Trac #29455: Bug in incidence_matrix of CombinatorialPolyhedron

The `incidence_matrix` method of a 0-dimensional
`CombinatorialPolyhedron` returns an error:
{{{
sage: P = Polyhedron([[0]]); P
A 0-dimensional polyhedron in ZZ^1 defined as the convex hull of 1
vertex
sage: C = P.combinatorial_polyhedron()
sage: C.incidence_matrix()
------------------------------------------------------------------------
---
ValueError                                Traceback (most recent call
last)
<ipython-input-7-dab311ba238f> in <module>()
----> 1 C.incidence_matrix()
...
ValueError: ``output_dimension`` must be the dimension of proper faces
}}}

We fix this and make the `0`-dimensional case consistent with
`Polyhedron_base`.

Also we make `incidence_matrix` a `chached_method`.

URL: https://trac.sagemath.org/29455
Reported by: gh-LaisRast
Ticket author(s): Jonathan Kliem
Reviewer(s): Laith Rastanawi

Author: Release Manager

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

@@ -955,6 +955,7 @@ cdef class CombinatorialPolyhedron(SageObject):
 
         return tuple(facets)
 
+    @cached_method
     def incidence_matrix(self):
         """
         Return the incidence matrix.
@@ -990,12 +991,41 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: C = P.combinatorial_polyhedron()
             sage: C.incidence_matrix() == P.incidence_matrix()
             True
+
+        The incidence matrix is consistent with
+        :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.incidence_matrix`::
+
+            sage: P = Polyhedron([[0,0]])
+            sage: P.incidence_matrix()
+            [1 1]
+            sage: P.combinatorial_polyhedron().incidence_matrix()
+            [1 1]
+
+        TESTS:
+
+        Check that :trac:`29455` is fixed::
+
+            sage: C = Polyhedron([[0]]).combinatorial_polyhedron()
+            sage: C.incidence_matrix()
+            [1]
+            sage: C = CombinatorialPolyhedron(-1)
+            sage: C.incidence_matrix()
+            []
         """
         from sage.rings.all import ZZ
         from sage.matrix.constructor import matrix
         incidence_matrix = matrix(ZZ, self.n_Vrepresentation(),
                                   self.n_Hrepresentation(), 0)
 
+        if self.dim() < 1:
+            # Small cases.
+            if self.dim() == 0:
+                # To be consistent with ``Polyhedron_base``,
+                for i in range(self.n_Hrepresentation()):
+                    incidence_matrix[0,i] = 1
+            incidence_matrix.set_immutable()
+            return incidence_matrix
+
         # If equalities are present, we add them as first columns.
         n_equalities = 0
         if self.facet_names() is not None:
@@ -1010,6 +1040,8 @@ cdef class CombinatorialPolyhedron(SageObject):
             for Vindex in facet.ambient_V_indices():
                 incidence_matrix[Vindex, Hindex] = 1
 
+        incidence_matrix.set_immutable()
+
         return incidence_matrix
 
     def edges(self, names=True):