fixing category of ncsym and dual

Author: fchapoton

src/sage/combinat/ncsym/dual.py

@@ -5,12 +5,12 @@
 
 - Travis Scrimshaw (08-04-2013): Initial version
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2013 Travis Scrimshaw <tscrim at ucdavis.edu>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.misc_c import prod
@@ -50,7 +50,7 @@ def __init__(self, R):
         # change the line below to assert(R in Rings()) once MRO issues from #15536, #15475 are resolved
         assert(R in Fields() or R in Rings()) # side effect of this statement assures MRO exists for R
         self._base = R # Won't be needed once CategoryObject won't override base_ring
-        category = GradedHopfAlgebras(R)  # TODO: .Commutative()
+        category = GradedHopfAlgebras(R).Commutative()
         Parent.__init__(self, category=category.WithRealizations())
 
         # Bases
@@ -103,7 +103,7 @@ def dual(self):
 
     class w(NCSymBasis_abstract):
         r"""
-        The Hopf algebra of symmetric functions in non-commuting variables
+        The dual Hopf algebra of symmetric functions in non-commuting variables
         in the `\mathbf{w}` basis.
 
         EXAMPLES::
@@ -134,10 +134,14 @@ def __init__(self, NCSymD):
             """
             def key_func_set_part(A):
                 return sorted(map(sorted, A))
-            CombinatorialFreeModule.__init__(self, NCSymD.base_ring(), SetPartitions(),
+
+            R = NCSymD.base_ring()
+            category = GradedHopfAlgebras(R).Commutative()
+            category &= NCSymDualBases(NCSymD)
+            CombinatorialFreeModule.__init__(self, R, SetPartitions(),
                                              prefix='w', bracket=False,
                                              sorting_key=key_func_set_part,
-                                             category=NCSymDualBases(NCSymD))
+                                             category=category)
 
         @lazy_attribute
         def to_symmetric_function(self):

src/sage/combinat/ncsym/ncsym.py

@@ -296,7 +296,7 @@ def __init__(self, R):
         # change the line below to assert(R in Rings()) once MRO issues from #15536, #15475 are resolved
         assert(R in Fields() or R in Rings()) # side effect of this statement assures MRO exists for R
         self._base = R # Won't be needed once CategoryObject won't override base_ring
-        category = GradedHopfAlgebras(R)  # TODO: .Cocommutative()
+        category = GradedHopfAlgebras(R).Cocommutative()
         Parent.__init__(self, category=category.WithRealizations())
 
     def _repr_(self):
@@ -361,9 +361,13 @@ def __init__(self, NCSym):
                 sage: NCSym = SymmetricFunctionsNonCommutingVariables(QQ)
                 sage: TestSuite(NCSym.m()).run()
             """
-            CombinatorialFreeModule.__init__(self, NCSym.base_ring(), SetPartitions(),
+            R = NCSym.base_ring()
+            category = GradedHopfAlgebras(R).Cocommutative()
+            category &= NCSymBases(NCSym)
+
+            CombinatorialFreeModule.__init__(self, R, SetPartitions(),
                                              prefix='m', bracket=False,
-                                             category=NCSymBases(NCSym))
+                                             category=category)
 
         @cached_method
         def _m_to_p_on_basis(self, A):