#18447: Implement dual-quasi-Schur basis in NCSF
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Reporter: zabrocki | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.7
Component: combinatorics | Resolution:
Keywords: ncsf, qsym, | Merged in:
quasiSchur | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3f0f3a6daffc8ce20820862d2df1584916848661
public/combinat/zabrocki/ncsf_quasi_schur_basis/18447| Stopgaps:
Dependencies: #18415 |
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Changes (by zabrocki):
* commit: => 3f0f3a6daffc8ce20820862d2df1584916848661
* branch: => public/combinat/zabrocki/ncsf_quasi_schur_basis/18447
Comment:
I am looking at how the quasisymmetric Schur basis was implemented and I
think that there is work that should be done. I would suggest that it is
better implemented through the monomial basis (right now it is implemented
in the fundamental basis).
It also seems that the notion of `CompositionTableau(x)` is too
restrictive since it doesn't allow for general fillings of composition
diagrams (which would be quite useful for the definitions of immaculate
tableaux). There is no documentation that indicates that the definition
of `CompositionTableau` comes from [QSCHUR] Haglund, Luoto, Mason, van
Willigenburg, *Quasisymmetric Schur functions*, J. Comb. Theory Ser. A 118
(2011), 463-490.
I think that the original implementation in #13505 was made with the
intention that one day it would be improved.
Here is a down and dirty implementation of the dual basis.
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Last 10 new commits:
||[http://git.sagemath.org/sage.git/commit/?id=ad57c95f4865dcf94bec776e223c71945bc6c6b3
ad57c95]||{{{add documentation on Phi and Psi under Concrete
representations, monomial and immaculate go under other}}}||
||[http://git.sagemath.org/sage.git/commit/?id=7060357c4c6d55c49d55e4ac01369c699f88aa38
7060357]||{{{cleanup of recent changes, indents, reference links}}}||
||[http://git.sagemath.org/sage.git/commit/?id=aa9301dc7d835896d3e2b9cf1be415ce78f448aa
aa9301d]||{{{changed coercions on complete/elementary/Phi/Psi to algebra
morphisms rather than module morphisms}}}||
||[http://git.sagemath.org/sage.git/commit/?id=e0cb35ed51155865cbdf3598cc2c62fe138ca5e9
e0cb35e]||{{{deleted complete._from_elementary_on_basis which was no
longer in use}}}||
||[http://git.sagemath.org/sage.git/commit/?id=8b2de9197d3785030858defdd7374b65995ad10d
8b2de91]||{{{make the headers nice in the NCSF/QSym section of reference
manual}}}||
||[http://git.sagemath.org/sage.git/commit/?id=d17ebcbe0d28f9d108a91ca57b8667160c8dea84
d17ebcb]||{{{Merge tag '6.7' into
public/combinat/zabrocki/ncsf_qsym_doc_cleanup/18415}}}||
||[http://git.sagemath.org/sage.git/commit/?id=960b32b2b9e546940e2785dd7f5b341ee6cc8ce4
960b32b]||{{{add generic_basis_code to the reference manual, correct
link}}}||
||[http://git.sagemath.org/sage.git/commit/?id=b90b61ae95a23d403cf1f29193ce7ef82914c1ae
b90b61a]||{{{delete weird endomorphism todo, allow to_descent_algebra to
guess at degree}}}||
||[http://git.sagemath.org/sage.git/commit/?id=f2d313a2ec96e09b054fb71a32c1afee4f3f26cd
f2d313a]||{{{correction of doc test with wrong base_ring}}}||
||[http://git.sagemath.org/sage.git/commit/?id=3f0f3a6daffc8ce20820862d2df1584916848661
3f0f3a6]||{{{quick and dirty implementation of dual Quasi-Schur basis}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/18447#comment:1>
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