Trac #10519: analytic combinatorics: new code for computing asymptoti…

…cs for multivariate generating functions

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.

URL: http://trac.sagemath.org/10519
Reported by: araichev
Ticket author(s): Daniel Krenn, Alex Raichev
Reviewer(s): Daniel Krenn, David Loeffler, Travis Scrimshaw

src/doc/en/reference/asymptotic/index.rst

@@ -64,5 +64,6 @@ Asymptotic Expansions --- Table of Contents
    sage/rings/asymptotic/growth_group_cartesian
    sage/rings/asymptotic/term_monoid
    sage/rings/asymptotic/misc
+   sage/rings/asymptotic/asymptotics_multivariate_generating_functions
 
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