorics
| Resolution:
Keywords: analytic combinatorics, multivariate generating functions,
asymptotics | Work issues: coverage, trailing whitespace
Report Upstream: N/A
| Reviewers: David Loeffler
Authors: Alex Raichev
| Merged in:
Dependencies:
| Stopgaps:
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Old description:
> This code 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.
New description:
This code 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.
Apply [attachment:trac_10519-asymptotic_multiple-v3.patch]
--
Comment (by chapoton):
I have removed all whitespaces in the new patch. All test pass.
'''BUT''' there remains 6 procedures with no doctest. Remember that it is
neccesary to have 100% doctesting.
Also the name '''amgf''' is not good. It should be changed to something
more descriptive.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10519#comment:28>
Sage <http://www.sagemath.org>
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