trac #9439 fine tuning the doc

Author: Frédéric Chapoton

src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py

@@ -1006,9 +1006,9 @@ def perpendicular_bisector(self): #UHP
         H = self._model.get_isometry(isom_mtrx)
         return self._model.get_geodesic(H(self._start), H(self._end))
 
-    def midpoint(self): #UHP
+    def midpoint(self):  # UHP
         r"""
-        Return the (hyperbolic) midpoint of ``self`` if .
+        Return the (hyperbolic) midpoint of ``self`` if it exists.
 
         EXAMPLES::
 
@@ -1051,7 +1051,7 @@ def angle(self, other): #UHP
 
         INPUT:
 
-        -``other`` -- a hyperbolic geodesic in the UHP model
+        - ``other`` -- a hyperbolic geodesic in the UHP model
 
         OUTPUT:
 

src/sage/geometry/hyperbolic_space/hyperbolic_model.py

@@ -46,7 +46,7 @@
    False
 
 The isometry groups of UHP and PD are projective, while that of HM is
-linear:
+linear::
 
     sage: U.is_isometry_group_projective()
     True
@@ -55,7 +55,7 @@
 
 The models are responsible for determining if the coordinates of points
 and the matrix of linear maps are appropriate for constructing points
-and isometries in hyperbolic space:
+and isometries in hyperbolic space::
 
     sage: U.point_in_model(2 + I)
     True
@@ -360,18 +360,19 @@ def get_point(self, coordinates, is_boundary=None, **graphics_options):
         r"""
         Return a point in ``self``.
 
-        Automatically determine the type of point to return given either
-        (1) the coordinates of a point in the interior or ideal boundary
-        of hyperbolic space or (2) a :class:`HyperbolicPoint` or
-        :class:`HyperbolicBdryPoint` object.
+        Automatically determine the type of point to return given either:
+
+        #. the coordinates of a point in the interior or ideal boundary
+           of hyperbolic space, or
+        #. a :class:`~sage.geometry.hyperbolic_space.hyperbolic_point.HyperbolicPoint` object.
 
         INPUT:
 
         - a point in hyperbolic space or on the ideal boundary
 
         OUTPUT:
 
-        - a :class:`HyperbolicPoint`
+        - a :class:`~sage.geometry.hyperbolic_space.hyperbolic_point.HyperbolicPoint`
 
         EXAMPLES:
 

src/sage/geometry/hyperbolic_space/hyperbolic_point.py

@@ -443,7 +443,7 @@ def graphics_options(self):
 
     def symmetry_involution(self):
         r"""
-        Return the involutary isometry fixing the given point.
+        Return the involutory isometry fixing the given point.
 
         EXAMPLES::
 
@@ -556,7 +556,7 @@ class HyperbolicPointUHP(HyperbolicPoint):
     """
     def symmetry_involution(self):
         r"""
-        Return the involutary isometry fixing the given point.
+        Return the involutory isometry fixing the given point.
 
         EXAMPLES::