#19063: Coercions and basic arithmetic for complex balls
-------------------------------------+-------------------------------------
       Reporter:  mmezzarobba        |        Owner:
           Type:  enhancement        |       Status:  needs_info
       Priority:  major              |    Milestone:  sage-6.9
      Component:  numerical          |   Resolution:
       Keywords:  arb                |    Merged in:
        Authors:  Marc Mezzarobba    |    Reviewers:  Clemens Heuberger
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/cheuberg/19063-acb               |  a33ceb40f76cd57791ad9e950fec234373278057
   Dependencies:  #18546             |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by cheuberg):

 * status:  needs_review => needs_info
 * reviewer:   => Clemens Heuberger


Comment:

 I have now reviewed this patch and added a few reviewer commits.

 Questions:

 * `ComplexBall.__init__`: why `Element.__init__` instead of
 `RingElement.__init__`

 * `.some_elements`: Is `1/3` intentional (this is an elaborate way of
 writing 0 in python)

 * Why is the representation `real - imag*I` restricted to exact negative
 imaginary parts and does not apply to
   `1 + [-0.333]*I`

 * `.__contains__`, `.contains_exact`: why do we have two distinct methods
 here? Why is an integer or a rational as the argument of `.__contains__`
 not handeled separately by the relevant .acb functions?

 Apart from that, a few documentation issues:

 * `_complex_mpfr_field_`: missing INPUT: section (parameter `parent`)

 * `_real_mpfi_`: missing INPUT: section (parameter parent), One-sentence-
 description mentions "real number" instead of "real interval".

 * `_mpfr_`: missing INPUT: section (parameter `parent`)

 * `.mid`, `.squash`: missing OUTPUT: section

 * `.mid` should have "see also" section (`.squash`)

 * `.identical` refers to a method `contains` which does not exist.

 * `.contains_exact`, `.identical`, `.overlaps`: missing INPUT: section
 (parameter `other`)

--
Ticket URL: <http://trac.sagemath.org/ticket/19063#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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