diff --git a/src/sage/matroids/circuits_matroid.pxd b/src/sage/matroids/circuits_matroid.pxd
index 0b79ea24044..2c876fa3a48 100644
--- a/src/sage/matroids/circuits_matroid.pxd
+++ b/src/sage/matroids/circuits_matroid.pxd
@@ -2,10 +2,11 @@ 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 frozenset _groundset
+    cdef int _matroid_rank
     cdef set _C  # circuits
     cdef dict _k_C  # k-circuits (k=len)
+    cdef list _sorted_C_lens
     cdef bint _nsc_defined
     cpdef groundset(self)
     cpdef _rank(self, X)
diff --git a/src/sage/matroids/circuits_matroid.pyx b/src/sage/matroids/circuits_matroid.pyx
index 778591efbf4..e9c3a94f3af 100644
--- a/src/sage/matroids/circuits_matroid.pyx
+++ b/src/sage/matroids/circuits_matroid.pyx
@@ -80,6 +80,7 @@ cdef class CircuitsMatroid(Matroid):
             except KeyError:
                 self._k_C[len(C)] = set()
                 self._k_C[len(C)].add(C)
+        self._sorted_C_lens = sorted(self._k_C)
         self._matroid_rank = self.rank(self._groundset)
         self._nsc_defined = nsc_defined
 
@@ -160,7 +161,7 @@ cdef class CircuitsMatroid(Matroid):
         """
         cdef set XX = set(X)
         cdef int i, l = len(XX)
-        for i in sorted(self._k_C):
+        for i in self._sorted_C_lens:
             if i > l:
                 break
             for C in self._k_C[i]:
@@ -220,7 +221,7 @@ cdef class CircuitsMatroid(Matroid):
         """
         cdef set XX = set(X)
         cdef int i, l = len(XX)
-        for i in sorted(self._k_C):
+        for i in self._sorted_C_lens:
             if i > l:
                 break
             for C in self._k_C[i]:
@@ -249,8 +250,9 @@ cdef class CircuitsMatroid(Matroid):
         cdef set XX = set(X)
         cdef frozenset S
         cdef int i
-        for i in sorted(self._k_C):
-            if i > len(XX) + 1: break
+        for i in self._sorted_C_lens:
+            if i > len(XX) + 1:
+                break
             for C in self._k_C[i]:
                 S = C - XX
                 if len(S) == 1:
@@ -569,7 +571,7 @@ cdef class CircuitsMatroid(Matroid):
             SetSystem of 0 sets over 8 elements
             sage: sorted([sorted(X) for X in M.dependent_r_sets(4)])
             [['a', 'b', 'c', 'd'], ['a', 'b', 'e', 'f'], ['a', 'b', 'g', 'h'],
-            ['c', 'd', 'e', 'f'], ['e', 'f', 'g', 'h']]
+             ['c', 'd', 'e', 'f'], ['e', 'f', 'g', 'h']]
         """
         cdef int i
         cdef set NB = set()
@@ -924,7 +926,7 @@ cdef class CircuitsMatroid(Matroid):
         cdef int i, j, k
         cdef frozenset C1, C2, C3, I12, U12
         cdef bint flag
-        for (i, j) in combinations_with_replacement(sorted(self._k_C), 2):
+        for (i, j) in combinations_with_replacement(self._sorted_C_lens, 2):
             # loop through all circuit length pairs (i, j) with i <= j
             for C1 in self._k_C[i]:
                 if not C1:  # the empty set can't be a circuit
diff --git a/src/sage/matroids/matroid.pyx b/src/sage/matroids/matroid.pyx
index 2c395309088..a274df52180 100644
--- a/src/sage/matroids/matroid.pyx
+++ b/src/sage/matroids/matroid.pyx
@@ -2855,9 +2855,9 @@ cdef class Matroid(SageObject):
             sage: M = matroids.catalog.Pappus()
             sage: M.independent_r_sets(4)
             SetSystem of 0 sets over 9 elements
-            sage: M.independent_r_sets(3)
+            sage: S = M.independent_r_sets(3); S
             SetSystem of 75 sets over 9 elements
-            sage: frozenset({'a', 'c', 'e'}) in _
+            sage: frozenset({'a', 'c', 'e'}) in S
             True
 
         .. SEEALSO::
@@ -8296,7 +8296,7 @@ cdef class Matroid(SageObject):
         For a matroid with loops, the broken circuit complex is not defined,
         and the method yields an error::
 
-            sage: M = Matroid(flats={0:['a'], 1:['ab', 'ac'], 2:['abc']})
+            sage: M = Matroid(flats={0: ['a'], 1: ['ab', 'ac'], 2: ['abc']})
             sage: M.broken_circuit_complex()
             Traceback (most recent call last):
             ...