#15949: Involutions on NSym and QSym part II
-------------------------------------+-------------------------------------
       Reporter:  darij              |        Owner:
           Type:  defect             |       Status:  positive_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  combinatorics      |   Resolution:
       Keywords:  partitions,        |    Merged in:
  symmetric functions, NSym, QSym,   |    Reviewers:  Travis Scrimshaw
  NCSF, Kronecker product,           |  Work issues:
        Authors:  Darij Grinberg     |       Commit:
Report Upstream:  N/A                |  5951b6d429c94fcba5f1c235be3465fdb845766a
         Branch:  public/combinat    |     Stopgaps:
  /invol-nsym-2                      |
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * status:  needs_review => positive_review
 * reviewer:   => Travis Scrimshaw


Comment:

 I get 2m 45s versus 8s:
 {{{
 sage: %time Psi[2,1,2,2,1].internal_product(Psi[1,1,1,1,1,1,1,1])
 CPU times: user 2min 17s, sys: 332 ms, total: 2min 18s
 Wall time: 2min 45s
 0
 sage: %time Psi.internal_product_on_basis_by_bracketing([2,1,2,2,1],
 [1,1,1,1,1,1,1,1])
 CPU times: user 6.61 s, sys: 4 ms, total: 6.62 s
 Wall time: 7.99 s
 0
 }}}
 Perhaps there was some caching going on that resulted in the speedup? Most
 of the time spent seems to be in computing the list of integer matrices
 (which definitely could use optimization). So I'm okay with a positive
 review here since the bottleneck is not in this code and it should be
 faster for "long" compositions.

 PS - this one seems to be the worst:
 {{{
 sage: %time Psi.internal_product_on_basis_by_bracketing([1,1,1,1,2,2],
 [1]*8)
 CPU times: user 14 s, sys: 56 ms, total: 14 s
 Wall time: 17.2 s
 0
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/15949#comment:19>
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