#17548: Partitions() is buggy
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       Reporter:  ferriszorro    |        Owner:  ferriszorro
           Type:  defect         |       Status:  needs_work
       Priority:  minor          |    Milestone:  sage-6.5
      Component:  combinatorics  |   Resolution:
       Keywords:  Partitions     |    Merged in:
        Authors:                 |    Reviewers:
Report Upstream:  N/A            |  Work issues:
         Branch:                 |       Commit:
   Dependencies:                 |     Stopgaps:  #17637
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Comment (by vdelecroix):

 Hello,

 Two bug-feature report.

 1. Depending on the input, the floor is sometimes `0` and sometimes `1`:
 {{{
 #!python
 sage: IntegerListsLex(5, length=3).list()               # it is 0
 [[5, 0, 0],
  [4, 1, 0],
  [4, 0, 1],
 ...
  [0, 2, 3],
  [0, 1, 4],
  [0, 0, 5]]
 sage: IntegerListsLex(5, length=3, max_slope=0).list()   # it is 0
 [[5, 0, 0], [4, 1, 0], [3, 2, 0], [3, 1, 1], [2, 2, 1]]
 sage: IntegerListsLex(5, max_slope=0).list()             # now it is 1!?
 [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]]
 }}}

 2. The iterator is sometimes completely wrong when the set is infinite:
 {{{
 sage: it = iter(IntegerListsLex(5))
 sage: for _ in range(10): print it.next()
 [5]
 [4, 1]
 [4, 0, 1]
 [4, 0, 0, 1]
 [4, 0, 0, 0, 1]
 [4, 0, 0, 0, 0, 1]
 [4, 0, 0, 0, 0, 0, 1]
 [4, 0, 0, 0, 0, 0, 0, 1]
 [4, 0, 0, 0, 0, 0, 0, 0, 1]
 [4, 0, 0, 0, 0, 0, 0, 0, 0, 1]
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/17548#comment:25>
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