#17220: Matrix_complex_ball_dense: Level 1 implementation (using acb_mat from 
Arb)
-------------------------------------+-------------------------------------
       Reporter:  cheuberg           |        Owner:
           Type:  enhancement        |       Status:  needs_info
       Priority:  major              |    Milestone:  sage-6.10
      Component:  numerical          |   Resolution:
       Keywords:  arb, acb_mat,      |    Merged in:
  complex balls, matrix              |    Reviewers:
        Authors:  Clemens Heuberger  |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  6c9f0c7cefae2ad60c2a152c233e515ee9bce176
  u/cheuberg/matrix/acb_dense        |     Stopgaps:
   Dependencies:  #18546, #19063     |
-------------------------------------+-------------------------------------
Changes (by cheuberg):

 * status:  needs_review => needs_info
 * dependencies:  #17218, #17194, #16747 => #18546, #19063
 * milestone:  sage-6.6 => sage-6.10


Old description:

> As a follow-up to #17194 and #17218, where the `arb` and `acb` types of
> the Arb library have been wrapped, this wraps the `acb_mat` type for
> matrices over complex balls.
>
> In this ticket, level 1 functionality of matrices is provided.

New description:

 Wrap the `acb_mat` type for matrices over complex balls.

 In this ticket, level 1 functionality of matrices is provided.

--

Comment:

 I merged #18546 and #19063 as these tickets have been closed.

 There is the following problem: #19063 uses the `experimental` decorator
 on `ComplexBallField.__init__`. On the other hand, `CBF` is defined in
 that module, which calls the constructor of `ComplexBallField`.

 Here, in `matrix.py` I need to import `ComplexBallField` in order to check
 whether the ring is a complex ball field. This immediately triggers the
 `experimental` warning even if no `ComplexBallField` is constructed
 explicitly, because `CBF` is constructed.

 I see four options:
 1. remove the `experimental` warning in `ComplexBallField` now.
 2. remove the `experimental` warning in `ComplexBallField` once #19152 is
 merged
 3. move `CBF = ComplexBallField()` to a separate module, e.g.
 `sage.rings.complex_ball_acb_default` and replace all lines `from
 sage.rings.complex_ball_acb import CBF` by `from
 sage.rings.complex_ball_acb_default import CBF` and undo this change once
 the `experimental` warning disappears
 4. fix doctests in 252 other modules whenever a matrix is constructed
 which falls back to the generic implementation.

 Suggestions?

--
Ticket URL: <http://trac.sagemath.org/ticket/17220#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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