Conform to doc requirements so that the docs look more beautiful

src/sage/algebras/free_algebra_quotient.py

@@ -295,6 +295,8 @@ def module(self):
         """
         The free module of the algebra.
 
+        EXAMPLES::
+
             sage: H = sage.algebras.free_algebra_quotient.hamilton_quatalg(QQ)[0]; H
             Free algebra quotient on 3 generators ('i', 'j', 'k') and dimension 4 over Rational Field
             sage: H.module()

src/sage/algebras/iwahori_hecke_algebra.py

@@ -2491,6 +2491,8 @@ def __init__(self, IHAlgebra, prefix=None):
             r"""
             Initialize the `A`-basis of the Iwahori-Hecke algebra ``IHAlgebra``.
 
+            EXAMPLES::
+
                 sage: R.<v> = LaurentPolynomialRing(QQ)
                 sage: H = IwahoriHeckeAlgebra('A3', v**2)
                 sage: A = H.A()

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -1337,8 +1337,8 @@ def __init__(self, A, basis, check=True):
             sage: type(R)
             <class 'sage.algebras.quatalg.quaternion_algebra.QuaternionOrder_with_category'>
 
-            Over QQ and number fields it is checked whether the given
-            basis actually gives an order (as a module over the maximal order):
+        Over QQ and number fields it is checked whether the given
+        basis actually gives an order (as a module over the maximal order)::
 
             sage: A.<i,j,k> = QuaternionAlgebra(-1,-1)
             sage: A.quaternion_order([1,i,j,i-j])

src/sage/categories/cartesian_product.py

@@ -155,7 +155,7 @@ def __call__(self, args, **kwds):
             sage: _.category()
             Category of Cartesian products of finite enumerated sets
 
-        Check that the empty product is handled correctly:
+        Check that the empty product is handled correctly::
 
             sage: C = cartesian_product([])
             sage: C

src/sage/categories/domains.py

@@ -57,18 +57,18 @@ def _test_zero_divisors(self, **options):
                 In rings whose elements can not be represented exactly, there
                 may be zero divisors in practice, even though these rings do
                 not have them in theory. For such inexact rings, these tests
-                are not performed:
-
-                sage: R = ZpFM(5); R
-                5-adic Ring of fixed modulus 5^20
-                sage: R.is_exact()
-                False
-                sage: a = R(5^19)
-                sage: a.is_zero()
-                False
-                sage: (a*a).is_zero()
-                True
-                sage: R._test_zero_divisors()
+                are not performed::
+
+                    sage: R = ZpFM(5); R
+                    5-adic Ring of fixed modulus 5^20
+                    sage: R.is_exact()
+                    False
+                    sage: a = R(5^19)
+                    sage: a.is_zero()
+                    False
+                    sage: (a*a).is_zero()
+                    True
+                    sage: R._test_zero_divisors()
 
             EXAMPLES::
 

src/sage/categories/examples/sets_cat.py

@@ -160,7 +160,7 @@ class PrimeNumbers_Abstract(UniqueRepresentation, Parent):
     datastructure will then be constructed by inheriting from
     :class:`PrimeNumbers_Abstract`.
 
-    This is used by:
+    This is used by::
 
         sage: P = Sets().example("facade")
         sage: P = Sets().example("inherits")

src/sage/categories/magmas.py

@@ -711,6 +711,8 @@ def one(self):
                     r"""
                     Return the unit element of ``self``.
 
+                    EXAMPLES::
+
                         sage: from sage.combinat.root_system.extended_affine_weyl_group import ExtendedAffineWeylGroup
                         sage: PvW0 = ExtendedAffineWeylGroup(['A',2,1]).PvW0()
                         sage: PvW0 in Magmas().Unital().Realizations()

src/sage/coding/abstract_code.py

@@ -337,7 +337,7 @@ def __iter__(self):
             ....:        super().__init__(10)
 
         We check we get a sensible error message while asking for an
-        iterator over the elements of our new class:
+        iterator over the elements of our new class::
 
             sage: C = MyCode()
             sage: list(C)
@@ -365,7 +365,7 @@ def __contains__(self, c):
             ....:        super().__init__(length)
 
         We check we get a sensible error message while asking if an element is
-        in our new class:
+        in our new class::
 
             sage: C = MyCode(3)
             sage: vector((1, 0, 0, 0, 0, 1, 1)) in C
@@ -461,7 +461,7 @@ def _repr_(self):
             ....:        super().__init__(10)
 
         We check we get a sensible error message while asking for a string
-        representation of an instance of our new class:
+        representation of an instance of our new class::
 
             sage: C = MyCode()
             sage: C #random
@@ -489,7 +489,7 @@ def _latex_(self):
             ....:        super().__init__(10)
 
         We check we get a sensible error message while asking for a string
-        representation of an instance of our new class:
+        representation of an instance of our new class::
 
             sage: C = MyCode()
             sage: latex(C)

src/sage/coding/guruswami_sudan/interpolation.py

@@ -184,7 +184,7 @@ def _interpolation_matrix_problem(points, tau, parameters, wy):
     EXAMPLES:
 
     The following parameters arise from Guruswami-Sudan decoding of an [6,2,5]
-    GRS code over F(11) with multiplicity 2 and list size 4.
+    GRS code over F(11) with multiplicity 2 and list size 4. ::
 
         sage: from sage.coding.guruswami_sudan.interpolation import _interpolation_matrix_problem
         sage: F = GF(11)

src/sage/coding/linear_code_no_metric.py

@@ -538,7 +538,7 @@ def systematic_generator_matrix(self, systematic_positions=None):
             [1 2 0 1]
             [0 0 1 2]
 
-        Specific systematic positions can also be requested:
+        Specific systematic positions can also be requested::
 
             sage: C.systematic_generator_matrix(systematic_positions=[3,2])
             [1 2 0 1]

src/sage/combinat/colored_permutations.py

@@ -87,6 +87,8 @@ def __len__(self):
         """
         Return the length of the one line form of ``self``.
 
+        EXAMPLES::
+
             sage: C = ColoredPermutations(2, 3)
             sage: s1,s2,t = C.gens()
             sage: len(s1)

src/sage/combinat/ordered_tree.py

@@ -224,7 +224,7 @@ def _auto_parent(cls):
 
         .. NOTE::
 
-            It is possible to bypass the automatic parent mechanism using:
+            It is possible to bypass the automatic parent mechanism using::
 
                 sage: t1 = OrderedTree.__new__(OrderedTree, Parent(), [])
                 sage: t1.__init__(Parent(), [])

src/sage/combinat/permutation.py

@@ -4271,7 +4271,7 @@ def permutohedron_join(self, other, side="right") -> Permutation:
             sage: p.permutohedron_join(p)
             [1]
 
-        The left permutohedron:
+        The left permutohedron::
 
             sage: p = Permutation([3,1,2])
             sage: q = Permutation([1,3,2])
@@ -4387,7 +4387,7 @@ def permutohedron_meet(self, other, side="right") -> Permutation:
             sage: p.permutohedron_meet(p)
             [1]
 
-        The left permutohedron:
+        The left permutohedron::
 
             sage: p = Permutation([3,1,2])
             sage: q = Permutation([1,3,2])

src/sage/combinat/posets/hasse_diagram.py

@@ -1994,7 +1994,7 @@ def orthocomplementations_iterator(self):
             []
 
         Unique orthocomplementations; second is not uniquely complemented,
-        but has only one orthocomplementation.
+        but has only one orthocomplementation::
 
             sage: H = posets.BooleanLattice(4)._hasse_diagram  # Uniquely complemented
             sage: len(list(H.orthocomplementations_iterator()))

src/sage/combinat/root_system/type_affine.py

@@ -51,7 +51,7 @@ class AmbientSpace(CombinatorialFreeModule):
         \delta,\delta\rangle=0` and similarly for the null coroot.
 
         In the current implementation, `\Lambda_0` and the null coroot
-        are identified:
+        are identified::
 
             sage: L = RootSystem(["A",3,1]).ambient_space()
             sage: Lambda = L.fundamental_weights()

src/sage/combinat/sf/dual.py

@@ -214,7 +214,7 @@ def _self_to_dual(self, x):
             sage: h._self_to_dual(h([2,1]) + 3*h[1,1,1])
             21*m[1, 1, 1] + 11*m[2, 1] + 4*m[3]
 
-        This is for internal use only. Please use instead:
+        This is for internal use only. Please use instead::
 
             sage: m(h([2,1]) + 3*h[1,1,1])
             21*m[1, 1, 1] + 11*m[2, 1] + 4*m[3]

src/sage/combinat/sf/sfa.py

@@ -501,7 +501,7 @@ def _repr_(self):
                 sage: Sym.macdonald(q=1,t=3).P()
                 Sym in the Macdonald P with q=1 and t=3 basis
 
-            Hall-Littlewood polynomials:
+            Hall-Littlewood polynomials::
 
                 sage: Sym.hall_littlewood().P()
                 Sym in the Hall-Littlewood P basis

src/sage/combinat/subset.py

@@ -342,9 +342,9 @@ def cardinality(self):
             sage: Subsets(3).cardinality()
             8
 
-        TESTS::
+        TESTS:
 
-            ``__len__`` should return a Python int.
+        ``__len__`` should return a Python int::
 
             sage: S = Subsets(Set([1,2,3]))
             sage: len(S)

src/sage/combinat/tableau.py

@@ -233,7 +233,7 @@ def __init__(self, parent, t, check=True):
 
         A tableau is shallowly immutable. See :trac:`15862`. The entries
         themselves may be mutable objects, though in that case the
-        resulting Tableau should be unhashable.
+        resulting Tableau should be unhashable. ::
 
             sage: T = Tableau([[1,2],[2]])
             sage: t0 = T[0]

src/sage/combinat/words/paths.py

@@ -384,7 +384,7 @@ def __init__(self, alphabet, steps):
             True
 
         If size of alphabet is twice the number of steps, then opposite
-        vectors are used for the second part of the alphabet.
+        vectors are used for the second part of the alphabet::
 
             sage: WordPaths('abcd',[(2,1),(2,4)])
             Word Paths over 4 steps

src/sage/functions/special.py

@@ -538,7 +538,7 @@ def _eval_(self, z, m):
             sage: elliptic_e(z, 1)
             elliptic_e(z, 1)
 
-        Here arccoth doesn't have 1 in its domain, so we just hold the expression:
+        Here arccoth doesn't have 1 in its domain, so we just hold the expression::
 
             sage: elliptic_e(arccoth(1), x^2*e)
             elliptic_e(+Infinity, x^2*e)

src/sage/game_theory/normal_form_game.py

@@ -2743,8 +2743,8 @@ def _is_degenerate_pure(self, certificate=False):
             sage: g._is_degenerate_pure()
             True
 
-            Whilst this game is not degenerate in pure strategies, it is
-            actually degenerate, but only in mixed strategies.
+        Whilst this game is not degenerate in pure strategies, it is
+        actually degenerate, but only in mixed strategies::
 
             sage: A = matrix([[3, 0], [0, 3], [1.5, 1.5]])
             sage: B = matrix([[4, 3], [2, 6], [3, 1]])

src/sage/geometry/cone.py

@@ -6370,7 +6370,7 @@ def random_cone(lattice=None, min_ambient_dim=0, max_ambient_dim=None,
     TESTS:
 
     It's hard to test the output of a random process, but we can at
-    least make sure that we get a cone back.
+    least make sure that we get a cone back::
 
         sage: from sage.geometry.cone import is_Cone
         sage: K = random_cone(max_ambient_dim=6, max_rays=10)

src/sage/geometry/fan.py

@@ -1390,7 +1390,7 @@ def _compute_cone_lattice(self):
 
         We use different algorithms depending on available information. One of
         the common cases is a fan which is KNOWN to be complete, i.e. we do
-        not even need to check if it is complete.
+        not even need to check if it is complete::
 
             sage: fan = toric_varieties.P1xP1().fan()                           # optional - palp
             sage: fan.cone_lattice() # indirect doctest                         # optional - palp

src/sage/geometry/lattice_polytope.py

@@ -3783,7 +3783,7 @@ def points(self, *args, **kwds):
             M( 0,  0, 0)
             in 3-d lattice M
 
-        Only two of the above points:
+        Only two of the above points::
 
             sage: p.points(1, 3)                                                # optional - palp
             M(0,  1, 0),

src/sage/geometry/newton_polygon.py

@@ -630,13 +630,15 @@ def __init__(self):
         """
         Parent class for all Newton polygons.
 
+        EXAMPLES::
+
             sage: from sage.geometry.newton_polygon import ParentNewtonPolygon
             sage: ParentNewtonPolygon()
             Parent for Newton polygons
 
         TESTS:
 
-        This class is a singleton.
+        This class is a singleton::
 
             sage: ParentNewtonPolygon() is ParentNewtonPolygon()
             True

src/sage/geometry/polyhedron/base3.py

@@ -604,7 +604,7 @@ def face_generator(self, face_dimension=None, algorithm=None, **kwds):
               A 1-dimensional face of a Polyhedron in ZZ^4 defined as the convex hull of 2 vertices,
               A 1-dimensional face of a Polyhedron in ZZ^4 defined as the convex hull of 2 vertices]
 
-        Check that we catch incorrect algorithms:
+        Check that we catch incorrect algorithms::
 
              sage: list(P.face_generator(2, algorithm='integrate'))[:4]
              Traceback (most recent call last):

src/sage/geometry/polyhedron/base_QQ.py

@@ -119,7 +119,7 @@ def integral_points_count(self, verbose=False, use_Hrepresentation=False,
             27
 
         We enlarge the polyhedron to force the use of the generating function methods
-        implemented in LattE integrale, rather than explicit enumeration.
+        implemented in LattE integrale, rather than explicit enumeration::
 
             sage: (1000000000*P).integral_points_count(verbose=True) # optional - latte_int
             This is LattE integrale...

src/sage/graphs/generic_graph.py

@@ -5605,7 +5605,7 @@ def layout_planar(self, set_embedding=False, on_embedding=None,
             sage: g.layout(layout='planar', external_face=(3,1))
             {0: [2, 1], 1: [0, 2], 2: [1, 1], 3: [1, 0]}
 
-        Choose the embedding:
+        Choose the embedding::
 
             sage: H = graphs.LadderGraph(4)
             sage: em = {0:[1,4], 4:[0,5], 1:[5,2,0], 5:[4,6,1], 2:[1,3,6], 6:[7,5,2], 3:[7,2], 7:[3,6]}
@@ -6356,7 +6356,7 @@ def num_faces(self, embedding=None):
             ...
             ValueError: no embedding is provided and the graph is not planar
 
-        Issue :trac:`22003` is fixed:
+        Issue :trac:`22003` is fixed::
 
             sage: Graph(1).num_faces()
             1
@@ -20622,7 +20622,7 @@ def plot(self, **options):
              9: (0.47..., 0.15...)}
             sage: P = G.plot(save_pos=True, layout='spring')
 
-            The following illustrates the format of a position dictionary.
+        The following illustrates the format of a position dictionary::
 
             sage: G.get_pos() # currently random across platforms, see #9593
             {0: [1.17..., -0.855...],

src/sage/groups/perm_gps/permgroup.py

@@ -654,15 +654,15 @@ def gap(self):
 
         TESTS:
 
-        see that this method does not harm pickling:
+        see that this method does not harm pickling::
 
             sage: A4 = PermutationGroup([[(1,2,3)],[(2,3,4)]])
             sage: A4.gap()
             Group([ (2,3,4), (1,2,3) ])
             sage: TestSuite(A4).run()
 
         the following test shows, that support for the ``self._libgap``
-        attribute is needed in the constructor of the class:
+        attribute is needed in the constructor of the class::
 
             sage: PG = PGU(6,2)
             sage: g, h = PG.gens()

src/sage/groups/perm_gps/permgroup_named.py

@@ -635,7 +635,7 @@ def algebra(self, base_ring, category=None):
             Category of finite dimensional unital cellular semigroup algebras
              over Rational Field
 
-        In the following case, a usual group algebra is returned:
+        In the following case, a usual group algebra is returned::
 
             sage: S = SymmetricGroup([2,3,5])
             sage: S.algebra(QQ)