a bunch of tiny details in the doc (missing ... and empty lines)

src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py

@@ -315,6 +315,7 @@ def _coerce_map_from_(self, R):
             True
             sage: L(prod(pbw.gens()))
             Traceback (most recent call last):
+            ...
             ValueError: PBW['X']*PBW['Y']*PBW['Z'] is not in the image
             sage: L(pbw.one())
             Traceback (most recent call last):

src/sage/categories/category.py

@@ -751,7 +751,7 @@ def __classcontains__(cls, x):
 
     def is_abelian(self):
         """
-        Returns whether this category is abelian.
+        Return whether this category is abelian.
 
         An abelian category is a category satisfying:
 
@@ -783,6 +783,7 @@ def is_abelian(self):
             True
             sage: Semigroups().is_abelian()
             Traceback (most recent call last):
+            ...
             NotImplementedError: is_abelian
         """
         raise NotImplementedError("is_abelian")

src/sage/categories/examples/infinite_enumerated_sets.py

@@ -135,12 +135,12 @@ def __call__(self, elt):
             Integer Ring
             sage: NN(-1)
             Traceback (most recent call last):
+            ...
             ValueError: Value -1 is not a non negative integer.
         """
         if elt in self:
             return self._element_constructor_(elt)
-        else:
-            raise ValueError("Value %s is not a non negative integer."%(elt))
+        raise ValueError("Value %s is not a non negative integer." % (elt))
 
     def an_element(self):
         """

src/sage/coding/linear_code.py

@@ -1204,7 +1204,6 @@ def dimension(self):
             ....:     def generator_matrix(self):
             ....:         G = identity_matrix(GF(5), 5).augment(matrix(GF(5), 5, 7))
             ....:         return G
-            ....:
             sage: MonkeyCode._registered_encoders["Monkey"] = MonkeyEncoder
             sage: C = MonkeyCode()
             sage: C.dimension()
@@ -3340,7 +3339,6 @@ class LinearCodeSystematicEncoder(Encoder):
         ....:
         ....:   def _repr_(self):
         ....:       return "Dual of the [%d, 1] Repetition Code over GF(%s)" % (self.length(), self.base_field().cardinality())
-        ....:
         sage: DualRepetitionCode(GF(3), 5).generator_matrix()
         [1 0 0 0 2]
         [0 1 0 0 2]
@@ -3357,7 +3355,6 @@ class LinearCodeSystematicEncoder(Encoder):
         ....:
         ....:   def _repr_(self):
         ....:       return "I am a badly defined code"
-        ....:
         sage: BadCodeFamily(GF(3), 5).generator_matrix()
         Traceback (most recent call last):
         ...

src/sage/combinat/abstract_tree.py

@@ -1925,7 +1925,7 @@ def __setitem__(self, idx, value):
             sage: with x.clone() as x:
             ....:     x[0] = OrderedTree([[]])
             Traceback (most recent call last):
-            ....:
+            ...
             IndexError: list assignment index out of range
 
             sage: x = OrderedTree([]); x = OrderedTree([x,x]); x = OrderedTree([x,x]); x = OrderedTree([x,x])

src/sage/combinat/backtrack.py

@@ -504,7 +504,6 @@ def __iter__(self):
             sage: from sage.combinat.backtrack import SearchForest
             sage: def children(l):
             ....:      return [l+[0], l+[1]]
-            ....:
             sage: C = SearchForest(([],), children)
             sage: f = C.__iter__()
             sage: next(f)

src/sage/combinat/combinatorial_map.py

@@ -191,7 +191,6 @@ def combinatorial_map_wrapper(f=None, order=None, name=None):
 
         sage: def major_index(p):
         ....:     return p.major_index()
-        ....:
         sage: major_index
         <function major_index at ...>
         sage: combinatorial_map(major_index)
@@ -219,15 +218,14 @@ class CombinatorialMap(object):
     """
     def __init__(self, f, order=None, name=None):
         """
-        Constructor for combinatorial maps
+        Constructor for combinatorial maps.
 
         EXAMPLES::
 
             sage: from sage.combinat.combinatorial_map import combinatorial_map_wrapper as combinatorial_map
             sage: def f(x):
             ....:     "doc of f"
             ....:     return x
-            ....:
             sage: x = combinatorial_map(f); x
             Combinatorial map: f
             sage: x.__doc__

src/sage/crypto/mq/rijndael_gf.py

@@ -2249,7 +2249,6 @@ def __init__(self, polynomial_constr, rgf, round_component_name=None):
 
                 sage: def my_poly_constr(row, col, algorithm='encrypt'):
                 ....:     return x * rgf._F.one() # example body with no checks
-                ....:
                 sage: rcpc = RijndaelGF.Round_Component_Poly_Constr(
                 ....: my_poly_constr, rgf, "My Poly Constr")
                 sage: rcpc(-1, 2)

src/sage/geometry/lattice_polytope.py

@@ -4987,6 +4987,7 @@ def _palp(command, polytopes, reduce_dimension=False):
         sage: p = LatticePolytope([(1,0,0), (0,1,0), (-1,0,0), (0,-1,0)])
         sage: lattice_polytope._palp("poly.x -f", [p])
         Traceback (most recent call last):
+        ...
         ValueError: Cannot run PALP for a 2-dimensional polytope in a 3-dimensional space!
 
         sage: result_name = lattice_polytope._palp("poly.x -f", [p], reduce_dimension=True)

src/sage/geometry/triangulation/point_configuration.py

@@ -1869,7 +1869,9 @@ def contained_simplex(self, large=True, initial_point=None, point_order=None):
             (P(-1, -1), P(1, 1), P(0, 1))
             sage: pc.contained_simplex(point_order = [pc[1],pc[3],pc[4],pc[2],pc[0]])
             (P(0, 1), P(1, 1), P(-1, -1)) 
-            sage: # lower-dimensional example:
+
+        Lower-dimensional example::
+
             sage: pc.contained_simplex(point_order = [pc[0],pc[3],pc[4]])
             (P(0, 0), P(1, 1))
             
@@ -1969,7 +1971,9 @@ def placing_triangulation(self, point_order=None):
             (<1,2,3>, <1,2,4>)
             sage: p0.pushing_triangulation(point_order=[0,1,2,3,4])
             (<0,1,3>, <0,1,4>, <0,2,3>, <0,2,4>)
-            sage: # the same triangulation with renumbered points 0->4, 1->0, etc.:
+
+        The same triangulation with renumbered points 0->4, 1->0, etc::
+
             sage: p1 = PointConfiguration([(+1,0),(-1,0),(0,+1),(0,-1),(0,0)])
             sage: p1.pushing_triangulation(point_order=[4,0,1,2,3])
             (<0,2,4>, <0,3,4>, <1,2,4>, <1,3,4>)

src/sage/manifolds/continuous_map.py

@@ -631,7 +631,9 @@ def _call_(self, point):
 
             sage: M = Manifold(2, 'R^2', latex_name=r'\RR^2', structure='topological') # Euclidean plane
             sage: c_cart.<x,y> = M.chart() # Cartesian coordinates
-            sage: # A pi/3 rotation around the origin defined in Cartesian coordinates:
+
+        A pi/3 rotation around the origin defined in Cartesian coordinates::
+
             sage: rot = M.continuous_map(M, ((x - sqrt(3)*y)/2, (sqrt(3)*x + y)/2),
             ....:                        name='R')
             sage: p = M.point((1,2), name='p')
@@ -1450,7 +1452,9 @@ def set_expr(self, chart1, chart2, coord_functions):
             sage: U = M.open_subset('U', coord_def={c_xy: (y!=0, x<0)}) # the complement of the segment y=0 and x>0
             sage: c_cart = c_xy.restrict(U) # Cartesian coordinates on U
             sage: c_spher.<r,ph> = U.chart(r'r:(0,+oo) ph:(0,2*pi):\phi') # spherical coordinates on U
-            sage: # Links between spherical coordinates and Cartesian ones:
+
+        Links between spherical coordinates and Cartesian ones::
+
             sage: ch_cart_spher = c_cart.transition_map(c_spher,
             ....:                                       [sqrt(x*x+y*y), atan2(y,x)])
             sage: ch_cart_spher.set_inverse(r*cos(ph), r*sin(ph))
@@ -1872,7 +1876,9 @@ def __invert__(self):
 
             sage: M = Manifold(2, 'R^2', latex_name=r'\RR^2', structure='topological')
             sage: c_cart.<x,y> = M.chart()
-            sage: # A pi/3 rotation around the origin:
+
+        A pi/3 rotation around the origin::
+
             sage: rot = M.homeomorphism(M, ((x - sqrt(3)*y)/2, (sqrt(3)*x + y)/2),
             ....:                       name='R')
             sage: rot.inverse()

src/sage/manifolds/differentiable/affine_connection.py

@@ -18,7 +18,7 @@
 - [ONe1983]_
 
 """
-#******************************************************************************
+# *****************************************************************************
 #       Copyright (C) 2015 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
 #       Copyright (C) 2015 Michal Bejger <bejger@camk.edu.pl>
 #       Copyright (C) 2015 Marco Mancini <marco.mancini@obspm.fr>
@@ -27,7 +27,7 @@
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
-#******************************************************************************
+# *****************************************************************************
 
 from sage.rings.integer import Integer
 from sage.structure.sage_object import SageObject
@@ -250,7 +250,6 @@ class AffineConnection(SageObject):
         ....:     for j in M.irange():
         ....:         for k in M.irange():
         ....:             nab.add_coef(eV)[i,j,k] = nab.coef(eVW)[i,j,k,c_uvW].expr()
-        ....:
 
     At this stage, the connection is fully defined on all the manifold::
 
@@ -301,7 +300,6 @@ class AffineConnection(SageObject):
         ....:     for j in M.irange():
         ....:         for k in M.irange():
         ....:             nab.add_coef(eV)[i,j,k] = nab.coef(eVW)[i,j,k,c_uvW].expr()
-        ....:
 
     At this stage, the connection is fully defined on all the manifold::
 
@@ -1635,7 +1633,6 @@ def torsion(self):
             ....:     for j in M.irange():
             ....:         for k in M.irange():
             ....:             nab.add_coef(eV)[i,j,k] = nab.coef(eVW)[i,j,k,c_uvW].expr()
-            ....:
             sage: t = nab.torsion() ; t
             Tensor field of type (1,2) on the 2-dimensional differentiable
              manifold M
@@ -1759,7 +1756,6 @@ def riemann(self):
             ....:     for j in M.irange():
             ....:         for k in M.irange():
             ....:             nab.add_coef(eV)[i,j,k] = nab.coef(eVW)[i,j,k,c_uvW].expr()
-            ....:
             sage: r = nab.riemann() ; r
             Tensor field of type (1,3) on the 2-dimensional differentiable
              manifold M
@@ -1790,7 +1786,6 @@ def riemann(self):
             ....:     for j in M.irange():
             ....:         for k in M.irange():
             ....:             nab.add_coef(eV)[i,j,k] = nab.coef(eVW)[i,j,k,c_uvW].expr()
-            ....:
             sage: r = nab.riemann() ; r
             Tensor field of type (1,3) on the 2-dimensional differentiable
              manifold M
@@ -1991,28 +1986,29 @@ def connection_form(self, i, j, frame=None):
             sage: nab.connection_form(1,1,e).comp(e)[:]
             [x*y^2*z, (x^2*y + 1)*z/y, -x*y*z]
 
-        Check of the formula `\omega^i_{\ \, j} = \Gamma^i_{\ \, jk} e^k`::
+        Check of the formula `\omega^i_{\ \, j} = \Gamma^i_{\ \, jk} e^k`:
+
+        First on the manifold's default frame (d/dx, d/dy, d:dz)::
 
-            sage: #... on the manifold's default frame (d/dx, d/dy, d:dz)
             sage: dx = M.default_frame().coframe() ; dx
             Coordinate coframe (M, (dx,dy,dz))
             sage: check = []
             sage: for i in M.irange():
             ....:     for j in M.irange():
             ....:         check.append( nab.connection_form(i,j) == \
             ....:               sum( nab[[i,j,k]]*dx[k] for k in M.irange() ) )
-            ....:
             sage: check
             [True, True, True, True, True, True, True, True, True]
-            sage: #... on the frame e
+
+        Then on the frame e::
+
             sage: ef = e.coframe() ; ef
             Coframe (M, (e^1,e^2,e^3))
             sage: check = []
             sage: for i in M.irange():
             ....:     for j in M.irange():
             ....:         s = nab.connection_form(i,j,e).comp(c_xyz.frame(), from_basis=e)
             ....:         check.append( nab.connection_form(i,j,e) == sum( nab.coef(e)[[i,j,k]]*ef[k] for k in M.irange() ) )
-            ....:
             sage: check
             [True, True, True, True, True, True, True, True, True]
 
@@ -2135,11 +2131,9 @@ def torsion_form(self, i, frame=None):
             sage: for i in M.irange():  # long time
             ....:     nab.torsion_form(i, e) == ef[i].exterior_derivative() + \
             ....:      sum(nab.connection_form(i,j,e).wedge(ef[j]) for j in M.irange())
-            ....:
             True
             True
             True
-
         """
         if frame is None:
             frame = self._domain._def_frame
@@ -2245,7 +2239,6 @@ def curvature_form(self, i, j, frame=None):
             ....:         check.append( nab.curvature_form(i,j,e) == \
             ....:                       omega(i,j,e).exterior_derivative() + \
             ....:         sum( omega(i,k,e).wedge(omega(k,j,e)) for k in M.irange()) )
-            ....:
             sage: check  # long time
             [True, True, True, True, True, True, True, True, True]
 

src/sage/manifolds/differentiable/chart.py

@@ -22,21 +22,21 @@
 - Chap. 1 of [Lee2013]_
 
 """
-
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2015 Eric Gourgoulhon <eric.gourgoulhon@obspm.fr>
 #       Copyright (C) 2015 Michal Bejger <bejger@camk.edu.pl>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.manifolds.chart import Chart, RealChart, CoordChange
 from sage.manifolds.differentiable.vectorframe import CoordFrame
 
+
 class DiffChart(Chart):
     r"""
     Chart on a differentiable manifold.
@@ -646,8 +646,8 @@ def symbolic_velocities(self, left='D', right=None):
                 # is not a string
 
             # If the argument of 'var' contains only one word, for
-            # instance:
-            # sage: var('Dt')
+            # instance::
+            # var('Dt')
             # then 'var' does not return a tuple containing one symbolic
             # expression, but the symbolic expression itself.
             # This is taken into account below in order to return a list

src/sage/manifolds/differentiable/curve.py

@@ -363,7 +363,9 @@ def coord_expr(self, chart=None):
             sage: U = M.open_subset('U', coord_def={c_xy: (y!=0, x<0)}) # the complement of the segment y=0 and x>0
             sage: c_cart = c_xy.restrict(U) # Cartesian coordinates on U
             sage: c_spher.<r,ph> = U.chart(r'r:(0,+oo) ph:(0,2*pi):\phi') # spherical coordinates on U
-            sage: # Links between spherical coordinates and Cartesian ones:
+
+        Links between spherical coordinates and Cartesian ones::
+
             sage: ch_cart_spher = c_cart.transition_map(c_spher, [sqrt(x*x+y*y), atan2(y,x)])
             sage: ch_cart_spher.set_inverse(r*cos(ph), r*sin(ph))
             Check of the inverse coordinate transformation:
@@ -902,12 +904,10 @@ def _graphics(self, plot_curve, ambient_coords, thickness=1,
             True
 
         """
-
         from sage.plot.graphics import Graphics
         from sage.plot.line import line
         from sage.manifolds.utilities import set_axes_labels
 
-
         #
         # The plot
         #

src/sage/manifolds/differentiable/levi_civita_connection.py

@@ -435,7 +435,9 @@ def coef(self, frame=None):
             [[[0, 0, 0], [0, -r, 0], [0, 0, -r*sin(th)^2]],
             [[0, 1/r, 0], [1/r, 0, 0], [0, 0, -cos(th)*sin(th)]],
             [[0, 0, 1/r], [0, 0, cos(th)/sin(th)], [1/r, cos(th)/sin(th), 0]]]
-            sage: # The only non-zero Christoffel symbols:
+
+        The only non-zero Christoffel symbols::
+
             sage: gam[1,2,2], gam[1,3,3]
             (-r, -r*sin(th)^2)
             sage: gam[2,1,2], gam[2,3,3]
@@ -455,14 +457,15 @@ def coef(self, frame=None):
             [[[0, 0, 0], [0, -1/r, 0], [0, 0, -1/r]],
             [[0, 1/r, 0], [0, 0, 0], [0, 0, -cos(th)/(r*sin(th))]],
             [[0, 0, 1/r], [0, 0, cos(th)/(r*sin(th))], [0, 0, 0]]]
-            sage: # The only non-zero connection coefficients:
+
+        The only non-zero connection coefficients::
+
             sage: gam_e[1,2,2], gam_e[2,1,2]
             (-1/r, 1/r)
             sage: gam_e[1,3,3], gam_e[3,1,3]
             (-1/r, 1/r)
             sage: gam_e[2,3,3], gam_e[3,2,3]
             (-cos(th)/(r*sin(th)), cos(th)/(r*sin(th)))
-
         """
         from sage.manifolds.differentiable.vectorframe import CoordFrame
         if frame is None: