#15998: Restore some documentation and doctests and a function removed with 
#15466
-------------------------------------+-------------------------------------
       Reporter:  darij              |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  combinatorics      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Darij Grinberg     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  public/combinat/re-15466           |  1c4454fad5d281acb2f5d51e57182cef16829e2d
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by darij):

 * status:  needs_info => needs_review


Comment:

 Done!

 Little bonus:

 before:

 {{{
 sage: %timeit Partitions(2, length=1).list()
 1000 loops, best of 3: 187 µs per loop
 sage: %timeit Partitions(5, length=1).list()
 1000 loops, best of 3: 200 µs per loop
 sage: %timeit Partitions(5, length=2).list()
 1000 loops, best of 3: 340 µs per loop
 sage: %timeit Partitions(7, length=2).list()
 1000 loops, best of 3: 472 µs per loop
 sage: %timeit Partitions(7, length=4).list()
 1000 loops, best of 3: 623 µs per loop
 sage: %timeit Partitions(7, length=6).list()
 1000 loops, best of 3: 336 µs per loop
 sage: %timeit Partitions(14, length=1).list()
 1000 loops, best of 3: 187 µs per loop
 sage: %timeit Partitions(14, length=4).list()
 100 loops, best of 3: 3.36 ms per loop
 sage: %timeit Partitions(14, length=8).list()
 100 loops, best of 3: 2.46 ms per loop
 sage: %timeit Partitions(14, length=12).list()
 1000 loops, best of 3: 621 µs per loop
 sage: %timeit Partitions(30, length=2).list()
 1000 loops, best of 3: 1.57 ms per loop
 sage: %timeit Partitions(30, length=5).list()
 10 loops, best of 3: 54.6 ms per loop
 sage: %timeit Partitions(30, length=10).list()
 10 loops, best of 3: 131 ms per loop
 sage: %timeit Partitions(30, length=20).list()
 10 loops, best of 3: 15.9 ms per loop
 sage: %timeit Partitions(60, length=2).list()
 100 loops, best of 3: 2.89 ms per loop
 sage: %timeit Partitions(60, length=5).list()
 1 loops, best of 3: 682 ms per loop
 sage: %timeit Partitions(60, length=40).list()
 1 loops, best of 3: 413 ms per loop
 sage: %timeit Partitions(100, length=2).list()
 100 loops, best of 3: 5.31 ms per loop
 sage: %timeit Partitions(200, length=2).list()
 100 loops, best of 3: 9.97 ms per loop
 sage: %timeit Partitions(300, length=3).list()
 1 loops, best of 3: 821 ms per loop
 sage: %timeit Partitions(300, length=280).list()
 1 loops, best of 3: 2.47 s per loop
 }}}

 after:

 {{{
 sage: %timeit Partitions(2, length=1).list()
 10000 loops, best of 3: 19.5 µs per loop
 sage: %timeit Partitions(5, length=1).list()
 100000 loops, best of 3: 16 µs per loop
 sage: %timeit Partitions(5, length=2).list()
 10000 loops, best of 3: 19.4 µs per loop
 sage: %timeit Partitions(7, length=2).list()
 10000 loops, best of 3: 16.2 µs per loop
 sage: %timeit Partitions(7, length=4).list()
 100000 loops, best of 3: 16 µs per loop
 sage: %timeit Partitions(7, length=6).list()
 10000 loops, best of 3: 19.5 µs per loop
 sage: %timeit Partitions(14, length=1).list()
 10000 loops, best of 3: 16.1 µs per loop
 sage: %timeit Partitions(14, length=4).list()
 100000 loops, best of 3: 16.3 µs per loop
 sage: %timeit Partitions(14, length=8).list()
 100000 loops, best of 3: 17.6 µs per loop
 sage: %timeit Partitions(14, length=12).list()
 100000 loops, best of 3: 16.1 µs per loop
 sage: %timeit Partitions(30, length=2).list()
 10000 loops, best of 3: 19.3 µs per loop
 sage: %timeit Partitions(30, length=5).list()
 10000 loops, best of 3: 20.8 µs per loop
 sage: %timeit Partitions(30, length=10).list()
 10000 loops, best of 3: 20 µs per loop
 sage: %timeit Partitions(30, length=20).list()
 100000 loops, best of 3: 18 µs per loop
 sage: %timeit Partitions(60, length=2).list()
 100000 loops, best of 3: 16.2 µs per loop
 sage: %timeit Partitions(60, length=5).list()
 10000 loops, best of 3: 58 µs per loop
 sage: %timeit Partitions(60, length=40).list()
 10000 loops, best of 3: 23.5 µs per loop
 sage: %timeit Partitions(100, length=2).list()
 100000 loops, best of 3: 16.6 µs per loop
 sage: %timeit Partitions(200, length=2).list()
 10000 loops, best of 3: 20.3 µs per loop
 sage: %timeit Partitions(300, length=3).list()
 10000 loops, best of 3: 77.2 µs per loop
 sage: %timeit Partitions(300, length=280).list()
 1 loops, best of 3: 283 ms per loop
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/15998#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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