Merge #31919

src/sage/geometry/convex_set.py

@@ -44,6 +44,15 @@ def is_universe(self):
         OUTPUT:
 
         Boolean.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.is_universe()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: <abstract method dim at ...>
         """
         if not self.is_full_dimensional():
             return False
@@ -53,6 +62,15 @@ def is_universe(self):
     def dim(self):
         r"""
         Return the dimension of ``self``.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.dim()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: <abstract method dim at ...>
         """
 
     def dimension(self):
@@ -88,6 +106,15 @@ def ambient(self):
     def ambient_dim(self):
         r"""
         Return the dimension of the ambient convex set or space.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.ambient_dim()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: <abstract method ambient_dim at ...>
         """
 
     def ambient_dimension(self):
@@ -111,11 +138,15 @@ def codimension(self):
         r"""
         Return the codimension of ``self`` in `self.ambient()``.
 
-        An alias is :meth:`codim`.
-
         EXAMPLES::
 
-            sage: Polyhedron(vertices=[(1,2,3)], rays=[(1,0,0)]).codimension()
+            sage: P = Polyhedron(vertices=[(1,2,3)], rays=[(1,0,0)])
+            sage: P.codimension()
+            2
+
+        An alias is :meth:`codim`::
+
+            sage: P.codim()
             2
         """
         return self.ambient_dim() - self.dim()
@@ -359,13 +390,28 @@ def _test_convex_set(self, tester=None, **options):
             tester.assertTrue(self == cl_self)
         if self.is_compact():
             tester.assertTrue(self.is_closed())
+        from sage.misc.sage_unittest import TestSuite
+        if relint_self is not None and relint_self is not self:
+            tester.info("\n  Running the test suite of self.relative_interior()")
+            TestSuite(relint_self).run(verbose=tester._verbose,
+                                       prefix=tester._prefix + "  ")
+            tester.info(tester._prefix + " ", newline=False)
 
     # Optional methods
 
     @abstract_method(optional=True)
     def affine_hull(self):
         r"""
         Return the affine hull of ``self``.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.affine_hull()
+            Traceback (most recent call last):
+            ...
+            TypeError: 'NotImplementedType' object is not callable
         """
 
     @abstract_method(optional=True)
@@ -380,6 +426,15 @@ def cartesian_product(self, other):
         OUTPUT:
 
         The Cartesian product of ``self`` and ``other``.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.cartesian_product(C)
+            Traceback (most recent call last):
+            ...
+            TypeError: 'NotImplementedType' object is not callable
         """
 
     @abstract_method(optional=True)
@@ -390,6 +445,15 @@ def contains(self, point):
         INPUT:
 
         - ``point`` -- a point or its coordinates
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.contains(vector([0, 0]))
+            Traceback (most recent call last):
+            ...
+            TypeError: 'NotImplementedType' object is not callable
         """
 
     def _test_contains(self, tester=None, **options):
@@ -463,6 +527,15 @@ def intersection(self, other):
         OUTPUT:
 
         The intersection.
+
+        TESTS::
+
+            sage: from sage.geometry.convex_set import ConvexSet_base
+            sage: C = ConvexSet_base()
+            sage: C.intersection(C)
+            Traceback (most recent call last):
+            ...
+            TypeError: 'NotImplementedType' object is not callable
         """
 
 

src/sage/geometry/polyhedron/base.py

@@ -4797,6 +4797,11 @@ def product(self, other):
             sage: P1 * 2.0
             A 1-dimensional polyhedron in RDF^1 defined as the convex hull of 2 vertices
 
+        An alias is :meth:`cartesian_product`::
+
+            sage: P1.cartesian_product(P2) == P1.product(P2)
+            True
+
         TESTS:
 
         Check that :trac:`15253` is fixed::
@@ -8455,7 +8460,15 @@ def interior(self):
             sage: P_lower.interior()
             The empty polyhedron in ZZ^2
 
+        TESTS::
+
+            sage: Empty = Polyhedron(ambient_dim=2); Empty
+            The empty polyhedron in ZZ^2
+            sage: Empty.interior() is Empty
+            True
         """
+        if self.is_open():
+            return self
         if not self.is_full_dimensional():
             return self.parent().element_class(self.parent(), None, None)
         return self.relative_interior()

src/sage/geometry/relative_interior.py

@@ -79,7 +79,8 @@ def ambient_dim(self):
             sage: segment.ambient_dim()
             2
             sage: ri_segment = segment.relative_interior(); ri_segment
-            Relative interior of a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
             sage: ri_segment.ambient_dim()
             2
         """
@@ -95,7 +96,8 @@ def dim(self):
             sage: segment.dim()
             1
             sage: ri_segment = segment.relative_interior(); ri_segment
-            Relative interior of a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
             sage: ri_segment.dim()
             1
         """
@@ -154,6 +156,28 @@ def closure(self):
         """
         return self._polyhedron
 
+    def is_universe(self):
+        r"""
+        Return whether ``self`` is the whole ambient space
+
+        OUTPUT:
+
+        Boolean.
+
+        EXAMPLES::
+
+            sage: segment = Polyhedron([[1, 2], [3, 4]])
+            sage: ri_segment = segment.relative_interior(); ri_segment
+            Relative interior of
+             a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
+            sage: ri_segment.is_universe()
+            False
+        """
+        # Relies on ``self`` not set up for polyhedra that are already
+        # relatively open themselves.
+        assert not self._polyhedron.is_universe()
+        return False
+
     def is_closed(self):
         r"""
         Return whether ``self`` is closed.