Removing Tabloid(s) class; improving class structure; adding functionality.

Author: tscrim

src/doc/en/reference/combinat/module_list.rst

@@ -362,7 +362,6 @@ Comprehensive Module List
     sage/combinat/tableau
     sage/combinat/tableau_residues
     sage/combinat/tableau_tuple
-    sage/combinat/tabloid
     sage/combinat/tamari_lattices
     sage/combinat/tiling
     sage/combinat/tools

src/sage/combinat/all.py

@@ -171,9 +171,6 @@
 lazy_import('sage.combinat.super_tableau',
             ["StandardSuperTableau", "SemistandardSuperTableau", "StandardSuperTableaux", "SemistandardSuperTableaux"])
 
-# Tabloids
-lazy_import('sage.combinat.tabloid', "Tabloids")
-
 # Words
 from .words.all import *
 

src/sage/combinat/catalog_partitions.py

@@ -10,7 +10,6 @@
 - :ref:`sage.combinat.superpartition`
 - :ref:`sage.combinat.tableau`
 - :ref:`sage.combinat.tableau_tuple`
-- :ref:`sage.combinat.tabloid`
 - :ref:`sage.combinat.skew_tableau`
 - :ref:`sage.combinat.ribbon`
 - :ref:`sage.combinat.ribbon_tableau`

src/sage/combinat/composition.py

@@ -45,6 +45,9 @@
 from sage.combinat.combinatorial_map import combinatorial_map
 from sage.misc.persist import register_unpickle_override
 
+from sage.misc.lazy_import import lazy_import
+lazy_import("sage.combinat.partition", "Partition")
+
 
 class Composition(CombinatorialElement):
     r"""
@@ -1186,7 +1189,6 @@ def to_partition(self):
             sage: Composition([]).to_partition()                                        # needs sage.combinat
             []
         """
-        from sage.combinat.partition import Partition
         return Partition(sorted(self, reverse=True))
 
     def to_skew_partition(self, overlap=1):
@@ -1754,7 +1756,7 @@ def _element_constructor_(self, lst) -> Composition:
             sage: P([3,3,1]) # indirect doctest
             [3, 3, 1]
         """
-        if isinstance(lst, Composition):
+        if isinstance(lst, (Composition, Partition)):
             lst = list(lst)
         elt = self.element_class(self, lst)
         if elt not in self:
@@ -1774,7 +1776,7 @@ def __contains__(self, x) -> bool:
             sage: [0,0] in Compositions()
             True
         """
-        if isinstance(x, Composition):
+        if isinstance(x, (Composition, Partition)):
             return True
         elif isinstance(x, list):
             for i in x:

src/sage/combinat/partition.py

@@ -5497,7 +5497,7 @@ def specht_module(self, base_ring=None):
             sage: SM = Partition([2,2,1]).specht_module(QQ); SM
             Specht module of [2, 2, 1] over Rational Field
             sage: s = SymmetricFunctions(QQ).s()
-            sage: s(SM.frobenius_image())                                               # needs sage.modules
+            sage: SM.frobenius_image()                                               # needs sage.modules
             s[2, 2, 1]
         """
         from sage.combinat.specht_module import SpechtModule
@@ -5570,6 +5570,24 @@ def simple_module_dimension(self, base_ring=None):
         from sage.combinat.specht_module import simple_module_rank
         return simple_module_rank(self, base_ring)
 
+    def tabloid_module(self, base_ring=None):
+        r"""
+        Return the tabloid module corresponding to ``self``.
+
+        EXAMPLES::
+
+            sage: TM = Partition([2,2,1]).tabloid_module(QQ); TM
+            Tabloid module of [2, 2, 1] over Rational Field
+            sage: TM.frobenius_image()
+            s[2, 2, 1] + s[3, 1, 1] + 2*s[3, 2] + 2*s[4, 1] + s[5]
+        """
+        from sage.combinat.specht_module import TabloidModule
+        from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra
+        if base_ring is None:
+            from sage.rings.rational_field import QQ
+            base_ring = QQ
+        R = SymmetricGroupAlgebra(base_ring, sum(self))
+        return TabloidModule(R, self)
 
 ##############
 # Partitions #

src/sage/combinat/permutation.py

@@ -7342,6 +7342,19 @@ def cardinality(self):
         """
         return factorial(self.n)
 
+    @cached_method
+    def gens(self):
+        r"""
+        Return a set of generators for ``self`` as a group.
+
+        EXAMPLES::
+
+            sage: P4 = Permutations(4)
+            sage: P4.gens()
+            ([2, 1, 3, 4], [1, 3, 2, 4], [1, 2, 4, 3])
+        """
+        return tuple(self.group_generators())
+
     def degree(self):
         """
         Return the degree of ``self``.