#18290: enhanced sets and cartesian products
-------------------------+-------------------------------------------------
       Reporter:         |        Owner:
  vdelecroix             |       Status:  needs_review
           Type:         |    Milestone:  sage-6.7
  enhancement            |   Resolution:
       Priority:  major  |    Merged in:
      Component:         |    Reviewers:
  categories             |  Work issues:
       Keywords:         |       Commit:
  cartesian_product      |  6389ff27cbcfcc1d51f2b6ad346c79ccd7eebbe3
        Authors:         |     Stopgaps:
  Vincent Delecroix      |
Report Upstream:  N/A    |
         Branch:         |
  public/18290           |
   Dependencies:         |
-------------------------+-------------------------------------------------
Changes (by vdelecroix):

 * commit:  c5d6006e918e9be9078d3ac1f16cbbdbe3aa8933 =>
     6389ff27cbcfcc1d51f2b6ad346c79ccd7eebbe3
 * branch:  u/nthiery/18290 => public/18290


Comment:

 As we discussed on the phone with Nicolas: I removed the abstract methods:
 `is_empty`, `is_finite` and `random_element` from `Sets`. For the first
 two, we might not want to call `cardinality` as this can easily lead to
 loop (e.g. #18400). As a rationale: a less specialized method should not
 try to call a more specialized one. For random_element: adding an optional
 abstract method would pollute the namespace.

 - unrank: `IndexError` is what is uniformly in `categories/*` and also in
 `combinat/cartesian_product`.
 - I moved is_empty from
 `Magmas.FinitelyGenerated.Unital.ParentMethods.is_empty` to
 `Magmas.Unital.is_empty` and everything looks fine
 - random_element: tuple removed

 I will add a second commit for `order` vs `cardinality` in `Groups`.

 Vincent
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=6389ff27cbcfcc1d51f2b6ad346c79ccd7eebbe3
 6389ff2]||{{{Trac 18290: reviewer comments}}}||

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Ticket URL: <http://trac.sagemath.org/ticket/18290#comment:31>
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