#15919: unrank via R[i] conflicts with notation for constructing polynomial 
rings
in CartesianProduct
-------------------------------------+-------------------------------------
       Reporter:  darij              |        Owner:
           Type:  defect             |       Status:  positive_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  algebra            |   Resolution:
       Keywords:  notation,          |    Merged in:
  algebra, polynomial                |    Reviewers:  Travis Scrimshaw
        Authors:  Nicolas M. Thiéry  |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  79d469861431ac8d6be5ad4edeace1c6ac8a62c8
  u/tscrim/ticket/15919              |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by nthiery):

 Replying to [comment:23 darij]:
 > The only thing that somewhat worries me is the speed. Before:
 > ...
 > I don't know how often this unranking is used, though, and whether these
 µs add up...

 Ah good point; the `isinstance` and `in EnumeratedSets` checks cause a
 little
 overhead which is non negligible for inputs that have super fast
 unranking (like lists).

 My impression is that this unranking is not used much. If it really
 became a bottleneck, a reasonable fix would be to have
 CartesianProduct build unranking functions once for all upon the first
 unrank (I started toying with this in
 u/nthiery/15919-unrank-unrank-from), so that the above checks would be
 done only once.

 Besides, things should eventually resolve by themselves as
 CartesianProduct gets
 progressively replaced by cartesian_product (for which the inputs are
 parents, or coerced into parents), and parents implement more
 systematically the unrank protocol.

 So altogether, in this balance between overhead and correctness, I
 would lean here toward correctness. What do you think?

--
Ticket URL: <http://trac.sagemath.org/ticket/15919#comment:24>
Sage <http://www.sagemath.org>
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