#17715: AsymptoticTerm
-------------------------------------+-------------------------------------
       Reporter:  behackl            |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.9
      Component:  asymptotic         |   Resolution:
  expansions                         |    Merged in:
       Keywords:  asymptotics,       |    Reviewers:  Daniel Krenn, Clemens
  gsoc15                             |  Heuberger
        Authors:  Benjamin Hackl     |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  347f080df240102799ded90067cbd01beaa386a4
  u/cheuberg/asy/asymptoticTerm      |     Stopgaps:
   Dependencies:  #17600, #18930,    |
  #19237                             |
-------------------------------------+-------------------------------------
Changes (by cheuberg):

 * status:  needs_review => needs_work
 * commit:  cc55be7405533455d24c378e8d2deb93a6831495 =>
     347f080df240102799ded90067cbd01beaa386a4
 * dependencies:  #17600, #18930 => #17600, #18930, #19237


Comment:

 I reviewed this ticket, added a few reviewer commits and have a few
 comments:
 - `absorption`: One-Sentence-Description should describe what this
 function ''does''. What happens if the elements are not comparable
 (documentation; probably only possible in a follow-up ticket)?
 - `can_absorb`: One-Sentence-Description, then NOTE section would be
 superfluous.
 - `GenericTerm.__init__`: Provide doctests for error conditions
 - `GenericTerm.can_absorb` and `GenericTerm._can_absorb_`: Why ''two''
 methods?
 - `GenericTerm.absorb`: what happens if `check` is not set? Why would one
 want to call that?
 - `GenericTerm.absorb`, last 3 lines of code: isn't it quite confusing to
 override `self` and `other` in the `lambda` expression?
 - `GenericTerm._absorb_`: the method is never called in the doctests, in
 particular, the `NotImplementedError` does not show up.
 - `GenericTermMonoid.__init__`: see
 [http://trac.sagemath.org/ticket/17600#comment:40 #17600, comment 40]:
 handling of tuples as parameter `category`, `__classcall__` for parameter
 `category`; same question for derived classes?
 - `GenericTermMonoid.__init__`: documentation says that `growth_group` has
 to be a "partially ordered group" with a `GenericGrowthGroup` only listed
 as an example; code explicitly requires a `GenericGrowthGroup`.
 - `GenericTermMonoid._element_constructor_`: why example
 `T_QQ.coerce(term1)` instead of `T_QQ(term1)`?
 - `GenericTermMonoid._element_constructor_`: why `type(data) ==
 self.element_class` and not `isinstance(data, self.element_class)` ?
 Similarly for other parents.
 - `OTermMonoid._coerce_map_from_`: documentation does not agree with code:
 according to the documentation, `S` must be an `OTermMonoid` or an
 `ExactTermMonoid`. However, the code does not enforce the former.
 - `TermWithCoefficient._le_`: The comparison of coefficients is not
 documented. Apart from that, do we really want that `x <= 2*I*x` when the
 coefficient ring is complex?
 - `TermWithCoefficientMonoid._init_`: check error condition
 - `TermWithCoefficientMonoid.base_ring`: why is this a property instead of
 a function? Compare with ring of polynomials.
 - `TermWithCoefficientMonoid._coerce_map_from_`: documentation mentions
 "this exact term monoid", but this is a `TermWithCoefficientMonoid`.
 - `ExactTerm._repr_`: I do not like the check `self.growth._raw_element_
 == 0`, `self.growth` is the identity element of that group, so we should
 check for that.
 - I'd prefer `.is_zero()` over `== 0`.
 - `TermMonoidFactory.create_key_and_extra_args`: test error conditions
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=88b9294a643390b05100846dd1aa0097a0e8104d
 88b9294]||{{{Trac #19237: Fix ReSt errors in reference/rings}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=a7361b2959748b960714484ba2d102bb8a8e72f9
 a7361b2]||{{{Trac #17715: Merge #19237 to ease review}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=148b0b81f4e1700bbdedc3a42f07f0672847e42b
 148b0b8]||{{{Trac #17715: minor documentation issues}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=9f8a2483bfac46210b42b8be8cf502932ef39769
 9f8a248]||{{{Trac #17715: remove duplicate line in doctest}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=d870c90a29a61dbe6ac6aa7b182569ba06f03710
 d870c90]||{{{Trac #17715: Documentation: language}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=d4c2b0ac06922bc7a38df79a99dd1a73fa5496b0
 d4c2b0a]||{{{Trac #17715: Fix/insert links}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=a2dfd227d212f55b2fa4aad882e95b8f06b6d77b
 a2dfd22]||{{{Trac #17715: ReSt error}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=f6882fe8cad7ee014bc4bf63d689e2e2ed59da37
 f6882fe]||{{{Trac #17715: additional doctest for explanation}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=347f080df240102799ded90067cbd01beaa386a4
 347f080]||{{{Trac #17715: emphasize that 'O' is capital letter and not
 digit}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/17715#comment:34>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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