From 364a7962398d54fc1679634c1f839739de794939 Mon Sep 17 00:00:00 2001
From: Jonathan Kliem <jonathan.kliem@fu-berlin.de>
Date: Wed, 12 Feb 2020 16:42:34 +0100
Subject: [PATCH] migrate is_pyramid to combinatorial polyhedron

---
 src/sage/geometry/polyhedron/base.py          | 12 +---
 .../combinatorial_polyhedron/base.pyx         | 66 ++++++++++++++++++-
 2 files changed, 66 insertions(+), 12 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index fc63004408e..76c783f9125 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -3009,17 +3009,7 @@ def is_pyramid(self, certificate=False):
         if not self.is_compact():
             raise ValueError("polyhedron has to be compact")
 
-        # Find a vertex that is incident to all elements in Hrepresentation but one.
-        IM = self.incidence_matrix()
-        for index in range(self.n_vertices()):
-            vertex_incidences = IM.row(index)
-            if sum(vertex_incidences) == IM.ncols() - 1:
-                if certificate:
-                    return (True, self.vertices()[index])
-                return True
-        if certificate:
-            return (False, None)
-        return False
+        return self.combinatorial_polyhedron().is_pyramid(certificate)
 
     def is_bipyramid(self, certificate=False):
         r"""
diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
index 7b115b09a61..1e66378e627 100644
--- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
+++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
@@ -741,7 +741,7 @@ cdef class CombinatorialPolyhedron(SageObject):
                 # The Polyhedron has no vertex.
                 return ()
         if names and self.Vrep():
-            return tuple(self.Vrep()[i]     for i in range(self.n_Vrepresentation()) if not i in self.far_face_tuple())
+            return tuple(self.Vrep()[i]  for i in range(self.n_Vrepresentation()) if not i in self.far_face_tuple())
         else:
             return tuple(smallInteger(i) for i in range(self.n_Vrepresentation()) if not i in self.far_face_tuple())
 
@@ -1471,6 +1471,70 @@ cdef class CombinatorialPolyhedron(SageObject):
                 d = dim
         return smallInteger(simplicity)
 
+    def is_pyramid(self, certificate=False):
+        r"""
+        Test whether the polytope is a pyramid over one of its facets.
+
+        INPUT:
+
+        - ``certificate`` -- boolean (default: ``False``); specifies whether
+          to return a vertex of the polytope which is the apex of a pyramid,
+          if found
+
+        OUTPUT:
+
+        If ``certificate`` is ``True``, returns a tuple containing:
+
+        1. Boolean.
+        2. The apex of the pyramid or ``None``.
+
+        If ``certificate`` is ``False`` returns a boolean.
+
+        AUTHORS:
+
+        - Laith Rastanawi
+        - Jonathan Kliem
+
+        EXAMPLES::
+
+            sage: C = polytopes.cross_polytope(4).combinatorial_polyhedron()
+            sage: C.is_pyramid()
+            False
+            sage: C.is_pyramid(certificate=True)
+            (False, None)
+            sage: C = polytopes.cross_polytope(4).pyramid().combinatorial_polyhedron()
+            sage: C.is_pyramid()
+            True
+            sage: C.is_pyramid(certificate=True)
+            (True, A vertex at (0, -1, 0, 0, 0))
+            sage: C = polytopes.simplex(5)
+            sage: C.is_pyramid(certificate=True)
+            (True, A vertex at (0, 0, 0, 0, 0, 1))
+
+        For unbounded polyhedra, an error is raised::
+
+            sage: C = CombinatorialPolyhedron([[0,1], [0,2]], far_face=[1,2], unbounded=True)
+            sage: C.is_pyramid()
+            Traceback (most recent call last):
+            ...
+            ValueError: polyhedron has to be compact
+        """
+        if not self.is_bounded():
+            raise ValueError("polyhedron has to be compact")
+
+        # Find a vertex that is incident to all elements in Hrepresentation but one.
+        vertex_iter = self._face_iter(True, 0)
+        n_facets = self.n_facets()
+        for index, vertex in enumerate(vertex_iter):
+            if vertex.n_ambient_Hrepresentation() == n_facets - 1:
+                if certificate:
+                    return (True, self.Vrepresentation()[index])
+                return True
+
+        if certificate:
+            return (False, None)
+        return False
+
     def face_iter(self, dimension=None, dual=None):
         r"""
         Iterator over all proper faces of specified dimension.