CombinatorialPolyhedron: Make it a factory function, rename class to …

…CombinatorialPolyhedron_class

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

@@ -7,7 +7,7 @@ from .face_data_structure       cimport face_t
 from .polyhedron_face_lattice   cimport PolyhedronFaceLattice
 
 @cython.final
-cdef class CombinatorialPolyhedron(Element):
+cdef class CombinatorialPolyhedron_class(Element):
     cdef public dict __cached_methods
 
     # Do not assume any of those attributes to be initialized, use the corresponding methods instead.
@@ -53,8 +53,8 @@ cdef class CombinatorialPolyhedron(Element):
     cdef tuple far_face_tuple(self)
 
     # Methods to obtain a different combinatorial polyhedron.
-    cpdef CombinatorialPolyhedron dual(self)
-    cpdef CombinatorialPolyhedron pyramid(self, new_vertex=*, new_facet=*)
+    cpdef CombinatorialPolyhedron_class dual(self)
+    cpdef CombinatorialPolyhedron_class pyramid(self, new_vertex=*, new_facet=*)
 
     # Space for edges, ridges, etc. is allocated with ``MemoryAllocators``.
     # Upon success they are copied to ``_mem_tuple``.

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

@@ -113,9 +113,10 @@ cdef extern from "Python.h":
 from .parent import CombinatorialPolyhedra
 cdef Parent unspecific_parent = CombinatorialPolyhedra()
 
-cdef class CombinatorialPolyhedron(Element):
+cpdef CombinatorialPolyhedron(data, Vrep=None, facets=None, unbounded=False,
+                              far_face=None, Vrepr=None, parent=None):
     r"""
-    The class of the Combinatorial Type of a Polyhedron, a Polytope.
+    Construct a combinatorial polyhedron, the labeled combinatorial type of a polyhedron.
 
     INPUT:
 
@@ -317,8 +318,15 @@ cdef class CombinatorialPolyhedron(Element):
         sage: CombinatorialPolyhedron(LatticePolytope([], lattice=ToricLattice(3)))
         A -1-dimensional combinatorial polyhedron with 0 facets
     """
-    def __init__(self, data, Vrep=None, facets=None, unbounded=False,
-                 far_face=None, Vrepr=None, parent=None):
+    if parent is None:
+        parent = unspecific_parent
+    return CombinatorialPolyhedron_class(parent, data, Vrep, facets,
+                                         unbounded, far_face, Vrepr)
+
+cdef class CombinatorialPolyhedron_class(Element):
+
+    def __init__(self, parent, data, Vrep=None, facets=None, unbounded=False,
+                 far_face=None, Vrepr=None):
         r"""
         Initialize :class:`CombinatorialPolyhedron`.
 
@@ -2788,9 +2796,9 @@ cdef class CombinatorialPolyhedron(Element):
         r"""
         Return whether ``self`` and ``other`` are equal.
         """
-        if not isinstance(other, CombinatorialPolyhedron):
+        if not isinstance(other, CombinatorialPolyhedron_class):
             return False
-        cdef CombinatorialPolyhedron other_C = other
+        cdef CombinatorialPolyhedron_class other_C = other
         return (self.n_facets() == other.n_facets()
                 and self.Vrepresentation() == other.Vrepresentation()
                 and self.facet_names() == other_C.facet_names()
@@ -2802,7 +2810,7 @@ cdef class CombinatorialPolyhedron(Element):
 
     # Methods to obtain a different combinatorial polyhedron.
 
-    cpdef CombinatorialPolyhedron dual(self):
+    cpdef CombinatorialPolyhedron_class dual(self):
         r"""
         Return the dual/polar of self.
 
@@ -2845,7 +2853,7 @@ cdef class CombinatorialPolyhedron(Element):
 
     polar = dual
 
-    cpdef CombinatorialPolyhedron pyramid(self, new_vertex=None, new_facet=None):
+    cpdef CombinatorialPolyhedron_class pyramid(self, new_vertex=None, new_facet=None):
         r"""
         Return the pyramid of ``self``.
 

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

@@ -69,7 +69,7 @@ from sage.misc.superseded        import deprecated_function_alias
 import numbers
 from sage.rings.integer         cimport smallInteger
 from .conversions               cimport bit_rep_to_Vrep_list
-from .base                      cimport CombinatorialPolyhedron
+from .base                       import CombinatorialPolyhedron
 from .face_iterator             cimport FaceIterator_base
 from .polyhedron_face_lattice   cimport PolyhedronFaceLattice
 from .face_data_structure       cimport face_len_atoms, face_init, face_copy

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

@@ -1,4 +1,4 @@
-r"""
+"""
 Face iterator for polyhedra
 
 This iterator in principle works on every graded lattice, where
@@ -178,7 +178,7 @@ from sage.rings.integer     cimport smallInteger
 from cysignals.signals      cimport sig_check
 from .conversions           cimport bit_rep_to_Vrep_list
 from .conversions            import facets_tuple_to_bit_rep_of_facets
-from .base                  cimport CombinatorialPolyhedron
+from .base                  cimport CombinatorialPolyhedron_class
 
 from sage.geometry.polyhedron.face import combinatorial_face_to_polyhedral_face, PolyhedronFace
 from .face_list_data_structure cimport *
@@ -195,7 +195,7 @@ cdef class FaceIterator_base(SageObject):
 
     See :class:`FaceIterator`.
     """
-    def __init__(self, CombinatorialPolyhedron C, bint dual, output_dimension=None):
+    def __init__(self, CombinatorialPolyhedron_class C, bint dual, output_dimension=None):
         r"""
         Initialize :class:`FaceIterator_base`.
 

src/sage/geometry/polyhedron/combinatorial_polyhedron/morphism.py

@@ -17,3 +17,49 @@ def __init__(self, Vrep_dict=None, parent=None, domain=None, codomain=None, chec
 
     def _repr_type(self):
         return "Combinatorial polyhedral set"
+
+    def __call__(self, p):
+        """
+        Apply the morphism to a combinatorial polyhedron.
+
+        EXAMPLES::
+
+            sage: C = polytopes.cube().combinatorial_polyhedron()
+            sage: C.Vrepresentation()
+            (A vertex at (1, -1, -1),
+            A vertex at (1, 1, -1),
+            A vertex at (1, 1, 1),
+            A vertex at (1, -1, 1),
+            A vertex at (-1, -1, 1),
+            A vertex at (-1, -1, -1),
+            A vertex at (-1, 1, -1),
+            A vertex at (-1, 1, 1))
+            sage: C.Hrepresentation()
+            (An inequality (-1, 0, 0) x + 1 >= 0,
+            An inequality (0, -1, 0) x + 1 >= 0,
+            An inequality (0, 0, -1) x + 1 >= 0,
+            An inequality (1, 0, 0) x + 1 >= 0,
+            An inequality (0, 0, 1) x + 1 >= 0,
+            An inequality (0, 1, 0) x + 1 >= 0)
+
+        Abstraction morphism::
+
+            sage: Vrep_dict = {vertex: index for index, vertex in enumerate(C.vertices())}
+            sage: phi = C.parent().hom(Vrep_dict)
+            sage: phi_C = phi(C); phi_C
+            A 3-dimensional combinatorial polyhedron with 6 facets
+            sage: phi_C.Vrepresentation()
+            (0, 1, 2, 3, 4, 5, 6, 7)
+            sage: phi_C.Hrepresentation()
+            (0, 1, 2, 3, 4, 5)
+
+        """
+        # For now, degenerations are not implemented
+        incidence_matrix = p.incidence_matrix()
+
+        Vrep = p.Vrepresentation()
+        def map_vrep_element(v):
+            return self._Vrep_dict[v]
+        Vrep = [map_vrep_element(v) for v in Vrep]
+
+        return self.codomain()(incidence_matrix, Vrep=Vrep)

src/sage/geometry/polyhedron/combinatorial_polyhedron/parent.py

@@ -14,13 +14,16 @@
 
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
+from .base import CombinatorialPolyhedron_class
 
 class CombinatorialPolyhedra(UniqueRepresentation, Parent):
 
     r"""
     Parent class for combinatorial polyhedra
     """
 
+    Element = CombinatorialPolyhedron_class
+
     def __init__(self):
         """
         Construct the parent of class ``CombinatorialPolyhedra``.
@@ -60,7 +63,10 @@ def hom(self, Vrep_dict, codomain=None, check=True, category=None):
 
             sage: C = polytopes.cube().combinatorial_polyhedron()
             sage: C.parent().hom({1: 2, 2: 2}, C.parent())
+            Combinatorial polyhedral set endomorphism of Combinatorial polyhedra
 
         """
+        if codomain is None:
+            codomain = self
         homset = self.Hom(codomain)
         return homset(Vrep_dict, check=check)

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

@@ -66,7 +66,8 @@ from .conversions \
 from .conversions cimport bit_rep_to_Vrep_list
 
 from sage.rings.integer        cimport smallInteger
-from .base                     cimport CombinatorialPolyhedron
+from .base                      import CombinatorialPolyhedron
+from .base                     cimport CombinatorialPolyhedron_class
 from .face_iterator            cimport FaceIterator
 from .face_list_data_structure cimport *
 
@@ -110,7 +111,7 @@ cdef class PolyhedronFaceLattice:
     by intersecting with all coatoms. Then each intersection is looked up in
     the sorted level sets.
     """
-    def __init__(self, CombinatorialPolyhedron C):
+    def __init__(self, CombinatorialPolyhedron_class C):
         r"""
         Initialize :class:`PolyhedronFaceLattice`.