Add class FlatsMatroid

src/doc/en/reference/matroids/index.rst

@@ -29,6 +29,7 @@ Concrete implementations
    sage/matroids/basis_matroid
    sage/matroids/circuits_matroid
    sage/matroids/circuit_closures_matroid
+   sage/matroids/flats_matroid
    sage/matroids/linear_matroid
    sage/matroids/rank_matroid
    sage/matroids/graphic_matroid

src/sage/matroids/constructor.py

@@ -113,6 +113,7 @@
 import sage.matroids.basis_exchange_matroid
 from .rank_matroid import RankMatroid
 from .circuits_matroid import CircuitsMatroid
+from .flats_matroid import FlatsMatroid
 from .circuit_closures_matroid import CircuitClosuresMatroid
 from .basis_matroid import BasisMatroid
 from .linear_matroid import LinearMatroid, RegularMatroid, BinaryMatroid, TernaryMatroid, QuaternaryMatroid
@@ -180,6 +181,7 @@ def Matroid(groundset=None, data=None, **kwds):
     - ``circuits`` -- The list of circuits of the matroid.
     - ``nonspanning_circuits`` -- The list of nonspanning_circuits of the
       matroid.
+    - ``flats`` -- The dictionary of flats indexed by their rank.
     - ``graph`` -- A graph, whose edges form the elements of the matroid.
     - ``matrix`` -- A matrix representation of the matroid.
     - ``reduced_matrix`` -- A reduced representation of the matroid: if
@@ -698,8 +700,9 @@ def Matroid(groundset=None, data=None, **kwds):
     key = None
     if data is None:
         for k in ['bases', 'independent_sets', 'circuits',
-                  'nonspanning_circuits', 'graph', 'matrix', 'reduced_matrix',
-                  'rank_function', 'revlex', 'circuit_closures', 'matroid']:
+                  'nonspanning_circuits', 'flats', 'graph', 'matrix',
+                  'reduced_matrix', 'rank_function', 'revlex',
+                  'circuit_closures', 'matroid']:
             if k in kwds:
                 data = kwds.pop(k)
                 key = k
@@ -791,6 +794,16 @@ def Matroid(groundset=None, data=None, **kwds):
             nsc_defined=True
         )
 
+    # Flats
+    elif key == 'flats':
+        # Determine groundset
+        if groundset is None:
+            groundset = set()
+            for i in data:
+                for F in data[i]:
+                    groundset.update(F)
+        M = FlatsMatroid(groundset=groundset, flats=data)
+
     # Graphs:
     elif key == 'graph':
         from sage.graphs.graph import Graph

src/sage/matroids/flats_matroid.pxd

@@ -0,0 +1,20 @@
+from sage.matroids.matroid cimport Matroid
+
+cdef class FlatsMatroid(Matroid):
+    cdef frozenset _groundset  # _E
+    cdef int _matroid_rank  # _R
+    cdef dict _F  # flats
+    cpdef groundset(self) noexcept
+    cpdef _rank(self, X) noexcept
+    cpdef full_rank(self) noexcept
+    cpdef _is_independent(self, F) noexcept
+
+    # enumeration
+    cpdef flats(self, k) noexcept
+    cpdef whitney_numbers2(self) noexcept
+
+    # isomorphism
+    cpdef _is_isomorphic(self, other, certificate=*) noexcept
+
+    # verification
+    cpdef is_valid(self) noexcept