#5457: Refactor symmetric functions and k-bounded subspace
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Reporter: nthiery | Owner: mhansen
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.3
Component: combinatorics | Resolution:
Keywords: symmetric functions, sd38, sd40 | Work issues:
Report Upstream: N/A | Reviewers: Dan Bump,
Franco Saliola
Authors: Mike Zabrocki, Anne Schilling | Merged in:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Mike Zabrocki, Anne Schilling', 'oldvalue': ''}):
* keywords: => symmetric functions, sd38, sd40
* reviewer: => Dan Bump, Franco Saliola
* author: => Mike Zabrocki, Anne Schilling
Old description:
> Refactor symmetric functions to:
> - use a single entry point, as in MuPAD-Combinat. Something like:
> - S = SymmetricFunctions(field)
> - S.schur
> - S.jack(t).P
> - S.macdonald(t,q).Q
> - S.kSchur(3).H
> - use the coercion framework
> - use the category framework
>
> See also:http://groups.google.com/group/sage-devel/msg/a49f3288fca1b75c
New description:
This patch restructures the implementation of symmetric functions in sage
The new implementation makes use of multiple realizations and the category
framework. The new access to symmetric functions is via
{{{
sage: Sym = SymmetricFunctions(QQ)
}}}
Further new features that are implemented:
- The ring of symmetric functions is now endowed with a Hopf algebra
structure.
The coproduct and antipode are implemented (which were missing before).
- A tutorial on how to use symmetric functions in sage is included at the
beginning of sf.py which is also accessible via
{{{
sage: SymmetricFunctions??
}}}
- Symmetric functions should now work a lot better with respect to
specializing parameters like `q` and `t` for Hall-Littlewood, Jack
and Macdonald symmetric functions. Certain functionalities before
this change were broken or not possible.
- Documentation was added to LLT polynomials (which had very sparse
documentation
previously).
- The `k`-bounded subspace of the ring of symmetric function was
implemented.
The `k`-Schur functions now live in the `k`-bounded subspace rather than
in the ring of symmetric functions as before.
This patch gained tremendously by the tutorial on symmetric functions
written
by Jason Bandlow and Nicolas Thiery, a draft on the `k`-bounded subspace
by
Jason Bandlow, and code multiple realizations written by Franco Saliola.
See also:http://groups.google.com/group/sage-devel/msg/a49f3288fca1b75c
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5457#comment:5>
Sage <http://www.sagemath.org>
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