diff --git a/src/sage/algebras/free_algebra.py b/src/sage/algebras/free_algebra.py
index 52e7471d1bf..bcfb0e3a62e 100644
--- a/src/sage/algebras/free_algebra.py
+++ b/src/sage/algebras/free_algebra.py
@@ -331,6 +331,7 @@ def create_object(self, version, key):
             return FreeAlgebra_letterplace(key[1], degrees=key[0])
         return FreeAlgebra_generic(key[0], len(key[1]), key[1])
 
+
 FreeAlgebra = FreeAlgebraFactory('FreeAlgebra')
 
 
diff --git a/src/sage/algebras/group_algebra.py b/src/sage/algebras/group_algebra.py
index c639106b239..e16b0c08a21 100644
--- a/src/sage/algebras/group_algebra.py
+++ b/src/sage/algebras/group_algebra.py
@@ -223,5 +223,6 @@ def _coerce_map_from_(self, S):
                 return SetMorphism(S.Hom(self, category=self.category() | S.category()),
                                    lambda x: self.sum_of_terms( (hom_G(g), hom_K(c)) for g,c in x ))
 
+
 from sage.misc.persist import register_unpickle_override
 register_unpickle_override('sage.algebras.group_algebras', 'GroupAlgebra',  GroupAlgebra_class)
diff --git a/src/sage/categories/cartesian_product.py b/src/sage/categories/cartesian_product.py
index 39e9a316b9a..27a5147b629 100644
--- a/src/sage/categories/cartesian_product.py
+++ b/src/sage/categories/cartesian_product.py
@@ -271,6 +271,7 @@ def base_ring(self):
         """
         return self.base_category().base_ring()
 
+
 # Moved to avoid circular imports
 lazy_import('sage.categories.sets_cat', 'cartesian_product')
 """
diff --git a/src/sage/categories/category_with_axiom.py b/src/sage/categories/category_with_axiom.py
index c14d468246e..5227792e725 100644
--- a/src/sage/categories/category_with_axiom.py
+++ b/src/sage/categories/category_with_axiom.py
@@ -2524,6 +2524,7 @@ def __init__(self, base_category):
 class CategoryWithAxiom_singleton(Category_singleton, CategoryWithAxiom):#, Category_singleton, FastHashable_class):
     pass
 
+
 """
 The following workaround is needed until any :class:`CategoryWithAxiom` of a
 :class:`Category_over_base_ring` becomes automatically a
diff --git a/src/sage/categories/examples/algebras_with_basis.py b/src/sage/categories/examples/algebras_with_basis.py
index 04511128301..e1d9350d18c 100644
--- a/src/sage/categories/examples/algebras_with_basis.py
+++ b/src/sage/categories/examples/algebras_with_basis.py
@@ -97,4 +97,5 @@ def algebra_generators(self):
         # for the specifying the order of the elements in the family
         #return Family(self._alphabet, lambda a: self.term(self.basis().keys()(a)))
 
+
 Example = FreeAlgebra
diff --git a/src/sage/categories/examples/commutative_additive_semigroups.py b/src/sage/categories/examples/commutative_additive_semigroups.py
index fdda759869a..95fb6da0c79 100644
--- a/src/sage/categories/examples/commutative_additive_semigroups.py
+++ b/src/sage/categories/examples/commutative_additive_semigroups.py
@@ -194,4 +194,5 @@ def __hash__(self):
             """
             return hash(tuple(self.value.items()))
 
+
 Example = FreeCommutativeAdditiveSemigroup
diff --git a/src/sage/categories/examples/cw_complexes.py b/src/sage/categories/examples/cw_complexes.py
index 8422fc0a418..0fefb254c20 100644
--- a/src/sage/categories/examples/cw_complexes.py
+++ b/src/sage/categories/examples/cw_complexes.py
@@ -158,4 +158,5 @@ def dimension(self):
             """
             return self._dim
 
+
 Example = Surface
diff --git a/src/sage/categories/examples/filtered_algebras_with_basis.py b/src/sage/categories/examples/filtered_algebras_with_basis.py
index 5a83c54d1fd..57d106e4555 100644
--- a/src/sage/categories/examples/filtered_algebras_with_basis.py
+++ b/src/sage/categories/examples/filtered_algebras_with_basis.py
@@ -198,4 +198,5 @@ def product_on_basis(self, s, t):
             cur = cur * self.monomial(self._indices.gen(a))
         return cur
 
+
 Example = PBWBasisCrossProduct
diff --git a/src/sage/categories/examples/filtered_modules_with_basis.py b/src/sage/categories/examples/filtered_modules_with_basis.py
index 35edb3314dc..a76726099bc 100644
--- a/src/sage/categories/examples/filtered_modules_with_basis.py
+++ b/src/sage/categories/examples/filtered_modules_with_basis.py
@@ -149,4 +149,5 @@ def _repr_term(self, t):
         """
         return 'P' + t._repr_()
 
+
 Example = FilteredPartitionModule
diff --git a/src/sage/categories/examples/finite_dimensional_algebras_with_basis.py b/src/sage/categories/examples/finite_dimensional_algebras_with_basis.py
index 0406e23c6e8..de06ca7ab54 100644
--- a/src/sage/categories/examples/finite_dimensional_algebras_with_basis.py
+++ b/src/sage/categories/examples/finite_dimensional_algebras_with_basis.py
@@ -143,4 +143,5 @@ def _repr_term(self, p):
         """
         return str(p)
 
+
 Example = KroneckerQuiverPathAlgebra
diff --git a/src/sage/categories/examples/finite_dimensional_lie_algebras_with_basis.py b/src/sage/categories/examples/finite_dimensional_lie_algebras_with_basis.py
index 58e613a6d45..9f221f1432e 100644
--- a/src/sage/categories/examples/finite_dimensional_lie_algebras_with_basis.py
+++ b/src/sage/categories/examples/finite_dimensional_lie_algebras_with_basis.py
@@ -404,4 +404,5 @@ def monomial_coefficients(self, copy=True):
             """
             return self.value.monomial_coefficients(copy)
 
+
 Example = AbelianLieAlgebra
diff --git a/src/sage/categories/examples/finite_monoids.py b/src/sage/categories/examples/finite_monoids.py
index 4d3e8fa7029..9ec09313a82 100644
--- a/src/sage/categories/examples/finite_monoids.py
+++ b/src/sage/categories/examples/finite_monoids.py
@@ -146,4 +146,5 @@ def an_element(self):
     class Element (ElementWrapper):
         wrapped_class = Integer
 
+
 Example = IntegerModMonoid
diff --git a/src/sage/categories/examples/finite_semigroups.py b/src/sage/categories/examples/finite_semigroups.py
index 60766b5d9d0..2e54d2130f4 100644
--- a/src/sage/categories/examples/finite_semigroups.py
+++ b/src/sage/categories/examples/finite_semigroups.py
@@ -187,4 +187,5 @@ class Element (ElementWrapper):
         wrapped_class = str
         __lt__ = ElementWrapper._lt_by_value
 
+
 Example = LeftRegularBand
diff --git a/src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py b/src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py
index 07afa9c44ec..2290419adb3 100644
--- a/src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py
+++ b/src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py
@@ -162,4 +162,5 @@ def coproduct_on_basis(self, i):
             for j in range(i+1)
         )
 
+
 Example = GradedConnectedCombinatorialHopfAlgebraWithPrimitiveGenerator
diff --git a/src/sage/categories/examples/graded_modules_with_basis.py b/src/sage/categories/examples/graded_modules_with_basis.py
index 8095beb11c2..8ddfb7eed04 100644
--- a/src/sage/categories/examples/graded_modules_with_basis.py
+++ b/src/sage/categories/examples/graded_modules_with_basis.py
@@ -163,4 +163,5 @@ def _repr_term(self, t):
         """
         return 'P' + t._repr_()
 
+
 Example = GradedPartitionModule
diff --git a/src/sage/categories/examples/graphs.py b/src/sage/categories/examples/graphs.py
index 21c2d2a150a..063eeff1427 100644
--- a/src/sage/categories/examples/graphs.py
+++ b/src/sage/categories/examples/graphs.py
@@ -117,4 +117,5 @@ def dimension(self):
                 return 2
             return 1
 
+
 Example = Cycle
diff --git a/src/sage/categories/examples/infinite_enumerated_sets.py b/src/sage/categories/examples/infinite_enumerated_sets.py
index c4bb3d8e55d..df4151f21c2 100644
--- a/src/sage/categories/examples/infinite_enumerated_sets.py
+++ b/src/sage/categories/examples/infinite_enumerated_sets.py
@@ -185,4 +185,5 @@ def _element_constructor_(self, i):
 
     Element = Integer
 
+
 Example = NonNegativeIntegers
diff --git a/src/sage/categories/examples/lie_algebras.py b/src/sage/categories/examples/lie_algebras.py
index 2382f1d0e7b..135c122efa2 100644
--- a/src/sage/categories/examples/lie_algebras.py
+++ b/src/sage/categories/examples/lie_algebras.py
@@ -332,4 +332,5 @@ def _bracket_(self, rhs):
             """
             return self.__class__(self.parent(), self.value * rhs.value - rhs.value * self.value)
 
+
 Example = LieAlgebraFromAssociative
diff --git a/src/sage/categories/examples/lie_algebras_with_basis.py b/src/sage/categories/examples/lie_algebras_with_basis.py
index a92f51b49db..ca711e1cdb4 100644
--- a/src/sage/categories/examples/lie_algebras_with_basis.py
+++ b/src/sage/categories/examples/lie_algebras_with_basis.py
@@ -100,6 +100,7 @@ def lift(self):
             I = UEA._indices
             return UEA.sum_of_terms((I.gen(t), c) for t, c in self)
 
+
 Example = AbelianLieAlgebra
 
 ##############
diff --git a/src/sage/categories/examples/manifolds.py b/src/sage/categories/examples/manifolds.py
index e1d7c851202..6a748884eec 100644
--- a/src/sage/categories/examples/manifolds.py
+++ b/src/sage/categories/examples/manifolds.py
@@ -89,4 +89,5 @@ def an_element(self):
 
     Element = ElementWrapper
 
+
 Example = Plane
diff --git a/src/sage/categories/examples/monoids.py b/src/sage/categories/examples/monoids.py
index 7336c680bdf..131e2b8a0e4 100644
--- a/src/sage/categories/examples/monoids.py
+++ b/src/sage/categories/examples/monoids.py
@@ -141,4 +141,5 @@ def monoid_generators(self):
     class Element (ElementWrapper):
         wrapped_class = str
 
+
 Example = FreeMonoid
diff --git a/src/sage/categories/realizations.py b/src/sage/categories/realizations.py
index 595ee38dc9a..1c40e597676 100644
--- a/src/sage/categories/realizations.py
+++ b/src/sage/categories/realizations.py
@@ -102,6 +102,7 @@ def Realizations(self):
     else:
         return getattr(self.__class__, "Realizations")(self)
 
+
 Category.Realizations = Realizations
 
 class Category_realization_of_parent(Category_over_base, BindableClass):
diff --git a/src/sage/categories/sets_cat.py b/src/sage/categories/sets_cat.py
index ea5695de6c2..3ebd6c44406 100644
--- a/src/sage/categories/sets_cat.py
+++ b/src/sage/categories/sets_cat.py
@@ -3154,5 +3154,6 @@ def _repr_(self):
                 """
                 return "{} in the realization {}".format(self.realization_of(), self._realization_name())
 
+
 # Moved from sage.categories.cartesian_product to avoid circular import errors
 cartesian_product = CartesianProductFunctor()
diff --git a/src/sage/categories/with_realizations.py b/src/sage/categories/with_realizations.py
index 003277dcd2a..d0dc8d148bd 100644
--- a/src/sage/categories/with_realizations.py
+++ b/src/sage/categories/with_realizations.py
@@ -280,6 +280,7 @@ def WithRealizations(self):
     """
     return WithRealizationsCategory.category_of(self)
 
+
 Category.WithRealizations = WithRealizations
 
 class WithRealizationsCategory(RegressiveCovariantConstructionCategory):
diff --git a/src/sage/coding/databases.py b/src/sage/coding/databases.py
index e0c8b6e4068..7839cd8c693 100644
--- a/src/sage/coding/databases.py
+++ b/src/sage/coding/databases.py
@@ -309,6 +309,7 @@ def self_orthogonal_binary_codes(n, k, b=2, parent=None, BC=None, equal=False,
                         if out_test(N):
                             yield N
 
+
 # Import the following function so that it is available as
 # sage.codes.databases.self_dual_binary_codes sage.codes.databases functions
 # somewhat like a catalog in this respect.
diff --git a/src/sage/coding/goppa_code.py b/src/sage/coding/goppa_code.py
index cc9fdb4791b..2a974cf1ef2 100644
--- a/src/sage/coding/goppa_code.py
+++ b/src/sage/coding/goppa_code.py
@@ -436,4 +436,5 @@ def generator_matrix(self):
         aux = codes.from_parity_check_matrix(pmat)
         return aux.generator_matrix()
 
+
 GoppaCode._registered_encoders["GoppaEncoder"] = GoppaCodeEncoder
diff --git a/src/sage/coding/linear_rank_metric.py b/src/sage/coding/linear_rank_metric.py
index 2b687775102..babb22ff1ce 100644
--- a/src/sage/coding/linear_rank_metric.py
+++ b/src/sage/coding/linear_rank_metric.py
@@ -891,7 +891,8 @@ def decoding_radius(self):
             sage: D.decoding_radius()
             1
         """
-        return (self.code().minimum_distance()-1) // 2
+        return (self.code().minimum_distance() - 1) // 2
+
 
 ####################### registration ###############################
 
diff --git a/src/sage/coding/parity_check_code.py b/src/sage/coding/parity_check_code.py
index 03f23bcc17f..d131ecaf80a 100644
--- a/src/sage/coding/parity_check_code.py
+++ b/src/sage/coding/parity_check_code.py
@@ -349,6 +349,7 @@ def message_space(self):
         """
         return VectorSpace(self.code().base_field(), self.code().dimension())
 
+
 ####################### registration ###############################
 
 ParityCheckCode._registered_encoders["ParityCheckCodeGeneratorMatrixEncoder"] = ParityCheckCodeGeneratorMatrixEncoder
diff --git a/src/sage/coding/punctured_code.py b/src/sage/coding/punctured_code.py
index df57fb90e54..7aafa4f3f27 100644
--- a/src/sage/coding/punctured_code.py
+++ b/src/sage/coding/punctured_code.py
@@ -709,6 +709,7 @@ def decoding_radius(self, number_erasures=None):
         elif "error-erasure" in D.decoder_type() and number_erasures is None:
             raise ValueError("You must provide the number of erasures")
 
+
 ####################### registration ###############################
 
 PuncturedCode._registered_encoders["PuncturedMatrix"] = PuncturedCodePuncturedMatrixEncoder
diff --git a/src/sage/coding/subfield_subcode.py b/src/sage/coding/subfield_subcode.py
index 2783c66ec4a..9ec9650c43a 100644
--- a/src/sage/coding/subfield_subcode.py
+++ b/src/sage/coding/subfield_subcode.py
@@ -419,6 +419,7 @@ def decoding_radius(self, **kwargs):
         """
         return self.original_decoder().decoding_radius(**kwargs)
 
+
 ####################### registration ###############################
 
 SubfieldSubcode._registered_decoders["OriginalCode"] = SubfieldSubcodeOriginalCodeDecoder
diff --git a/src/sage/crypto/sboxes.py b/src/sage/crypto/sboxes.py
index bfb3834d5aa..27ca13fbcc3 100644
--- a/src/sage/crypto/sboxes.py
+++ b/src/sage/crypto/sboxes.py
@@ -397,6 +397,7 @@ def monomial_function(n, e):
     X = R.gen()
     return SBox(X**e)
 
+
 # Bijective S-Boxes mapping 9 bits to 9
 # =====================================
 
diff --git a/src/sage/databases/findstat.py b/src/sage/databases/findstat.py
index 8fc3ef8ec15..86ab944744a 100644
--- a/src/sage/databases/findstat.py
+++ b/src/sage/databases/findstat.py
@@ -4516,6 +4516,7 @@ def name(self, style="singular"):
             return self._data["NamePlural"]
         raise ValueError("argument 'style' (=%s) must be 'singular' or 'plural'" % style)
 
+
 from collections import namedtuple
 _SupportedFindStatCollection = namedtuple("SupportedFindStatCollection",
                                           ["string_to_element",
diff --git a/src/sage/doctest/external.py b/src/sage/doctest/external.py
index 8744bd93e72..9768202e76f 100644
--- a/src/sage/doctest/external.py
+++ b/src/sage/doctest/external.py
@@ -372,6 +372,7 @@ def external_software():
     """
     return sorted(f.name for f in external_features())
 
+
 external_software = external_software()
 
 
diff --git a/src/sage/functions/gamma.py b/src/sage/functions/gamma.py
index 54a3a5aa3ba..8ecf834a8a8 100644
--- a/src/sage/functions/gamma.py
+++ b/src/sage/functions/gamma.py
@@ -183,6 +183,7 @@ def __init__(self):
                                             'fricas':'Gamma',
                                             'giac':'Gamma'})
 
+
 gamma1 = Function_gamma()
 
 
@@ -486,7 +487,8 @@ def _evalf_(self, x, y, parent=None, algorithm='pari'):
         else:
             return C(v)
 
-# synonym.
+
+# shorter alias
 gamma_inc = Function_gamma_inc()
 
 
@@ -649,7 +651,8 @@ def _mathematica_init_evaled_(self, *args):
         x, z = args_mathematica
         return "Gamma[%s,0,%s]" % (x, z)
 
-# synonym.
+
+# shorter alias
 gamma_inc_lower = Function_gamma_inc_lower()
 
 
@@ -750,6 +753,7 @@ def _mathematica_gamma3(*args):
     assert len(args) == 3
     return gamma_inc(args[0], args[1]) - gamma_inc(args[0], args[2])
 
+
 register_symbol(_mathematica_gamma3, dict(mathematica='Gamma'), 3)
 
 
@@ -893,6 +897,7 @@ def _maxima_init_evaled_(self, *args):
         n, x = args_maxima
         return "psi[%s](%s)" % (n, x)
 
+
 psi1 = Function_psi1()
 psi2 = Function_psi2()
 
@@ -945,6 +950,7 @@ def psi(x, *args, **kwds):
         raise TypeError("Symbolic function psi takes at most 2 arguments (%s given)" % (len(args) + 1))
     return psi2(x, args[0], **kwds)
 
+
 # We have to add the wrapper function manually to the symbol_table when we have
 # two functions with different number of arguments and the same name
 symbol_table['functions']['psi'] = psi
@@ -953,6 +959,7 @@ def psi(x, *args, **kwds):
 def _swap_psi(a, b):
     return psi(b, a)
 
+
 register_symbol(_swap_psi, {'giac': 'Psi'}, 2)
 
 
@@ -1075,4 +1082,5 @@ def _method_arguments(self, x, y):
         """
         return [x, y]
 
+
 beta = Function_beta()
diff --git a/src/sage/functions/other.py b/src/sage/functions/other.py
index 38276c57fbe..9dbe9787545 100644
--- a/src/sage/functions/other.py
+++ b/src/sage/functions/other.py
@@ -127,6 +127,7 @@ def __init__(self):
                                                 giac='abs',
                                                 fricas='abs'))
 
+
 abs = abs_symbolic = Function_abs()
 
 
@@ -466,6 +467,7 @@ def _eval_(self, x):
                 return Integer(math.ceil(x))
         return None
 
+
 ceil = Function_ceil()
 
 
@@ -634,6 +636,7 @@ def _eval_(self, x):
                 return Integer(math.floor(x))
         return None
 
+
 floor = Function_floor()
 
 
@@ -698,6 +701,7 @@ def _sympy_(self, arg):
         import sympy
         return sympy.O(*sympy.sympify(arg, evaluate=False))
 
+
 Order = Function_Order()
 
 
@@ -771,6 +775,7 @@ def _eval_(self, x):
                     return x - ret
         return None
 
+
 frac = Function_frac()
 
 
@@ -955,6 +960,7 @@ def _derivative_(self, base, exp, diff_param=None):
         """
         return 1/exp * self(base, exp)**(1-exp)
 
+
 real_nth_root = Function_real_nth_root()
 
 
@@ -1107,6 +1113,7 @@ def _evalf_(self, x, parent=None, algorithm=None):
 
         return parent(x).arg()
 
+
 arg=Function_arg()
 
 
@@ -1206,6 +1213,7 @@ def __call__(self, x, **kwargs):
         else:
             return GinacFunction.__call__(self, x, **kwargs)
 
+
 real = real_part = Function_real_part()
 
 
@@ -1891,6 +1899,7 @@ def _sympy_(self, term, k, a, n):
         import sympy
         return sympy.Product(term, (k, a, n))
 
+
 symbolic_product = Function_prod()
 
 
@@ -1996,6 +2005,7 @@ def _print_latex_(self, ex, var, to, direction=''):
         return r"\lim_{{{} \to {}{}}}\, {}".format(latex(var),
                 latex(to), dir_str, latex(ex))
 
+
 symbolic_limit = Function_limit()
 
 
@@ -2208,6 +2218,7 @@ def _evalf_(self, poly, index, parent=None, algorithm=None):
         sobj = CRootOf(Poly(poly._sympy_()), int(index))
         return parent(sobj.n(1 + prec_to_dps(prec))._sage_())
 
+
 complex_root_of = Function_crootof()
 
 
@@ -2282,4 +2293,5 @@ def _print_latex_(self, ex, s):
         """
         return r"{} \in {}".format(latex(ex), latex(s))
 
+
 element_of = Function_elementof()
diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py
index 701b8e43ee8..26c7d9a3819 100644
--- a/src/sage/geometry/lattice_polytope.py
+++ b/src/sage/geometry/lattice_polytope.py
@@ -398,6 +398,7 @@ def ReflexivePolytope(dim, n):
     else:
         raise NotImplementedError("only 2- and 3-dimensional reflexive polytopes are available!")
 
+
 # Sequences of reflexive polytopes
 _rp = [None] * 4
 
@@ -5545,6 +5546,7 @@ def all_polars(polytopes):
     result.close()
     os.remove(result_name)
 
+
 # Synonym for the above function
 all_facet_equations = all_polars
 
diff --git a/src/sage/groups/galois_group.py b/src/sage/groups/galois_group.py
index d4023125644..bc1b9a807f1 100644
--- a/src/sage/groups/galois_group.py
+++ b/src/sage/groups/galois_group.py
@@ -622,5 +622,6 @@ class GaloisSubgroup_ab(AbelianGroup_subgroup, _SubGaloisMixin):
     """
     pass
 
+
 GaloisGroup_perm.Subgroup = GaloisSubgroup_perm
 GaloisGroup_ab.Subgroup = GaloisSubgroup_ab
diff --git a/src/sage/groups/group_exp.py b/src/sage/groups/group_exp.py
index 4f3d27a8def..ffae5e73cb2 100644
--- a/src/sage/groups/group_exp.py
+++ b/src/sage/groups/group_exp.py
@@ -357,4 +357,5 @@ def group_generators(self):
             raise AttributeError("Additive group has no method 'gens'")
         return tuple([self(x) for x in additive_generators])
 
+
 GroupExp_Class.Element = GroupExpElement
diff --git a/src/sage/interfaces/axiom.py b/src/sage/interfaces/axiom.py
index fe4637a7b19..83f9cb95817 100644
--- a/src/sage/interfaces/axiom.py
+++ b/src/sage/interfaces/axiom.py
@@ -916,6 +916,7 @@ def __init__(self, object, name):
             name = name[:-2] + "!"
         FunctionElement.__init__(self, object, name)
 
+
 AxiomFunctionElement = PanAxiomFunctionElement
 
 
@@ -936,6 +937,7 @@ def __init__(self, parent, name):
             name = name[:-2] + "!"
         ExpectFunction.__init__(self, parent, name)
 
+
 AxiomExpectFunction = PanAxiomExpectFunction
 
 
diff --git a/src/sage/interfaces/frobby.py b/src/sage/interfaces/frobby.py
index 17c7f06f05f..ed6f5431dc3 100644
--- a/src/sage/interfaces/frobby.py
+++ b/src/sage/interfaces/frobby.py
@@ -466,5 +466,6 @@ def _monomial_to_string(self, monomial):
         strings = [str(exponents[var]) for var in range(len(exponents))]
         return ' '.join(strings) + '\n'
 
+
 # This singleton instance is what should be used outside this file.
 frobby = Frobby()
diff --git a/src/sage/interfaces/gap.py b/src/sage/interfaces/gap.py
index 44900d525c8..b7f9b5edd51 100644
--- a/src/sage/interfaces/gap.py
+++ b/src/sage/interfaces/gap.py
@@ -222,10 +222,11 @@
     # suppress unaligned access to 0x..., ip=0x... warnings
     gap_cmd = 'prctl --unaligned=silent ' + gap_cmd
 
+
 def gap_command(use_workspace_cache=True, local=True):
     if use_workspace_cache:
         if local:
-            return "%s -L %s"%(gap_cmd, WORKSPACE), False
+            return "%s -L %s" % (gap_cmd, WORKSPACE), False
         else:
             # TO DO: Use remote workspace
             return gap_cmd, False
@@ -1037,7 +1038,6 @@ def _matrix_(self, R):
         entries = [[R(self[r,c]) for c in range(1,m+1)] for r in range(1,n+1)]
         return M(entries)
 
-############
 
 class Gap(Gap_generic):
     r"""
@@ -1465,8 +1465,6 @@ def _tab_completion(self):
         return [n for n in names if n[0] in string.ascii_letters]
 
 
-############
-
 def gap_reset_workspace(max_workspace_size=None, verbose=False):
     r"""
     Call this to completely reset the GAP workspace, which is used by
@@ -1765,10 +1763,10 @@ def intmod_gap_to_sage(x):
         return Mod(Integer(m.group(1)), Integer(m.group(2)))
     raise ValueError("Unable to convert Gap element '%s'" % s)
 
-#############
 
 gap = Gap()
 
+
 def reduce_load_GAP():
     """
     Returns the GAP interface object defined in sage.interfaces.gap.
diff --git a/src/sage/interfaces/genus2reduction.py b/src/sage/interfaces/genus2reduction.py
index 6fa64b68cca..0a03059f9b0 100644
--- a/src/sage/interfaces/genus2reduction.py
+++ b/src/sage/interfaces/genus2reduction.py
@@ -457,6 +457,7 @@ def __call__(self, Q, P):
     def __reduce__(self):
         return _reduce_load_genus2reduction, tuple([])
 
+
 # An instance
 genus2reduction = Genus2reduction()
 
diff --git a/src/sage/interfaces/gnuplot.py b/src/sage/interfaces/gnuplot.py
index b423866fd15..025a8155212 100644
--- a/src/sage/interfaces/gnuplot.py
+++ b/src/sage/interfaces/gnuplot.py
@@ -187,6 +187,7 @@ def interact(self, cmd):
     def console(self):
         gnuplot_console()
 
+
 # An instance
 gnuplot = Gnuplot()
 
diff --git a/src/sage/interfaces/lisp.py b/src/sage/interfaces/lisp.py
index c4d8542a5ed..5c28b82bf88 100644
--- a/src/sage/interfaces/lisp.py
+++ b/src/sage/interfaces/lisp.py
@@ -537,6 +537,7 @@ def is_LispElement(x):
 
     return isinstance(x, LispElement)
 
+
 # An instance
 lisp = Lisp()
 
@@ -550,6 +551,7 @@ def reduce_load_Lisp():
     """
     return lisp
 
+
 import os
 def lisp_console():
     """
diff --git a/src/sage/interfaces/macaulay2.py b/src/sage/interfaces/macaulay2.py
index 58ec79a48ee..956ca018838 100644
--- a/src/sage/interfaces/macaulay2.py
+++ b/src/sage/interfaces/macaulay2.py
@@ -1854,6 +1854,7 @@ def is_Macaulay2Element(x):
 
     return isinstance(x, Macaulay2Element)
 
+
 # An instance
 macaulay2 = Macaulay2()
 
diff --git a/src/sage/interfaces/magma.py b/src/sage/interfaces/magma.py
index 4ff6477107f..e47d47f8fd2 100644
--- a/src/sage/interfaces/magma.py
+++ b/src/sage/interfaces/magma.py
@@ -2751,7 +2751,6 @@ def ideal(self, gens):
         """
         return self.parent().bar_call(self, 'ideal', gens, nvals=1)
 
-###########################################################################
 
 magma = Magma()
 
diff --git a/src/sage/interfaces/matlab.py b/src/sage/interfaces/matlab.py
index a2678b4dbcc..24c40a3647c 100644
--- a/src/sage/interfaces/matlab.py
+++ b/src/sage/interfaces/matlab.py
@@ -356,6 +356,7 @@ def set(self, i, j, x):
         z = P(x)
         P.eval('{0}({1},{2}) = {3}'.format(self.name(), i, j, z.name()))
 
+
 # An instance
 matlab = Matlab()
 
diff --git a/src/sage/interfaces/maxima_lib.py b/src/sage/interfaces/maxima_lib.py
index cd1be891872..c8f9d574763 100644
--- a/src/sage/interfaces/maxima_lib.py
+++ b/src/sage/interfaces/maxima_lib.py
@@ -305,6 +305,7 @@ def max_to_string(s):
     """
     return maxprint(s).python()[1:-1]
 
+
 my_mread=ecl_eval("""
 (defun my-mread (cmd)
   (caddr (mread (make-string-input-stream cmd))))
@@ -1278,6 +1279,7 @@ def sage_rat(x,y):
     """
     return x/y
 
+
 mplus=EclObject("MPLUS")
 mtimes=EclObject("MTIMES")
 rat=EclObject("RAT")
@@ -1683,6 +1685,7 @@ def sr_to_max(expr):
         except TypeError:
             return maxima(expr).ecl()
 
+
 # This goes from EclObject to SR
 from sage.symbolic.expression import symbol_table
 max_to_pynac_table = symbol_table['maxima']
diff --git a/src/sage/interfaces/mupad.py b/src/sage/interfaces/mupad.py
index 8a101ab0995..d5115f297d3 100644
--- a/src/sage/interfaces/mupad.py
+++ b/src/sage/interfaces/mupad.py
@@ -638,6 +638,7 @@ def __len__(self):
         """
         return mupad.nops(self)
 
+
 # An instance
 mupad = Mupad()
 
diff --git a/src/sage/interfaces/mwrank.py b/src/sage/interfaces/mwrank.py
index ae65d0ffea0..fca82e687ec 100644
--- a/src/sage/interfaces/mwrank.py
+++ b/src/sage/interfaces/mwrank.py
@@ -67,6 +67,7 @@ def Mwrank(options="", server=None, server_tmpdir=None):
     instances[options] = weakref.ref(X)
     return X
 
+
 import re
 # regex matching '[a1,a2,a3,a4,a6]', no spaces, each ai a possibly signed integer
 AINVS_LIST_RE = re.compile(r'\[[+-]?(\d+)(,[+-]?\d+){4}]')
diff --git a/src/sage/interfaces/octave.py b/src/sage/interfaces/octave.py
index f8f426c67e6..cf4f828151c 100644
--- a/src/sage/interfaces/octave.py
+++ b/src/sage/interfaces/octave.py
@@ -808,6 +808,7 @@ def _sage_(self):
         else:
             raise NotImplementedError('octave type is not recognized')
 
+
 # An instance
 octave = Octave()
 
diff --git a/src/sage/interfaces/qepcad.py b/src/sage/interfaces/qepcad.py
index f54c8e181d7..8322aa361d0 100644
--- a/src/sage/interfaces/qepcad.py
+++ b/src/sage/interfaces/qepcad.py
@@ -662,6 +662,7 @@ def _qepcad_cmd(memcells=None):
         memcells_arg = ''
     return "env qe=%s qepcad %s"%(SAGE_LOCAL, memcells_arg)
 
+
 _command_info_cache = None
 
 
diff --git a/src/sage/interfaces/r.py b/src/sage/interfaces/r.py
index 7d18f1e467e..acf984ddba9 100644
--- a/src/sage/interfaces/r.py
+++ b/src/sage/interfaces/r.py
@@ -2030,6 +2030,7 @@ def is_RElement(x):
 
     return isinstance(x, RElement)
 
+
 # An instance of R
 r = R()
 
@@ -2045,6 +2046,7 @@ def reduce_load_R():
     """
     return r
 
+
 import os
 def r_console():
     """
diff --git a/src/sage/interfaces/scilab.py b/src/sage/interfaces/scilab.py
index 75ab263a53e..2e00b08372a 100644
--- a/src/sage/interfaces/scilab.py
+++ b/src/sage/interfaces/scilab.py
@@ -511,6 +511,7 @@ def set(self, i, j, x):
         z = P(x)
         P.eval('%s(%s,%s) = %s'%(self.name(), i, j, z.name()))
 
+
 # An instance
 scilab = Scilab()
 
diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
index 4b5c76e2bfa..7ecc3db56f1 100644
--- a/src/sage/interfaces/singular.py
+++ b/src/sage/interfaces/singular.py
@@ -847,9 +847,9 @@ def cputime(self, t=None):
         else:
             return float(self.eval('timer'))/1000.0
 
-    ###################################################################
+    ###########################################################
     # Singular libraries
-    ###################################################################
+    ###########################################################
     def lib(self, lib, reload=False):
         """
         Load the Singular library named lib.
@@ -873,9 +873,9 @@ def lib(self, lib, reload=False):
     LIB = lib
     load = lib
 
-    ###################################################################
+    ##########################################################
     # constructors
-    ###################################################################
+    ##########################################################
     def ideal(self, *gens):
         """
         Return the ideal generated by gens.
@@ -2418,10 +2418,10 @@ def get_docstring(name):
     except KeyError:
         return ""
 
-##################################
 
 singular = Singular()
 
+
 def reduce_load_Singular():
     """
     EXAMPLES::
diff --git a/src/sage/interfaces/tachyon.py b/src/sage/interfaces/tachyon.py
index 6dd359d9e36..6053d2519e4 100644
--- a/src/sage/interfaces/tachyon.py
+++ b/src/sage/interfaces/tachyon.py
@@ -891,4 +891,5 @@ def help(self, use_pager=True):
         """
         deprecation(34066, "type 'sage.interfaces.tachyon?' for help")
 
+
 tachyon_rt = TachyonRT()
diff --git a/src/sage/logic/propcalc.py b/src/sage/logic/propcalc.py
index 2ff45801bf0..2533cdac702 100644
--- a/src/sage/logic/propcalc.py
+++ b/src/sage/logic/propcalc.py
@@ -310,5 +310,6 @@ def consistent(*formulas):
     # if conjunction is a contradiction, the formulas are inconsistent
     return not conjunction.is_contradiction()
 
+
 # define function ``valid_consequence`` for backward compatibility
 valid_consequence = deprecated_function_alias(28052, boolformula.is_consequence)
diff --git a/src/sage/manifolds/manifold.py b/src/sage/manifolds/manifold.py
index bb3f6cc42f5..b19177da9e5 100644
--- a/src/sage/manifolds/manifold.py
+++ b/src/sage/manifolds/manifold.py
@@ -2720,8 +2720,9 @@ def set_simplify_function(self, simplifying_func, method=None):
             chart.calculus_method().set_simplify_function(simplifying_func,
                                                           method=method)
 
-##############################################################################
-## Constructor function
+
+###########################################################
+# Constructor function
 
 _manifold_id = Integer(0)
 
diff --git a/src/sage/manifolds/utilities.py b/src/sage/manifolds/utilities.py
index 852dd0be1f1..c66d54e774e 100644
--- a/src/sage/manifolds/utilities.py
+++ b/src/sage/manifolds/utilities.py
@@ -1357,4 +1357,5 @@ def exterior_derivative(form):
     """
     return form.exterior_derivative()
 
+
 xder = exterior_derivative
diff --git a/src/sage/misc/call.py b/src/sage/misc/call.py
index c70b7972ef9..966ee34514b 100644
--- a/src/sage/misc/call.py
+++ b/src/sage/misc/call.py
@@ -181,5 +181,6 @@ def call_method(obj, name, *args, **kwds):
     """
     return getattr(obj, name)(*args, **kwds)
 
+
 from sage.misc.persist import register_unpickle_override
 register_unpickle_override("sage.misc.misc", "call_method", call_method)
diff --git a/src/sage/misc/explain_pickle.py b/src/sage/misc/explain_pickle.py
index c2e663432bb..30c3988850b 100644
--- a/src/sage/misc/explain_pickle.py
+++ b/src/sage/misc/explain_pickle.py
@@ -294,6 +294,7 @@ def explain_pickle_string(pickle, in_current_sage=False,
     else:
         return ans
 
+
 valid_name_re = re.compile('^[a-zA-Z_][a-zA-Z0-9_]*$')
 def name_is_valid(name):
     r"""
@@ -313,6 +314,7 @@ def name_is_valid(name):
     # Technically, we also need to reject keywords...
     return bool(valid_name_re.match(name))
 
+
 # The pickle interpreter can push and pop "marks" on the stack.
 # This string is used as the representation of a mark.
 the_mark = 'mark'
@@ -3051,6 +3053,7 @@ def __repr__(self):
         """
         return "TestGlobalFunnyName"
 
+
 TestGlobalFunnyName.__name__ = "funny$name"
 #This crashed Sphinx. Instead, we manually execute this just before the test.
 #globals()['funny$name'] = TestGlobalFunnyName
diff --git a/src/sage/misc/rest_index_of_methods.py b/src/sage/misc/rest_index_of_methods.py
index 52b5d841893..82b988deda2 100644
--- a/src/sage/misc/rest_index_of_methods.py
+++ b/src/sage/misc/rest_index_of_methods.py
@@ -349,4 +349,5 @@ def hey(f):
         return f
     return hey
 
+
 __doc__ = __doc__.format(INDEX_OF_FUNCTIONS=gen_rest_table_index([gen_rest_table_index]))
diff --git a/src/sage/misc/sh.py b/src/sage/misc/sh.py
index a16c987731f..968cb48cb74 100644
--- a/src/sage/misc/sh.py
+++ b/src/sage/misc/sh.py
@@ -32,5 +32,6 @@ def eval(self, code, globals=None, locals=None):
         # gets printed when doing %sh in the notebook.
         return ''
 
+
 # Create the sh object, so that %sh mode works in the notebook.
 sh = Sh()
diff --git a/src/sage/misc/test_nested_class.py b/src/sage/misc/test_nested_class.py
index a8dcdb11125..40712bfc9fb 100644
--- a/src/sage/misc/test_nested_class.py
+++ b/src/sage/misc/test_nested_class.py
@@ -186,6 +186,7 @@ class C():
         """
         pass
 
+
 C = ALB.C
 
 
diff --git a/src/sage/misc/viewer.py b/src/sage/misc/viewer.py
index de84f31ddf4..439dedc5e75 100644
--- a/src/sage/misc/viewer.py
+++ b/src/sage/misc/viewer.py
@@ -30,6 +30,7 @@
 
 VIEWERS = ['browser', 'dvi_viewer', 'pdf_viewer', 'png_viewer']
 
+
 def default_viewer(viewer=None):
     """
     Set up default programs for opening web pages, PDFs, PNGs, and DVI files.
@@ -138,6 +139,7 @@ def default_viewer(viewer=None):
 # _viewer_prefs: a dictionary holding global preferences for viewers.
 _viewer_prefs = {}
 
+
 class Viewer(SageObject):
     """
     Set defaults for various viewing applications: a web browser, a
@@ -301,8 +303,10 @@ def __call__(self, x=None):
         elif x.startswith('pdf'):
             return self.pdf_viewer()
 
+
 viewer = Viewer()
 
+
 def browser():
     """
     Return the program used to open a web page.  By default, the
@@ -319,6 +323,7 @@ def browser():
     """
     return viewer.browser()
 
+
 def dvi_viewer():
     """
     Return the program used to display a dvi file.  By default, the
@@ -336,6 +341,7 @@ def dvi_viewer():
     viewer()
     return viewer.dvi_viewer()
 
+
 def pdf_viewer():
     """
     Return the program used to display a pdf file.  By default, the
@@ -356,6 +362,7 @@ def pdf_viewer():
     viewer()
     return viewer.pdf_viewer()
 
+
 def png_viewer():
     """
     Return the program used to display a png file. By default, the
diff --git a/src/sage/modules/free_module.py b/src/sage/modules/free_module.py
index 313ffb25798..519bad41d24 100644
--- a/src/sage/modules/free_module.py
+++ b/src/sage/modules/free_module.py
@@ -291,6 +291,7 @@ def create_object(self, version, key):
 
         return FreeModule_ambient(base_ring, rank, sparse=sparse)
 
+
 FreeModuleFactory_with_standard_basis = FreeModuleFactory("FreeModule")
 
 def FreeModule(base_ring, rank_or_basis_keys=None, sparse=False, inner_product_matrix=None, *,
@@ -7665,6 +7666,7 @@ def has_user_basis(self):
         """
         return False
 
+
 FreeModule_generic_pid._submodule_class = FreeModule_submodule_pid
 
 
@@ -8142,6 +8144,7 @@ def has_user_basis(self):
         """
         return False
 
+
 FreeModule_generic_field._submodule_class = FreeModule_submodule_field
 
 
diff --git a/src/sage/modules/vector_symbolic_dense.py b/src/sage/modules/vector_symbolic_dense.py
index e4d9efff0b3..ce134c0462e 100644
--- a/src/sage/modules/vector_symbolic_dense.py
+++ b/src/sage/modules/vector_symbolic_dense.py
@@ -108,6 +108,7 @@ def apply(self, *args, **kwds):
 class Vector_symbolic_dense(free_module_element.FreeModuleElement_generic_dense):
     pass
 
+
 # Add elementwise methods.
 for method in ['simplify', 'simplify_factorial',
                'simplify_log', 'simplify_rational',
diff --git a/src/sage/modules/vector_symbolic_sparse.py b/src/sage/modules/vector_symbolic_sparse.py
index 30ec55214c6..73cb41ae611 100644
--- a/src/sage/modules/vector_symbolic_sparse.py
+++ b/src/sage/modules/vector_symbolic_sparse.py
@@ -110,6 +110,7 @@ def apply(self, *args, **kwds):
 class Vector_symbolic_sparse(free_module_element.FreeModuleElement_generic_sparse):
     pass
 
+
 # Add elementwise methods.
 for method in ['simplify', 'simplify_factorial',
                'simplify_log', 'simplify_rational',
diff --git a/src/sage/monoids/string_monoid.py b/src/sage/monoids/string_monoid.py
index 5f4e3819b5e..91cb82e4229 100644
--- a/src/sage/monoids/string_monoid.py
+++ b/src/sage/monoids/string_monoid.py
@@ -247,6 +247,7 @@ def encoding(self, S, padic=False):
     #     """
     #     return 2
 
+
 BinaryStrings = BinaryStringMonoid
 
 
@@ -309,6 +310,7 @@ def __call__(self, x, check=True):
         else:
             raise TypeError("Argument x (= %s) is of the wrong type." % x)
 
+
 OctalStrings = OctalStringMonoid
 
 
@@ -421,6 +423,7 @@ def encoding(self, S, padic=False):
             hex_string.extend(hex_chars)
         return self(hex_string)
 
+
 HexadecimalStrings = HexadecimalStringMonoid
 
 
@@ -487,6 +490,7 @@ def __call__(self, x, check=True):
         else:
             raise TypeError("Argument x (= %s) is of the wrong type." % x)
 
+
 Radix64Strings = Radix64StringMonoid
 
 
@@ -798,4 +802,5 @@ def encoding(self, S):
         """
         return self(strip_encoding(S))
 
+
 AlphabeticStrings = AlphabeticStringMonoid
diff --git a/src/sage/rings/finite_rings/finite_field_prime_modn.py b/src/sage/rings/finite_rings/finite_field_prime_modn.py
index 8bb35604697..95c1803abf4 100644
--- a/src/sage/rings/finite_rings/finite_field_prime_modn.py
+++ b/src/sage/rings/finite_rings/finite_field_prime_modn.py
@@ -340,6 +340,7 @@ def degree(self):
         """
         return Integer(1)
 
+
 register_unpickle_override(
     'sage.rings.finite_field_prime_modn', 'FiniteField_prime_modn',
     FiniteField_prime_modn)
diff --git a/src/sage/rings/function_field/constructor.py b/src/sage/rings/function_field/constructor.py
index 8e5ecd281ee..31156bc9c6f 100644
--- a/src/sage/rings/function_field/constructor.py
+++ b/src/sage/rings/function_field/constructor.py
@@ -111,8 +111,10 @@ def create_object(self, version, key,**extra_args):
             from .function_field_rational import RationalFunctionField
             return RationalFunctionField(key[0], names=key[1])
 
+
 FunctionField=FunctionFieldFactory("sage.rings.function_field.constructor.FunctionField")
 
+
 class FunctionFieldExtensionFactory(UniqueFactory):
     """
     Create a function field defined as an extension of another
@@ -210,5 +212,6 @@ def create_object(self,version,key,**extra_args):
                     return function_field_polymod.FunctionField_char_zero(f, names)
         return function_field_polymod.FunctionField_polymod(f, names)
 
+
 FunctionFieldExtension = FunctionFieldExtensionFactory(
     "sage.rings.function_field.constructor.FunctionFieldExtension")
diff --git a/src/sage/rings/function_field/valuation.py b/src/sage/rings/function_field/valuation.py
index 5567c4db1ce..3f504868e4c 100644
--- a/src/sage/rings/function_field/valuation.py
+++ b/src/sage/rings/function_field/valuation.py
@@ -454,6 +454,7 @@ def create_object(self, version, key, **extra_args):
 
         raise NotImplementedError("valuation on %r from %r on %r" % (domain, valuation, valuation.domain()))
 
+
 FunctionFieldValuation = FunctionFieldValuationFactory("sage.rings.function_field.valuation.FunctionFieldValuation")
 
 
diff --git a/src/sage/rings/infinity.py b/src/sage/rings/infinity.py
index d4cbe9372bb..e084e6099b7 100644
--- a/src/sage/rings/infinity.py
+++ b/src/sage/rings/infinity.py
@@ -757,6 +757,7 @@ def _coerce_map_from_(self, R):
         """
         return isinstance(R, Ring) or R in (int, float, complex)
 
+
 UnsignedInfinityRing = UnsignedInfinityRing_class()
 
 
@@ -966,10 +967,12 @@ def _richcmp_(self, other, op):
             return rich_to_bool(op, 1)
         return rich_to_bool(op, 0)
 
+
 unsigned_infinity = UnsignedInfinityRing.gen(0)
 less_than_infinity = UnsignedInfinityRing.less_than_infinity()
 
-def is_Infinite(x):
+
+def is_Infinite(x) -> bool:
     """
     This is a type check for infinity elements.
 
@@ -1082,7 +1085,7 @@ def gens(self):
         """
         return [self.gen(0), self.gen(1)]
 
-    def is_zero(self):
+    def is_zero(self) -> bool:
         """
         The Infinity Ring is not zero
 
@@ -1093,7 +1096,7 @@ def is_zero(self):
         """
         return False
 
-    def is_commutative(self):
+    def is_commutative(self) -> bool:
         """
         The Infinity Ring is commutative
 
@@ -1746,6 +1749,7 @@ def _gap_init_(self):
         """
         return 'infinity'
 
+
 InfinityRing = InfinityRing_class()
 infinity = InfinityRing.gen(0)
 Infinity = infinity
diff --git a/src/sage/rings/monomials.py b/src/sage/rings/monomials.py
index 0beb25a1044..f0c1f92162f 100644
--- a/src/sage/rings/monomials.py
+++ b/src/sage/rings/monomials.py
@@ -34,8 +34,10 @@ def _monomials(gens, R, n, i):
             z *= gens[i]
         return v
 
+
 from sage.structure.sequence import Sequence
 
+
 def monomials(v, n):
     """
     Given two lists ``v`` and ``n``, of exactly the same length,
diff --git a/src/sage/rings/number_field/galois_group.py b/src/sage/rings/number_field/galois_group.py
index 748122fe924..07b58b7b2a2 100644
--- a/src/sage/rings/number_field/galois_group.py
+++ b/src/sage/rings/number_field/galois_group.py
@@ -1292,6 +1292,7 @@ def ramification_degree(self, P):
         w = [(self(g) - g).valuation(P) for g in gens]
         return min(w)
 
+
 GaloisGroup_v2.Element = GaloisGroupElement
 GaloisGroup_v2.Subgroup = GaloisGroup_subgroup
 GaloisGroup_subgroup.Element = GaloisGroupElement
diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
index 143191e05f1..2e2989d413f 100644
--- a/src/sage/rings/number_field/number_field_rel.py
+++ b/src/sage/rings/number_field/number_field_rel.py
@@ -2731,4 +2731,5 @@ def NumberField_relative_v1(base_field, poly, name, latex_name, canonical_embedd
     return NumberField(poly.change_ring(base_field), name, check=False,
                        embedding=canonical_embedding, latex_name=latex_name)
 
+
 NumberField_extension_v1 = NumberField_relative_v1  # historical reasons only
diff --git a/src/sage/rings/padics/factory.py b/src/sage/rings/padics/factory.py
index 2004f295d20..e001b9e5086 100644
--- a/src/sage/rings/padics/factory.py
+++ b/src/sage/rings/padics/factory.py
@@ -815,6 +815,7 @@ def create_object(self, version, key):
         else:
             raise ValueError("unexpected type")
 
+
 Qp = Qp_class("Qp")
 
 
@@ -2027,6 +2028,7 @@ def create_object(self, version, key):
         else:
             raise ValueError("unexpected type")
 
+
 Zp = Zp_class("Zp")
 
 
@@ -3431,8 +3433,10 @@ def create_object(self, version, key, approx_modulus=None, shift_seed=None):
                   'max_ram_terms': print_max_ram_terms, 'max_unram_terms': print_max_unram_terms, 'max_terse_terms': print_max_terse_terms, 'show_prec': show_prec},
                  shift_seed, names, implementation)
 
+
 ExtensionFactory = pAdicExtension = pAdicExtension_class("pAdicExtension")
 
+
 ######################################################
 # Helper functions for the Extension Factory
 ######################################################
diff --git a/src/sage/rings/padics/padic_valuation.py b/src/sage/rings/padics/padic_valuation.py
index 0c0883dfa96..dbd8830a4d4 100644
--- a/src/sage/rings/padics/padic_valuation.py
+++ b/src/sage/rings/padics/padic_valuation.py
@@ -416,8 +416,10 @@ def create_object(self, version, key, **extra_args):
                 raise NotImplementedError
             return parent.__make_element_class__(pAdicFromLimitValuation)(parent, v, G.change_ring(R.base_ring()), approximants)
 
+
 pAdicValuation = PadicValuationFactory("sage.rings.padics.padic_valuation.pAdicValuation")
 
+
 class pAdicValuation_base(DiscreteValuation):
     r"""
     Abstract base class for `p`-adic valuations.
diff --git a/src/sage/rings/pari_ring.py b/src/sage/rings/pari_ring.py
index c46fceed07b..98b42c2634a 100644
--- a/src/sage/rings/pari_ring.py
+++ b/src/sage/rings/pari_ring.py
@@ -230,4 +230,5 @@ def zeta(self):
         """
         return self(-1)
 
+
 _inst = PariRing()
diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
index 6e0265cad53..28d93c1aa6c 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
@@ -303,9 +303,11 @@ def __call__(self, *args, **kwds):
             raise ValueError("Coefficient ring must be a field for function '%s'."%(self.f.__name__))
         return self.f(self._instance, *args, **kwds)
 
+
 require_field = RequireField
 
-def is_MPolynomialIdeal(x):
+
+def is_MPolynomialIdeal(x) -> bool:
     """
     Return ``True`` if the provided argument ``x`` is an ideal in a
     multivariate polynomial ring.
@@ -335,6 +337,7 @@ def is_MPolynomialIdeal(x):
     """
     return isinstance(x, MPolynomialIdeal)
 
+
 class MPolynomialIdeal_magma_repr:
     def _magma_init_(self, magma):
         """
diff --git a/src/sage/rings/polynomial/multi_polynomial_sequence.py b/src/sage/rings/polynomial/multi_polynomial_sequence.py
index 22c92ba44d6..1cfabbeda6e 100644
--- a/src/sage/rings/polynomial/multi_polynomial_sequence.py
+++ b/src/sage/rings/polynomial/multi_polynomial_sequence.py
@@ -1673,6 +1673,7 @@ def weil_restriction(self):
         J += FieldIdeal(J.ring())
         return PolynomialSequence(J)
 
+
 from sage.misc.persist import register_unpickle_override
 register_unpickle_override("sage.crypto.mq.mpolynomialsystem","MPolynomialSystem_generic", PolynomialSequence_generic)
 register_unpickle_override("sage.crypto.mq.mpolynomialsystem","MPolynomialRoundSystem_generic", PolynomialSequence_generic)
diff --git a/src/sage/rings/polynomial/polynomial_element_generic.py b/src/sage/rings/polynomial/polynomial_element_generic.py
index 77b9a7d8c92..f7b4ba226b9 100644
--- a/src/sage/rings/polynomial/polynomial_element_generic.py
+++ b/src/sage/rings/polynomial/polynomial_element_generic.py
@@ -1607,6 +1607,7 @@ class Polynomial_generic_dense_cdvf(Polynomial_generic_dense_cdv, Polynomial_gen
 class Polynomial_generic_sparse_cdvf(Polynomial_generic_sparse_cdv, Polynomial_generic_cdvf):
     pass
 
+
 ############################################################################
 # XXX:  Ensures that the generic polynomials implemented in Sage via PARI  #
 # until at least until 4.5.0 unpickle correctly as polynomials implemented #
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
index 07d5e0cb837..2a6a155b5ae 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
@@ -53,12 +53,14 @@
 from sage.rings.quotient_ring import QuotientRing_generic
 
 from sage.structure.category_object import normalize_names
+from sage.structure.coerce_maps import DefaultConvertMap_unique
 from sage.structure.factory import UniqueFactory
 
 from sage.rings.polynomial.infinite_polynomial_ring import GenDictWithBasering
 
 from sage.structure.richcmp import richcmp
 
+
 class PolynomialQuotientRingFactory(UniqueFactory):
     r"""
     Create a quotient of a polynomial ring.
@@ -2167,7 +2169,7 @@ def _test_isomorphic_ring(self, **options):
             tester.assertIn(y, ring)
             tester.assertEqual(from_isomorphic_ring(y), x)
 
-from sage.structure.coerce_maps import DefaultConvertMap_unique
+
 class PolynomialQuotientRing_coercion(DefaultConvertMap_unique):
     r"""
     A coercion map from a :class:`PolynomialQuotientRing` to a
diff --git a/src/sage/rings/rational_field.py b/src/sage/rings/rational_field.py
index cbd5a4ba483..642f95dc232 100644
--- a/src/sage/rings/rational_field.py
+++ b/src/sage/rings/rational_field.py
@@ -1673,10 +1673,12 @@ def valuation(self, p):
         from sage.rings.padics.padic_valuation import pAdicValuation
         return pAdicValuation(self, p)
 
+
 QQ = RationalField()
 Q = QQ
 
-def is_RationalField(x):
+
+def is_RationalField(x) -> bool:
     """
     Check to see if ``x`` is the rational field.
 
@@ -1690,7 +1692,8 @@ def is_RationalField(x):
     """
     return isinstance(x, RationalField)
 
-def frac(n,d):
+
+def frac(n, d):
     """
     Return the fraction ``n/d``.
 
diff --git a/src/sage/rings/semirings/non_negative_integer_semiring.py b/src/sage/rings/semirings/non_negative_integer_semiring.py
index c041f18f99f..9d91e9cf777 100644
--- a/src/sage/rings/semirings/non_negative_integer_semiring.py
+++ b/src/sage/rings/semirings/non_negative_integer_semiring.py
@@ -101,4 +101,5 @@ def _latex_(self):
         """
         return '\\Bold{N}'
 
+
 NN = NonNegativeIntegerSemiring()
diff --git a/src/sage/rings/tate_algebra.py b/src/sage/rings/tate_algebra.py
index d1371b431f7..993f1a95aa1 100644
--- a/src/sage/rings/tate_algebra.py
+++ b/src/sage/rings/tate_algebra.py
@@ -329,6 +329,7 @@ def create_object(self, version, key):
         (base, prec, log_radii, names, order) = key
         return TateAlgebra_generic(base, prec, log_radii, names, order)
 
+
 TateAlgebra = TateAlgebraFactory("TateAlgebra")
 
 
diff --git a/src/sage/sandpiles/examples.py b/src/sage/sandpiles/examples.py
index e38ce664483..a902a156318 100644
--- a/src/sage/sandpiles/examples.py
+++ b/src/sage/sandpiles/examples.py
@@ -246,4 +246,5 @@ def Wheel(self, n):
         """
         return Sandpile(graphs.WheelGraph(n),0)
 
+
 sandpiles = SandpileExamples()
diff --git a/src/sage/structure/sequence.py b/src/sage/structure/sequence.py
index 7a8c77ad1cf..00ee377ac82 100644
--- a/src/sage/structure/sequence.py
+++ b/src/sage/structure/sequence.py
@@ -889,6 +889,8 @@ def __getattr__(self, name):
             return self.__hash
         else:
             raise AttributeError("'Sequence_generic' object has no attribute '%s'"%name)
+
+
 seq = Sequence
 
 from sage.misc.persist import register_unpickle_override
diff --git a/src/sage/structure/set_factories_example.py b/src/sage/structure/set_factories_example.py
index 5414edea03d..df1d7d7f49c 100644
--- a/src/sage/structure/set_factories_example.py
+++ b/src/sage/structure/set_factories_example.py
@@ -169,6 +169,7 @@ def _repr_(self):
         """
         return "Factory for XY pairs"
 
+
 XYPairs = XYPairsFactory()
 XYPairs.__doc__ = XYPairsFactory.__call__.__doc__
 
diff --git a/src/sage/structure/test_factory.py b/src/sage/structure/test_factory.py
index b45996c5a80..145311b9dd3 100644
--- a/src/sage/structure/test_factory.py
+++ b/src/sage/structure/test_factory.py
@@ -50,4 +50,5 @@ def create_object(self, version, key, **extra_args):
         print("Making object", key)
         return A()
 
+
 test_factory = UniqueFactoryTester('sage.structure.test_factory.test_factory')
diff --git a/src/sage/tests/functools_partial_src.py b/src/sage/tests/functools_partial_src.py
index 1fb24e15b34..d352d160230 100644
--- a/src/sage/tests/functools_partial_src.py
+++ b/src/sage/tests/functools_partial_src.py
@@ -21,4 +21,5 @@ def base(x):
     x = x * 7
     return x
 
+
 test_func = partial(base, 6)