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5457 Refactor symmetric functions and k-bounded subspace nthiery mhansen "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, 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
Apply
* [attachment:trac_5457-symmetric_functions-mz.2.patch]
" enhancement closed major sage-5.4 combinatorics fixed symmetric functions, days38, sd40 sage-combinat saliola bump chrisjamesberg zabrocki SimonKing sage-5.4.beta0 Mike Zabrocki, Anne Schilling, Jason Bandlow Dan Bump, Nicolas M. Thiéry, Jeroen Demeyer N/A #11563, #13109, #12969