NBC_sets: Return :class:SetSystem

src/sage/matroids/circuits_matroid.pyx

@@ -707,7 +707,7 @@ cdef class CircuitsMatroid(Matroid):
 
         - ``ordering`` -- list (optional); a total ordering of the groundset
 
-        OUTPUT: list of frozensets
+        OUTPUT: :class:`SetSystem`
 
         EXAMPLES::
 
@@ -774,7 +774,7 @@ cdef class CircuitsMatroid(Matroid):
                 else:
                     B.add(S)
 
-        return list(B)
+        return SetSystem(list(self.groundset()), B)
 
     cpdef no_broken_circuits_sets(self, ordering=None, reduced=False):
         r"""
@@ -787,7 +787,7 @@ cdef class CircuitsMatroid(Matroid):
 
         - ``ordering`` -- list (optional); a total ordering of the groundset
 
-        OUTPUT: list of frozensets
+        OUTPUT: :class:`SetSystem`
 
         EXAMPLES::
 
@@ -817,10 +817,11 @@ cdef class CircuitsMatroid(Matroid):
             True
         """
         from sage.topology.simplicial_complex import SimplicialComplex
-        return [frozenset(f) for f in SimplicialComplex(
-                    self.no_broken_circuits_facets(ordering, reduced),
-                    maximality_check=False
-                ).face_iterator()]
+        cdef set NBC = set()
+        for f in SimplicialComplex(self.no_broken_circuits_facets(ordering, reduced),
+                                   maximality_check=False).face_iterator():
+            NBC.add(frozenset(f))
+        return SetSystem(list(self.groundset()), NBC)
 
     cpdef broken_circuit_complex(self, ordering=None, reduced=False):
         r"""

src/sage/matroids/flats_matroid.pyx

@@ -446,7 +446,7 @@ cdef class FlatsMatroid(Matroid):
         `(W_0, ..., W_r)`, where `W_i` is the number of flats of rank `i`, and
         `r` is the rank of the matroid.
 
-        OUTPUT: a list of integers
+        OUTPUT: list of integers
 
         EXAMPLES::
 

src/sage/matroids/matroid.pyx

@@ -3104,7 +3104,7 @@ cdef class Matroid(SageObject):
         number of independent sets of rank `i`, and `r` is the rank of the
         matroid.
 
-        OUTPUT: a list of integers
+        OUTPUT: list of integers
 
         EXAMPLES::
 
@@ -3136,7 +3136,7 @@ cdef class Matroid(SageObject):
         matroid's characteristic polynomial. Moreover, `|w_i|` is the number of
         `(i-1)`-dimensional faces of the broken circuit complex of the matroid.
 
-        OUTPUT: a list of integers
+        OUTPUT: list of integers
 
         EXAMPLES::
 
@@ -3163,7 +3163,7 @@ cdef class Matroid(SageObject):
         `(W_0, \ldots, W_r)`, where `W_i` is the number of flats of rank `i`,
         and `r` is the rank of the matroid.
 
-        OUTPUT: a list of integers
+        OUTPUT: list of integers
 
         EXAMPLES::
 
@@ -3232,7 +3232,7 @@ cdef class Matroid(SageObject):
 
         - ``ordering`` -- list (optional); a total ordering of the groundset
 
-        OUTPUT: list of frozensets
+        OUTPUT: :class:`SetSystem`
 
         EXAMPLES::
 
@@ -3307,7 +3307,7 @@ cdef class Matroid(SageObject):
                 if is_indep:
                     B.append(frozenset(H))
                     next_level.extend(Ht)
-        return B
+        return SetSystem(list(self.groundset()), B)
 
     def no_broken_circuits_sets_iterator(self, ordering=None):
         r"""
@@ -7733,7 +7733,7 @@ cdef class Matroid(SageObject):
                         exist = False
                         if ((u in Y) and
                             (v in E-Y) and
-                            (not self.is_independent(Y|set([v]))) and
+                            (self.is_dependent(Y|set([v]))) and
                             (self.is_independent((Y|set([v])) - set([u])))):
                             exist = True
                         if ((u in E-Y) and