Refactor symmetric functions and k-bounded subspace

[nthiery]

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

Depends on #11563
Depends on #13109
Depends on #12969

CC: @sagetrac-sage-combinat @saliola @dwbump @sagetrac-chrisjamesberg @zabrocki @simon-king-jena

Component: combinatorics

Keywords: symmetric functions, days38, sd40

Author: Mike Zabrocki, Anne Schilling, Jason Bandlow

Reviewer: Dan Bump, Nicolas M. Thiéry, Jeroen Demeyer

Merged: sage-5.4.beta0

Issue created by migration from https://trac.sagemath.org/ticket/5457

[nthiery]

Description changed:

--- 
+++ 
@@ -1,10 +1,10 @@
 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
+     -  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
 

[anneschilling]

Dependencies: 13109

[anneschilling]

Changed dependencies from 13109 to none

[anneschilling]

Reviewer: Dan Bump, Franco Saliola

[anneschilling]

Author: Mike Zabrocki, Anne Schilling

[anneschilling]

Description changed:

--- 
+++ 
@@ -1,11 +1,38 @@
-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
+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

[anneschilling]

Changed keywords from none to symmetric functions, sd38, sd40