#5200: [with patch, needs review] subsets and subwords bug fix + improvements.
---------------------------+------------------------------------------------
 Reporter:  hivert         |       Owner:  mhansen          
     Type:  enhancement    |      Status:  new              
 Priority:  major          |   Milestone:  sage-combinat    
Component:  combinatorics  |    Keywords:  subsets, subwords
---------------------------+------------------------------------------------
 This patches deals with several issues concerning subwords and subsets:
   1. It implements subsets for finite multisets (sets with repetitions).
      Before the patch:
 {{{
 sage: Subsets([2,2,3]).list()
 [{}, {2}, {3}, {2, 3}]
 }}}
      After:
 {{{
 sage: Subsets([2,2,3]).list()
 [[], [2], [3], [2, 2], [2, 3], [2, 2, 3]]
 }}}
   1. It implement {{{__contains__}}} which was missing for subsets and
 subwords:
      Before:
 {{{
 sage: st = Subsets([1,2,2,3]); Set([1,2]) in st
 ---------------------------------------------------------------------------
 NotImplementedError                       Traceback (most recent call
 last)
 }}}
      After:
 {{{
 sage: st = Subsets([1,2,2,3]); Set([1,2]) in st
 True
 }}}
   1. It fixes a bug in smallest_positions:
      Before:
 {{{
 sage: sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3])
 [4, 4, 4]
 }}}
      After:
 {{{
 sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3])
 False
 }}}
      which means that 113 is not a subword of 243312.
   4. It finally improves the doc and the tests.

 Since this is my first trac submission, any comment about this text or the
 patch is strongly welcome...

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5200>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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