store incidence matrix, if initialized from it

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -427,6 +427,12 @@ cdef class CombinatorialPolyhedron(SageObject):
             self._n_Hrepresentation = data.ncols()
             self._n_Vrepresentation = data.nrows()
 
+            # Store the incidence matrix.
+            if not data.is_immutable():
+                data = data.__copy__()
+                data.set_immutable()
+            self.incidence_matrix.set_cache(data)
+
             # Initializing the facets in their Bit-representation.
             self._bitrep_facets = incidence_matrix_to_bit_rep_of_facets(data)
 
@@ -984,11 +990,22 @@ cdef class CombinatorialPolyhedron(SageObject):
             [0 0 0 1 1 1]
             [0 1 0 1 1 0]
             [0 1 1 1 0 0]
-            sage: P.incidence_matrix() == C.incidence_matrix()
+
+        In this case the incidence matrix is only computed once::
+
+            sage: P.incidence_matrix() is C.incidence_matrix()
+            True
+            sage: C.incidence_matrix.clear_cache()
+            sage: C.incidence_matrix() is P.incidence_matrix()
+            False
+            sage: C.incidence_matrix() == P.incidence_matrix()
             True
 
+        ::
+
             sage: P = polytopes.permutahedron(5)
             sage: C = P.combinatorial_polyhedron()
+            sage: C.incidence_matrix.clear_cache()
             sage: C.incidence_matrix() == P.incidence_matrix()
             True
 
@@ -998,6 +1015,8 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: P = Polyhedron([[0,0]])
             sage: P.incidence_matrix()
             [1 1]
+            sage: C = P.combinatorial_polyhedron()
+            sage: C.incidence_matrix.clear_cache()
             sage: P.combinatorial_polyhedron().incidence_matrix()
             [1 1]
 
@@ -1006,9 +1025,11 @@ cdef class CombinatorialPolyhedron(SageObject):
         Check that :trac:`29455` is fixed::
 
             sage: C = Polyhedron([[0]]).combinatorial_polyhedron()
+            sage: C.incidence_matrix.clear_cache()
             sage: C.incidence_matrix()
             [1]
             sage: C = CombinatorialPolyhedron(-1)
+            sage: C.incidence_matrix.clear_cache()
             sage: C.incidence_matrix()
             []
         """