A little bit of reviewer cleanup.

Author: Travis Scrimshaw

src/sage/geometry/cone.py

@@ -510,16 +510,16 @@ def _ambient_space_point(body, data):
     Try to convert ``data`` to a point of the ambient space of ``body``.
 
     INPUT:
-    
-    - ``body`` -- a cone, fan, or lattice polytope with ``lattice()`` method.
 
-    - ``data`` -- anything.
+    - ``body`` -- a cone, fan, or lattice polytope with ``lattice()`` method
+
+    - ``data`` -- anything
 
     OUTPUT:
 
     - integral, rational or numeric point of the ambient space of ``body``
       if ``data`` were successfully interpreted in such a way, otherwise a
-      ``TypeError`` exception is raised.
+      ``TypeError`` exception is raised
 
     TESTS::
 
@@ -531,7 +531,7 @@ def _ambient_space_point(body, data):
         Traceback (most recent call last):
         ...
         TypeError: the point M(1, 1) and
-        2-d cone in 2-d lattice N have incompatible lattices!
+         2-d cone in 2-d lattice N have incompatible lattices
         sage: _ambient_space_point(c, [1,1/3])
         (1, 1/3)
         sage: _ambient_space_point(c, [1/2,1/sqrt(3)])
@@ -540,7 +540,7 @@ def _ambient_space_point(body, data):
         Traceback (most recent call last):
         ...
         TypeError: [1, 1, 3] does not represent a valid point
-        in the ambient space of 2-d cone in 2-d lattice N!
+         in the ambient space of 2-d cone in 2-d lattice N
     """
     L = body.lattice()
     try: # to make a lattice element...
@@ -549,7 +549,7 @@ def _ambient_space_point(body, data):
         # Special treatment for toric lattice elements
         if is_ToricLattice(parent(data)):
             raise TypeError("the point %s and %s have incompatible "
-                            "lattices!" % (data, body))
+                            "lattices" % (data, body))
     try: # ... or an exact point...
         return L.base_extend(QQ)(data)
     except TypeError:
@@ -560,7 +560,7 @@ def _ambient_space_point(body, data):
         pass
     # Raise TypeError with our own message
     raise TypeError("%s does not represent a valid point in the ambient "
-                    "space of %s!" % (data, body))
+                    "space of %s" % (data, body))
 
 
 def integral_length(v):
@@ -569,9 +569,11 @@ def integral_length(v):
 
     INPUT:
 
-    -  ``v`` - any object which can be converted to a list of rationals
+    - ``v`` -- any object which can be converted to a list of rationals
+
+    OUTPUT:
 
-    OUTPUT: Rational number ``r`` such that ``v = r u``, where ``u`` is the
+    Rational number `r`` such that ``v = r * u``, where ``u`` is the
     primitive integral vector in the direction of ``v``.
 
     EXAMPLES::

src/sage/geometry/lattice_polytope.py

@@ -560,7 +560,7 @@ def __contains__(self, point):
             False
         """
         return self._contains(point)
-    
+
     def __eq__(self, other):
         r"""
         Compare ``self`` with ``other``.
@@ -755,8 +755,7 @@ def _compute_facets(self):
             constants = (constants[1], constants[0])
         self.is_reflexive.set_cache(all(c == 1 for c in constants))
         if self.is_reflexive():
-            polar = LatticePolytope(
-                normals, compute_vertices=False, lattice=N)
+            polar = LatticePolytope(normals, compute_vertices=False, lattice=N)
             polar.dim.set_cache(self.dim())
             polar.is_reflexive.set_cache(True)
             polar._polar = self
@@ -798,20 +797,17 @@ def _contains(self, point, region='whole polytope'):
 
         INPUT:
 
-        - ``point`` -- anything. An attempt will be made to convert it into a
-          single element of the ambient space of ``self``. If it fails,
-          ``False`` is returned;
+        - ``point`` -- an attempt will be made to convert it into a
+          single element of the ambient space of ``self``; if it fails,
+          ``False`` is returned
 
-        - ``region`` -- string. Can be either 'whole polytope' (default),
-          'interior', or 'relative interior'.
+        - ``region`` -- string; can be either ``'whole polytope'`` (default),
+          ``'interior'``, or ``'relative interior'``
 
         OUTPUT:
 
         - ``True`` if ``point`` is contained in the specified ``region`` of
-          ``self``, ``False`` otherwise.
-
-        Raises a ``ValueError`` if ``region`` is not one of the
-        three allowed values.
+          ``self``, ``False`` otherwise
 
         TESTS::
 
@@ -822,9 +818,9 @@ def _contains(self, point, region='whole polytope'):
         try:
             point = _ambient_space_point(self, point)
         except TypeError as ex:
-            if str(ex).endswith("have incompatible lattices!"):
+            if str(ex).endswith("have incompatible lattices"):
                 warnings.warn("you have checked if a cone contains a point "
-                              "from an incompatible lattice, this is False!",
+                              "from an incompatible lattice, this is False",
                               stacklevel=3)
             return False
 
@@ -1666,14 +1662,14 @@ def contains(self, *args):
 
         INPUT:
 
-        - anything. An attempt will be made to convert all arguments into a
-          single element of the ambient space of ``self``. If it fails,
-          ``False`` will be returned.
+        - an attempt will be made to convert all arguments into a
+          single element of the ambient space of ``self``; if it fails,
+          ``False`` will be returned
 
         OUTPUT:
 
         - ``True`` if the given point is contained in ``self``, ``False``
-          otherwise.
+          otherwise
 
         EXAMPLES::
 
@@ -1697,8 +1693,9 @@ def dim(self):
         r"""
         Return the dimension of this polytope.
 
-        EXAMPLES: We create a 3-dimensional octahedron and check its
-        dimension::
+        EXAMPLES:
+
+        We create a 3-dimensional octahedron and check its dimension::
 
             sage: o = lattice_polytope.cross_polytope(3)
             sage: o.dim()
@@ -1763,9 +1760,9 @@ def distances(self, point=None):
             [0 2 2 0 1]
             sage: p.distances((1/2, 3, 0))
             (9/2, -3/2, -5/2, 7/2)
-            
+
         This point is not even in the affine subspace of the polytope::
-        
+
             sage: p.distances((1, 1, 1))
             (3, 1, -1, 1)
         """
@@ -2121,24 +2118,24 @@ def faces(self, dim=None, codim=None):
     def facet_constant(self, i):
         r"""
         Return the constant in the ``i``-th facet inequality of this polytope.
-        
-        This is equivalent to ``facet_constants()[i]``
+
+        This is equivalent to ``facet_constants()[i]``.
 
         INPUT:
 
-        - ``i`` - integer, the index of the facet
+        - ``i`` -- integer; the index of the facet
 
         OUTPUT:
 
         - integer -- the constant in the ``i``-th facet inequality.
 
         .. SEEALSO::
-        
+
             :meth:`facet_constants`,
             :meth:`facet_normal`,
             :meth:`facet_normals`,
             :meth:`facets`.
-        
+
         EXAMPLES::
 
             sage: o = lattice_polytope.cross_polytope(3)
@@ -2158,15 +2155,15 @@ def facet_constants(self):
 
         OUTPUT:
 
-        - an integer vector.
+        - an integer vector
 
         .. SEEALSO::
-        
+
             :meth:`facet_constant`,
             :meth:`facet_normal`,
             :meth:`facet_normals`,
             :meth:`facets`.
-        
+
         EXAMPLES:
 
         For reflexive polytopes all constants are 1::
@@ -2207,23 +2204,23 @@ def facet_normal(self, i):
         r"""
         Return the inner normal to the ``i``-th facet of this polytope.
 
-        This is equivalent to ``facet_normals()[i]``
+        This is equivalent to ``facet_normals()[i]``.
 
         INPUT:
 
-        - ``i`` -- integer, the index of the facet
+        - ``i`` -- integer; the index of the facet
 
         OUTPUT:
 
         - a vector
-        
+
         .. SEEALSO::
-        
+
             :meth:`facet_constant`,
             :meth:`facet_constants`,
             :meth:`facet_normals`,
             :meth:`facets`.
-        
+
         EXAMPLES::
 
             sage: o = lattice_polytope.cross_polytope(3)
@@ -2247,12 +2244,12 @@ def facet_normals(self):
           :meth:`dual_lattice` of ``self``.
 
         .. SEEALSO::
-        
+
             :meth:`facet_constant`,
             :meth:`facet_constants`,
             :meth:`facet_normal`,
             :meth:`facets`.
-        
+
         EXAMPLES:
 
         Normals to facets of an octahedron are vertices of a cube::