Trac #28605: CombinatorialPolyhedron: replace attributes by methods

Replace attributes in `CombinatorialPolyhedron` by methods, such that
they can potentially be lazily evaluated.

More precisely we replace an attribute by a private attribute (with
leading `_`) and add a method without leading `_`. E.g. the attribute
`far_face_tuple` is replaced by `_far_face_tuple` and we add a method
`far_face_tuple(self)`. Thus we gain flexibility in the sense that those
attributes must not be set on initialization.

This is motivated by #10777.

We remove the attribute `Vinv` completely, as it is not being used.

URL: https://trac.sagemath.org/28605
Reported by: gh-kliem
Ticket author(s): Jonathan Kliem
Reviewer(s): Laith Rastanawi, Jean-Philippe Labbé

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

@@ -8,19 +8,19 @@ from .polyhedron_face_lattice   cimport PolyhedronFaceLattice
 
 @cython.final
 cdef class CombinatorialPolyhedron(SageObject):
+    # Do not assume any of those attributes to be initialized, use the corresponding methods instead.
     cdef tuple _V                       # the names of VRep, if they exist
-    cdef dict _Vinv                     # dictionary to look up enumeration of vertices
     cdef tuple _H                       # the names of HRep, if they exist
     cdef tuple _equalities              # stores equalities, given on input (might belong to Hrep)
     cdef int _dimension                 # stores dimension, -2 on init
     cdef unsigned int _length_Hrepr     # Hrepr might include equalities
     cdef unsigned int _length_Vrepr     # Vrepr might include rays/lines
     cdef size_t _n_facets               # length Hrep without equalities
     cdef bint _unbounded                # ``True`` iff Polyhedron is unbounded
-    cdef ListOfFaces bitrep_facets      # facets in bit representation
-    cdef ListOfFaces bitrep_Vrepr       # vertices in bit representation
-    cdef ListOfFaces far_face           # a 'face' containing all none-vertices of Vrepr
-    cdef tuple far_face_tuple
+    cdef ListOfFaces _bitrep_facets     # facets in bit representation
+    cdef ListOfFaces _bitrep_Vrepr      # vertices in bit representation
+    cdef ListOfFaces _far_face          # a 'face' containing all none-vertices of Vrepr
+    cdef tuple _far_face_tuple
     cdef tuple _f_vector
 
     # Edges, ridges and incidences are stored in a pointer of pointers.
@@ -40,6 +40,17 @@ cdef class CombinatorialPolyhedron(SageObject):
     cdef size_t _n_face_lattice_incidences
     cdef PolyhedronFaceLattice _all_faces          # class to generate Hasse diagram incidences
 
+    cdef tuple V(self)
+    cdef tuple H(self)
+    cdef tuple equalities(self)
+    cdef unsigned int length_Vrepr(self)
+    cdef unsigned int length_Hrepr(self)
+    cdef bint unbounded(self)
+    cdef ListOfFaces bitrep_facets(self)
+    cdef ListOfFaces bitrep_Vrepr(self)
+    cdef ListOfFaces far_face(self)
+    cdef tuple far_face_tuple(self)
+
     # Space for edges, ridges, etc. is allocated with ``MemoryAllocators``.
     # Upon success they are copied to ``_mem_tuple``.
     # Thus deallocation (at the correct time) is taken care of.