ConvexSet_base.an_element, some_elements: Go through generator method…

… _some_elements_, make some_elements return a list

src/sage/geometry/convex_set.py

@@ -449,24 +449,45 @@ def an_element(self):
 
         If ``self`` is empty, an :class:`EmptySetError` will be raised.
 
-        The default implementation delegates to :meth:`some_elements`.
+        The default implementation delegates to :meth:`_some_elements_`.
 
         EXAMPLES::
 
             sage: from sage.geometry.convex_set import ConvexSet_compact
             sage: class BlueBox(ConvexSet_compact):
-            ....:     def some_elements(self):
+            ....:     def _some_elements_(self):
             ....:         yield 'blue'
             ....:         yield 'cyan'
             sage: BlueBox().an_element()
+            'blue'
         """
         try:
-            return next(iter(self.some_elements()))
+            return next(iter(self._some_elements_()))
         except StopIteration:
             raise EmptySetError
 
-    @abstract_method(optional=True)
     def some_elements(self):
+        r"""
+        Return a list of some points of ``self``.
+
+        If ``self`` is empty, an empty list is returned; no exception will be raised.
+
+        The default implementation delegates to :meth:`_some_elements_`.
+
+        EXAMPLES::
+
+            sage: from sage.geometry.convex_set import ConvexSet_compact
+            sage: class BlueBox(ConvexSet_compact):
+            ....:     def _some_elements_(self):
+            ....:         yield 'blue'
+            ....:         yield 'cyan'
+            sage: BlueBox().some_elements()
+            ['blue', 'cyan']
+        """
+        return list(self._some_elements_())
+
+    @abstract_method(optional=True)
+    def _some_elements_(self):
         r"""
         Generate some points of ``self``.
 
@@ -476,7 +497,7 @@ def some_elements(self):
 
             sage: from sage.geometry.convex_set import ConvexSet_base
             sage: C = ConvexSet_base()
-            sage: C.some_elements(C)
+            sage: C._some_elements_(C)
             Traceback (most recent call last):
             ...
             TypeError: 'NotImplementedType' object is not callable

src/sage/geometry/polyhedron/base.py

@@ -3302,7 +3302,7 @@ def representative_point(self):
         accumulator.set_immutable()
         return accumulator
 
-    def some_elements(self):
+    def _some_elements_(self):
         r"""
         Generate some points of ``self``.
 
@@ -3311,7 +3311,9 @@ def some_elements(self):
         EXAMPLES::
 
             sage: P = polytopes.simplex()
-            sage: list(P.some_elements())
+            sage: P.an_element()            # indirect doctest
+            (1/4, 1/4, 1/4, 1/4)
+            sage: P.some_elements()         # indirect doctest
             [(1/4, 1/4, 1/4, 1/4),
              (0, 0, 0, 1),
              (0, 0, 1/2, 1/2),

src/sage/geometry/polyhedron/face.py

@@ -764,7 +764,7 @@ def as_polyhedron(self):
         Vrep = (self.vertices(), self.rays(), self.lines())
         return P.__class__(parent, Vrep, None)
 
-    def some_elements(self):
+    def _some_elements_(self):
         r"""
         Generate some points of ``self``.
 
@@ -779,7 +779,9 @@ def some_elements(self):
             A 2-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 3 vertices
             sage: face.as_polyhedron().vertices()
             (A vertex at (0, -1, 0), A vertex at (0, 0, -1), A vertex at (1, 0, 0))
-            sage: list(face.some_elements())
+            sage: face.an_element()              # indirect doctest
+            (1/3, -1/3, -1/3)
+            sage: face.some_elements()           # indirect doctest
             [(1/3, -1/3, -1/3), (0, -1, 0), (0, -1/2, -1/2), (1/2, -1/4, -1/4)]
         """
         yield from self.as_polyhedron().some_elements()

src/sage/geometry/relative_interior.py

@@ -229,7 +229,7 @@ def is_closed(self):
         assert not self._polyhedron.is_relatively_open()
         return False
 
-    def some_elements(self):
+    def _some_elements_(self):
         r"""
         Generate some points of ``self``.
 
@@ -238,7 +238,10 @@ def some_elements(self):
         EXAMPLES::
 
             sage: P = polytopes.simplex()
-            sage: list(P.relative_interior().some_elements())
+            sage: ri_P = P.relative_interior()
+            sage: ri_P.an_element()              # indirect doctest
+            (1/4, 1/4, 1/4, 1/4)
+            sage: ri_P.some_elements()           # indirect doctest
             [(1/4, 1/4, 1/4, 1/4), (1/2, 1/4, 1/8, 1/8)]
         """
         for p in self._polyhedron.some_elements():