#18447: Implement dual-quasi-Schur basis in NCSF
-------------------------------------+-------------------------------------
       Reporter:  zabrocki           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  minor              |    Milestone:  sage-6.7
      Component:  combinatorics      |   Resolution:
       Keywords:  ncsf, qsym,        |    Merged in:
  quasiSchur, quasisymmetric         |    Reviewers:  Travis Scrimshaw
        Authors:  Mike Zabrocki      |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  09fe2c952b5857583300ee9f7f183973289418a0
  public/combinat/zabrocki/ncsf_quasi_schur_basis/18447|     Stopgaps:
   Dependencies:  #18415             |
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Changes (by tscrim):

 * cc: darij (added)
 * reviewer:   => Travis Scrimshaw


Comment:

 Those are some nice timing improvements Mike.

 I made a couple of changes which should result in a speedup to the
 multiplication. I cached the output of `composition_order` in the matrix
 function so that it doesn't get recomputed every time a multiplication is
 done. I also did some other optimizations where I got a good speed
 reduction in some of my testings.

 Did you test to see what the change in timings going from the
 Quasisymmetric-Schur to the Fundamental basis is? Mainly I'm wondering if
 we should leave that in as a direct coercion (instead of going through the
 Monomial basis) and implement an iterator over standard composition
 tableaux.

--
Ticket URL: <http://trac.sagemath.org/ticket/18447#comment:21>
Sage <http://www.sagemath.org>
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