#14541: Family over enumerated set has wrong category
-------------------------------------+-------------------------------------
       Reporter:  cnassau            |        Owner:  nthiery
           Type:  defect             |       Status:  needs_work
       Priority:  minor              |    Milestone:  sage-7.3
      Component:  categories         |   Resolution:
       Keywords:  Family, Category   |    Merged in:
  of finite enumerated sets,         |
  CartesianProduct                   |
        Authors:  Christian Nassau,  |    Reviewers:
  Nathann Cohen                      |
Report Upstream:  N/A                |  Work issues:
         Branch:  u/ncohen/14541     |       Commit:
                                     |  fd3d6d51a3251999e327cf18c38f3389b2ee2a1b
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * stopgaps:  wrongAnswerMarker =>
 * milestone:  sage-6.4 => sage-7.3


Comment:

 The first and second issues are fixed
 {{{
 sage: F = Family(Permutations(), lambda i: i)
 sage: F.category()
 Category of infinite enumerated sets
 sage: Family(cartesian_product([ZZ,ZZ]),lambda (x,y) :
 (x+y,x-y)).cardinality()
 +Infinity
 }}}
 However, the last issue is still outstanding:
 {{{
 sage: X=CombinatorialFreeModule(ZZ,ZZ)
 sage: X.basis().category()
 Category of infinite enumerated sets
 sage: TX = tensor((X,))
 sage: TX.basis().cardinality()
 +Infinity
 sage: TX.basis().category()
 Category of finite enumerated sets
 }}}
 This seems to be due to falling into a default of finite (enumerated) sets
 instead of just pulling the information from the category of the keys:
 {{{
 sage: TX.basis().keys()
 Image of Cartesian product of Integer Ring by <type 'tuple'>
 sage: TX.basis().keys().category()
 Category of sets
 }}}

 Also, the stopgap field is to be used for ticket(s) for the stopgaps.

--
Ticket URL: <https://trac.sagemath.org/ticket/14541#comment:18>
Sage <http://www.sagemath.org>
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