Add class CircuitsMatroid

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

@@ -27,6 +27,7 @@ Concrete implementations
    :maxdepth: 1
 
    sage/matroids/basis_matroid
+   sage/matroids/circuits_matroid
    sage/matroids/circuit_closures_matroid
    sage/matroids/linear_matroid
    sage/matroids/rank_matroid

src/sage/matroids/circuits_matroid.pxd

@@ -0,0 +1,31 @@
+from sage.matroids.matroid cimport Matroid
+from sage.matroids.set_system cimport SetSystem
+
+cdef class CircuitsMatroid(Matroid):
+    cdef frozenset _groundset  # _E
+    cdef int _matroid_rank  # _R
+    cdef SetSystem _C  # circuits
+    cdef dict _k_C  # k-circuits (k=len)
+    cdef bint _nsc_defined
+    cpdef groundset(self) noexcept
+    cpdef _rank(self, X) noexcept
+    cpdef full_rank(self) noexcept
+    cpdef _is_independent(self, F) noexcept
+    cpdef _max_independent(self, F) noexcept
+    cpdef _circuit(self, F) noexcept
+
+    # enumeration
+    cpdef bases(self) noexcept
+    cpdef circuits(self, k=*) noexcept
+    cpdef nonspanning_circuits(self) noexcept
+    cpdef no_broken_circuits_sets(self, ordering=*) noexcept
+
+    # properties
+    cpdef girth(self) noexcept
+    cpdef is_paving(self) noexcept
+
+    # isomorphism
+    cpdef _is_isomorphic(self, other, certificate=*) noexcept
+
+    # verification
+    cpdef is_valid(self) noexcept