#18194: Speedup of calculation of Macdonald H and Ht bases
-------------------------------------+-------------------------------------
       Reporter:  zabrocki           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  minor              |    Milestone:  sage-6.7
      Component:  combinatorics      |   Resolution:
       Keywords:  sf, days67, sage-  |    Merged in:
  combinat                           |    Reviewers:  Travis Scrimshaw
        Authors:  Mike Zabrocki      |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  da67e9a2aa6c6c99a48ec6897c8726bc899982de
  public/combinat/mac_speedup-18194  |     Stopgaps:
   Dependencies:                     |
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Comment (by tscrim):

 Really? O_o I really don't believe that is faster because `homogeneous
 component` is:
 {{{#!python
 degree_on_basis = self.parent().degree_on_basis
 return self.parent().sum_of_terms((i, c)
                                   for (i, c) in self
                                   if degree_on_basis(i) == n)
 }}}
 Plus there is a `sorted` being called in `support`, not to mention the
 intermediate element created. I don't see how we'd be doing fewer terms in
 the sum.

 Ahhh...here's a thought, it's the call to `sorted` that results in the
 speedup because the smaller elements result in fewer terms that have to be
 resolved until the end. I'm going to experiment, but if that's true, then
 that's one subtle issue.

 Although that call to `QQqt` is superfluous as `_Lmunu` returns an element
 of `QQqt`.

--
Ticket URL: <http://trac.sagemath.org/ticket/18194#comment:49>
Sage <http://www.sagemath.org>
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