#10519: analytic combinatorics: new code for computing asymptotics for 
multivariate
generating functions
-------------------------------------+-------------------------------------
       Reporter:  araichev           |        Owner:  sage-combinat
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.1
      Component:  combinatorics      |   Resolution:
       Keywords:  analytic           |    Merged in:
  combinatorics, multivariate        |    Reviewers:  Daniel Krenn, David
  generating functions, asymptotics  |  Loeffler, Travis Scrimshaw
        Authors:  Daniel Krenn,      |  Work issues:
  Alex Raichev                       |       Commit:
Report Upstream:  N/A                |  badafce7372353c16c1b6ca658c183957ac2021b
         Branch:                     |     Stopgaps:
  public/combinat/10519              |
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * reviewer:  Daniel Krenn, David Loeffler => Daniel Krenn, David Loeffler,
     Travis Scrimshaw


Comment:

 So I made my pass through the code (finally). I think it looks good with
 my changes:

 - I added a `__classcall_private__` to parse the input for
 `UniqueRepresentation`.
 - I moved the (other) static methods to separate functions within the
 module since (IMO) they were not strongly associated with the
 `FractionWithFactoredDenominatorRing` class. It also allows their doc to
 be included by default (since they do not have to be _hidden) and allows
 them to potentially be used outside of the class.
 - I moved around some of the documentation within methods as I feel the
 descriptive information should come before the `INPUT`/`OUTPUT` blocks.
 The input signature of the method is the first set of information given by
 `?` and the documentation.
 - I moved more common imports to the start. There is no danger of circular
 imports when the file in question is not imported into the global
 namespace (it is also faster, easier to maintain in the long term, and I'm
 not as paranoid about these thing).
 - Replaced some Sage implementations with there standard python
 equivalents.
 - Other misc changes.

 If you're happy with my changes, then you can set a positive review.

 Perhaps for a followup, we should figure out what the best way is to
 expose this functionality into the global namespace. Should we just do a
 lazy import of `FractionWithFactoredDenominatorRing`?

--
Ticket URL: <http://trac.sagemath.org/ticket/10519#comment:121>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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