From 1f8dae9a1e18051509c9bd927588fa170a3e4825 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Wed, 16 Oct 2024 21:18:19 +0200
Subject: [PATCH] fix all pep E302 in manifolds and geometry

---
 src/sage/geometry/cone_catalog.py                    |  1 +
 src/sage/geometry/cone_critical_angles.py            |  1 +
 .../geometry/hyperbolic_space/hyperbolic_coercion.py | 12 ++++++++++++
 .../geometry/hyperbolic_space/hyperbolic_isometry.py |  3 +++
 .../geometry/hyperbolic_space/hyperbolic_point.py    |  1 +
 .../hyperplane_arrangement/check_freeness.py         |  2 ++
 src/sage/geometry/lattice_polytope.py                |  3 +++
 src/sage/geometry/polyhedron/backend_polymake.py     |  2 ++
 src/sage/geometry/polyhedron/base0.py                |  1 +
 src/sage/geometry/polyhedron/base2.py                |  1 +
 src/sage/geometry/polyhedron/base3.py                |  1 +
 src/sage/geometry/polyhedron/base4.py                |  1 +
 src/sage/geometry/polyhedron/base5.py                |  1 +
 src/sage/geometry/polyhedron/base6.py                |  1 +
 src/sage/geometry/polyhedron/base7.py                |  1 +
 src/sage/geometry/polyhedron/cdd_file_format.py      |  4 ++++
 src/sage/geometry/polyhedron/double_description.py   |  1 +
 src/sage/geometry/polyhedron/face.py                 |  1 +
 src/sage/geometry/polyhedron/library.py              |  2 ++
 src/sage/geometry/ribbon_graph.py                    |  3 +++
 src/sage/manifolds/catalog.py                        |  2 ++
 src/sage/manifolds/chart.py                          |  1 +
 src/sage/manifolds/chart_func.py                     |  1 +
 src/sage/manifolds/continuous_map.py                 |  1 +
 src/sage/manifolds/continuous_map_image.py           |  1 +
 .../manifolds/differentiable/affine_connection.py    |  1 +
 .../manifolds/differentiable/automorphismfield.py    |  1 +
 .../differentiable/automorphismfield_group.py        |  1 +
 src/sage/manifolds/differentiable/chart.py           |  1 +
 src/sage/manifolds/differentiable/curve.py           |  1 +
 .../manifolds/differentiable/de_rham_cohomology.py   |  2 ++
 src/sage/manifolds/differentiable/degenerate.py      |  2 ++
 .../differentiable/degenerate_submanifold.py         |  1 +
 .../manifolds/differentiable/diff_form_module.py     |  1 +
 src/sage/manifolds/differentiable/diff_map.py        |  1 +
 .../manifolds/differentiable/examples/euclidean.py   |  2 ++
 .../manifolds/differentiable/examples/real_line.py   |  1 +
 src/sage/manifolds/differentiable/examples/sphere.py |  1 +
 .../manifolds/differentiable/integrated_curve.py     |  2 ++
 .../differentiable/levi_civita_connection.py         |  1 +
 src/sage/manifolds/differentiable/manifold_homset.py |  4 ++++
 .../manifolds/differentiable/mixed_form_algebra.py   |  1 +
 .../manifolds/differentiable/multivector_module.py   |  1 +
 .../manifolds/differentiable/multivectorfield.py     |  1 +
 .../manifolds/differentiable/pseudo_riemannian.py    |  1 +
 .../manifolds/differentiable/scalarfield_algebra.py  |  1 +
 .../manifolds/differentiable/symplectic_form_test.py |  1 +
 src/sage/manifolds/differentiable/tangent_space.py   |  1 +
 .../manifolds/differentiable/tensorfield_module.py   |  1 +
 src/sage/manifolds/differentiable/vector_bundle.py   |  2 ++
 src/sage/manifolds/differentiable/vectorfield.py     |  1 +
 src/sage/manifolds/differentiable/vectorframe.py     |  2 ++
 src/sage/manifolds/family.py                         |  2 ++
 src/sage/manifolds/local_frame.py                    |  3 +++
 src/sage/manifolds/manifold_homset.py                |  1 +
 src/sage/manifolds/operators.py                      |  5 +++++
 src/sage/manifolds/point.py                          |  1 +
 src/sage/manifolds/scalarfield_algebra.py            |  1 +
 src/sage/manifolds/section.py                        |  2 ++
 src/sage/manifolds/section_module.py                 |  2 ++
 src/sage/manifolds/structure.py                      |  7 +++++++
 src/sage/manifolds/subset.py                         |  1 +
 src/sage/manifolds/subsets/closure.py                |  1 +
 src/sage/manifolds/trivialization.py                 |  2 ++
 src/sage/manifolds/utilities.py                      |  5 +++++
 src/sage/manifolds/vector_bundle.py                  |  1 +
 src/sage/manifolds/vector_bundle_fiber.py            |  1 +
 src/sage/manifolds/vector_bundle_fiber_element.py    |  1 +
 68 files changed, 121 insertions(+)

diff --git a/src/sage/geometry/cone_catalog.py b/src/sage/geometry/cone_catalog.py
index da2ab39a0e6..d58302d5915 100644
--- a/src/sage/geometry/cone_catalog.py
+++ b/src/sage/geometry/cone_catalog.py
@@ -72,6 +72,7 @@
 # the top-level non-underscore functions defined in this module.
 #
 
+
 def _preprocess_args(ambient_dim, lattice):
     r"""
     Preprocess arguments for cone-constructing functions.
diff --git a/src/sage/geometry/cone_critical_angles.py b/src/sage/geometry/cone_critical_angles.py
index 55636a15da8..9e5252a4bf9 100644
--- a/src/sage/geometry/cone_critical_angles.py
+++ b/src/sage/geometry/cone_critical_angles.py
@@ -40,6 +40,7 @@
 from sage.rings.real_double import RDF
 from sage.symbolic.constants import pi
 
+
 def _normalize_gevp_solution(gevp_solution):
     r"""
     Normalize the results of :func:`solve_gevp_nonzero` and
diff --git a/src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py b/src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py
index c88d573e0cb..1e2c7270b39 100644
--- a/src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py
+++ b/src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py
@@ -29,6 +29,7 @@
 from sage.misc.lazy_import import lazy_import
 lazy_import('sage.misc.call', 'attrcall')
 
+
 class HyperbolicModelCoercion(Morphism):
     """
     Abstract base class for morphisms between the hyperbolic models.
@@ -148,6 +149,7 @@ def __invert__(self):
 # From UHP #
 ############
 
+
 class CoercionUHPtoPD(HyperbolicModelCoercion):
     """
     Coercion from the UHP to PD model.
@@ -188,6 +190,7 @@ def image_isometry_matrix(self, x):
             return matrix([[1,-I],[-I,1]]) * x * matrix([[1,I],[I,1]]).conjugate()/Integer(2)
         return matrix([[1,-I],[-I,1]]) * x * matrix([[1,I],[I,1]])/Integer(2)
 
+
 class CoercionUHPtoKM(HyperbolicModelCoercion):
     """
     Coercion from the UHP to KM model.
@@ -227,6 +230,7 @@ def image_isometry_matrix(self, x):
         """
         return SL2R_to_SO21(x)
 
+
 class CoercionUHPtoHM(HyperbolicModelCoercion):
     """
     Coercion from the UHP to HM model.
@@ -269,6 +273,7 @@ def image_isometry_matrix(self, x):
 # From PD #
 ###########
 
+
 class CoercionPDtoUHP(HyperbolicModelCoercion):
     """
     Coercion from the PD to UHP model.
@@ -318,6 +323,7 @@ def image_isometry_matrix(self, x):
             return matrix([[1,I],[I,1]]) * x * matrix([[1,-I],[-I,1]]).conjugate() / Integer(2)
         return matrix([[1,I],[I,1]]) * x * matrix([[1,-I],[-I,1]]) / Integer(2)
 
+
 class CoercionPDtoKM(HyperbolicModelCoercion):
     """
     Coercion from the PD to KM model.
@@ -444,6 +450,7 @@ def image_isometry_matrix(self, x):
         """
         return SO21_to_SL2R(x)
 
+
 class CoercionKMtoPD(HyperbolicModelCoercion):
     """
     Coercion from the KM to PD model.
@@ -482,6 +489,7 @@ def image_isometry_matrix(self, x):
         return (matrix(2,[1,-I,-I,1]) * SO21_to_SL2R(x) *
                 matrix(2,[1,I,I,1])/Integer(2))
 
+
 class CoercionKMtoHM(HyperbolicModelCoercion):
     """
     Coercion from the KM to HM model.
@@ -524,6 +532,7 @@ def image_isometry_matrix(self, x):
 # From HM #
 ###########
 
+
 class CoercionHMtoUHP(HyperbolicModelCoercion):
     """
     Coercion from the HM to UHP model.
@@ -560,6 +569,7 @@ def image_isometry_matrix(self, x):
         """
         return SO21_to_SL2R(x)
 
+
 class CoercionHMtoPD(HyperbolicModelCoercion):
     """
     Coercion from the HM to PD model.
@@ -596,6 +606,7 @@ def image_isometry_matrix(self, x):
         return (matrix(2,[1,-I,-I,1]) * SO21_to_SL2R(x) *
                 matrix(2,[1,I,I,1])/Integer(2))
 
+
 class CoercionHMtoKM(HyperbolicModelCoercion):
     """
     Coercion from the HM to KM model.
@@ -635,6 +646,7 @@ def image_isometry_matrix(self, x):
 #####################################################################
 ## Helper functions
 
+
 def SL2R_to_SO21(A):
     r"""
     Given a matrix in `SL(2, \RR)` return its irreducible representation in
diff --git a/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py b/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py
index 03a646b7059..2dd20676215 100644
--- a/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py
+++ b/src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py
@@ -620,6 +620,7 @@ def attracting_fixed_point(self):
         fp = self._cached_isometry.attracting_fixed_point()
         return self.domain().get_point(fp)
 
+
 class HyperbolicIsometryUHP(HyperbolicIsometry):
     r"""
     Create a hyperbolic isometry in the UHP model.
@@ -881,6 +882,7 @@ def attracting_fixed_point(self):  # UHP
             return self.domain().get_point(infinity)
         return self.domain().get_point(v[0] / v[1])
 
+
 class HyperbolicIsometryPD(HyperbolicIsometry):
     r"""
     Create a hyperbolic isometry in the PD model.
@@ -982,6 +984,7 @@ def _orientation_preserving(A): #PD
         return bool(A[1][0] == A[0][1].conjugate() and A[1][1] == A[0][0].conjugate()
                     and abs(A[0][0]) - abs(A[0][1]) != 0)
 
+
 class HyperbolicIsometryKM(HyperbolicIsometry):
     r"""
     Create a hyperbolic isometry in the KM model.
diff --git a/src/sage/geometry/hyperbolic_space/hyperbolic_point.py b/src/sage/geometry/hyperbolic_space/hyperbolic_point.py
index 3c408e69d95..16e96692a92 100644
--- a/src/sage/geometry/hyperbolic_space/hyperbolic_point.py
+++ b/src/sage/geometry/hyperbolic_space/hyperbolic_point.py
@@ -74,6 +74,7 @@
 
 from sage.geometry.hyperbolic_space.hyperbolic_isometry import HyperbolicIsometry
 
+
 class HyperbolicPoint(Element):
     r"""
     Abstract base class for hyperbolic points.  This class should never
diff --git a/src/sage/geometry/hyperplane_arrangement/check_freeness.py b/src/sage/geometry/hyperplane_arrangement/check_freeness.py
index f1691634f69..42943d72669 100644
--- a/src/sage/geometry/hyperplane_arrangement/check_freeness.py
+++ b/src/sage/geometry/hyperplane_arrangement/check_freeness.py
@@ -26,6 +26,7 @@
 from sage.matrix.constructor import matrix
 import sage.libs.singular.function_factory as fun_fact
 
+
 def less_generators(X):
     """
     Reduce the generator matrix of the module defined by ``X``.
@@ -63,6 +64,7 @@ def less_generators(X):
         Kd = set(range(X.nrows())).difference(K)
         X = X.matrix_from_rows(sorted(Kd))
 
+
 def construct_free_chain(A):
     """
     Construct the free chain for the hyperplanes ``A``.
diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py
index 65cacb35d0c..857eadba882 100644
--- a/src/sage/geometry/lattice_polytope.py
+++ b/src/sage/geometry/lattice_polytope.py
@@ -415,6 +415,7 @@ def ReflexivePolytope(dim, n):
 # Sequences of reflexive polytopes
 _rp = [None] * 4
 
+
 def ReflexivePolytopes(dim):
     r"""
     Return the sequence of all 2- or 3-dimensional reflexive polytopes.
@@ -494,6 +495,7 @@ def is_LatticePolytope(x):
     deprecation(34307, "is_LatticePolytope is deprecated, use isinstance instead")
     return isinstance(x, LatticePolytopeClass)
 
+
 @richcmp_method
 class LatticePolytopeClass(ConvexSet_compact, Hashable, sage.geometry.abc.LatticePolytope):
     r"""
@@ -4982,6 +4984,7 @@ def part_of_point(self, i):
 
 _palp_dimension = None
 
+
 def _palp(command, polytopes, reduce_dimension=False):
     r"""
     Run ``command`` on vertices of given
diff --git a/src/sage/geometry/polyhedron/backend_polymake.py b/src/sage/geometry/polyhedron/backend_polymake.py
index 9b497b421ac..84fdd48177b 100644
--- a/src/sage/geometry/polyhedron/backend_polymake.py
+++ b/src/sage/geometry/polyhedron/backend_polymake.py
@@ -724,6 +724,8 @@ def _test_polymake_pickling(self, tester=None, other=None, **options):
         tester.assertEqual(P.AFFINE_HULL, P1.AFFINE_HULL)
 
 #########################################################################
+
+
 class Polyhedron_QQ_polymake(Polyhedron_polymake, Polyhedron_QQ):
     r"""
     Polyhedra over `\QQ` with polymake.
diff --git a/src/sage/geometry/polyhedron/base0.py b/src/sage/geometry/polyhedron/base0.py
index 7ba3007ea35..c710c5dfa62 100644
--- a/src/sage/geometry/polyhedron/base0.py
+++ b/src/sage/geometry/polyhedron/base0.py
@@ -35,6 +35,7 @@
 from sage.structure.element import Element
 import sage.geometry.abc
 
+
 class Polyhedron_base0(Element, sage.geometry.abc.Polyhedron):
     """
     Initialization and basic access for polyhedra.
diff --git a/src/sage/geometry/polyhedron/base2.py b/src/sage/geometry/polyhedron/base2.py
index f9a48e45b1c..f2626b6efa3 100644
--- a/src/sage/geometry/polyhedron/base2.py
+++ b/src/sage/geometry/polyhedron/base2.py
@@ -37,6 +37,7 @@
 from sage.modules.free_module_element import vector
 from .base1 import Polyhedron_base1
 
+
 class Polyhedron_base2(Polyhedron_base1):
     """
     Methods related to lattice points.
diff --git a/src/sage/geometry/polyhedron/base3.py b/src/sage/geometry/polyhedron/base3.py
index 6347132e0fb..b0a4284a743 100644
--- a/src/sage/geometry/polyhedron/base3.py
+++ b/src/sage/geometry/polyhedron/base3.py
@@ -38,6 +38,7 @@
 from sage.rings.rational_field import QQ
 from .base2 import Polyhedron_base2
 
+
 class Polyhedron_base3(Polyhedron_base2):
     """
     Methods related to the combinatorics of a polyhedron.
diff --git a/src/sage/geometry/polyhedron/base4.py b/src/sage/geometry/polyhedron/base4.py
index a6fd6dad1ea..ea0423c60fe 100644
--- a/src/sage/geometry/polyhedron/base4.py
+++ b/src/sage/geometry/polyhedron/base4.py
@@ -36,6 +36,7 @@
 from sage.misc.cachefunc import cached_method
 from .base3 import Polyhedron_base3
 
+
 class Polyhedron_base4(Polyhedron_base3):
     """
     Methods relying on :mod:`sage.graphs`.
diff --git a/src/sage/geometry/polyhedron/base5.py b/src/sage/geometry/polyhedron/base5.py
index 21a463f1234..c94efd9428c 100644
--- a/src/sage/geometry/polyhedron/base5.py
+++ b/src/sage/geometry/polyhedron/base5.py
@@ -42,6 +42,7 @@
 
 from .base4 import Polyhedron_base4
 
+
 class Polyhedron_base5(Polyhedron_base4):
     """
     Methods constructing new polyhedra
diff --git a/src/sage/geometry/polyhedron/base6.py b/src/sage/geometry/polyhedron/base6.py
index f9bc49d7821..bccb57a09f4 100644
--- a/src/sage/geometry/polyhedron/base6.py
+++ b/src/sage/geometry/polyhedron/base6.py
@@ -37,6 +37,7 @@
 from sage.geometry.convex_set import AffineHullProjectionData
 from .base5 import Polyhedron_base5
 
+
 class Polyhedron_base6(Polyhedron_base5):
     r"""
     Methods related to plotting including affine hull projection.
diff --git a/src/sage/geometry/polyhedron/base7.py b/src/sage/geometry/polyhedron/base7.py
index 7b86d534017..1b232a00fa2 100644
--- a/src/sage/geometry/polyhedron/base7.py
+++ b/src/sage/geometry/polyhedron/base7.py
@@ -37,6 +37,7 @@
 from sage.rings.rational_field import QQ
 from .base6 import Polyhedron_base6
 
+
 class Polyhedron_base7(Polyhedron_base6):
     r"""
     Methods related to triangulation and volume.
diff --git a/src/sage/geometry/polyhedron/cdd_file_format.py b/src/sage/geometry/polyhedron/cdd_file_format.py
index 9dfedcad58d..edc04b4cb8f 100644
--- a/src/sage/geometry/polyhedron/cdd_file_format.py
+++ b/src/sage/geometry/polyhedron/cdd_file_format.py
@@ -14,6 +14,8 @@
 from .misc import _set_to_None_if_empty, _common_length_of, _to_space_separated_string
 
 #########################################################################
+
+
 def cdd_Vrepresentation(cdd_type, vertices, rays, lines, file_output=None):
     r"""
     Return a string containing the V-representation in cddlib's ext format.
@@ -92,6 +94,8 @@ def cdd_Vrepresentation(cdd_type, vertices, rays, lines, file_output=None):
         return s
 
 #########################################################################
+
+
 def cdd_Hrepresentation(cdd_type, ieqs, eqns, file_output=None):
     r"""
     Return a string containing the H-representation in cddlib's ine format.
diff --git a/src/sage/geometry/polyhedron/double_description.py b/src/sage/geometry/polyhedron/double_description.py
index b38e108640f..82bb0685d61 100644
--- a/src/sage/geometry/polyhedron/double_description.py
+++ b/src/sage/geometry/polyhedron/double_description.py
@@ -704,6 +704,7 @@ def add_inequality(self, a):
         self.R = R_pos + R_nul + R_new
         self.A.append(a)
 
+
 class StandardAlgorithm(Problem):
     """
     Standard implementation of the double description algorithm.
diff --git a/src/sage/geometry/polyhedron/face.py b/src/sage/geometry/polyhedron/face.py
index 9b72f1fc691..1f1969353a2 100644
--- a/src/sage/geometry/polyhedron/face.py
+++ b/src/sage/geometry/polyhedron/face.py
@@ -991,6 +991,7 @@ def stacking_locus(self):
 
         return parent.element_class(parent, None, [locus_ieqs, locus_eqns])
 
+
 def combinatorial_face_to_polyhedral_face(polyhedron, combinatorial_face):
     r"""
     Convert a combinatorial face to a face of a polyhedron.
diff --git a/src/sage/geometry/polyhedron/library.py b/src/sage/geometry/polyhedron/library.py
index 97ca4131fe9..5c58abb9564 100644
--- a/src/sage/geometry/polyhedron/library.py
+++ b/src/sage/geometry/polyhedron/library.py
@@ -91,6 +91,7 @@
 lazy_import('sage.graphs.graph', 'Graph')
 lazy_import('sage.combinat.root_system.associahedron', 'Associahedron')
 
+
 def zero_sum_projection(d, base_ring=None):
     r"""
     Return a matrix corresponding to the projection on the orthogonal of
@@ -319,6 +320,7 @@ def gale_transform_to_polytope(vectors, base_ring=None, backend=None):
 
     return P
 
+
 def gale_transform_to_primal(vectors, base_ring=None, backend=None):
     r"""
     Return a point configuration dual to a totally cyclic vector configuration.
diff --git a/src/sage/geometry/ribbon_graph.py b/src/sage/geometry/ribbon_graph.py
index 6f10912ff79..5c2950519ad 100644
--- a/src/sage/geometry/ribbon_graph.py
+++ b/src/sage/geometry/ribbon_graph.py
@@ -32,6 +32,7 @@
 
 #Auxiliary functions that will be used in the classes.
 
+
 def _find(l, k):
     r"""
     Return the two coordinates of the element ``k`` in the list of
@@ -1078,6 +1079,7 @@ def normalize(self):
                         PermutationConstructor([tuple(x) for x in aux_rho])
                         )
 
+
 def make_ribbon(g, r):
     r"""
     Return a ribbon graph whose thickening has genus ``g`` and ``r``
@@ -1151,6 +1153,7 @@ def make_ribbon(g, r):
     return RibbonGraph(PermutationConstructor([tuple(x) for x in repr_sigma]),
                        PermutationConstructor([tuple(x) for x in repr_rho]))
 
+
 def bipartite_ribbon_graph(p, q):
     r"""
     Return the bipartite graph modeling the corresponding
diff --git a/src/sage/manifolds/catalog.py b/src/sage/manifolds/catalog.py
index 0cbd69b6768..c3c40c42b9a 100644
--- a/src/sage/manifolds/catalog.py
+++ b/src/sage/manifolds/catalog.py
@@ -93,6 +93,7 @@ def Minkowski(positive_spacelike=True, names=None):
     g[1,1], g[2,2], g[3,3] = sgn, sgn, sgn
     return M
 
+
 def Kerr(m=1, a=0, coordinates='BL', names=None):
     """
     Generate a Kerr spacetime.
@@ -217,6 +218,7 @@ def Kerr(m=1, a=0, coordinates='BL', names=None):
     raise NotImplementedError("coordinates system not implemented, see help"
                               " for details")
 
+
 def Torus(R=2, r=1, names=None):
     """
     Generate a 2-dimensional torus embedded in Euclidean space.
diff --git a/src/sage/manifolds/chart.py b/src/sage/manifolds/chart.py
index 86c3087d101..d0d3148be7e 100644
--- a/src/sage/manifolds/chart.py
+++ b/src/sage/manifolds/chart.py
@@ -3270,6 +3270,7 @@ def _plot_xx_list(xx_list, rem_coords, ranges, steps, number_values):
 
 # *****************************************************************************
 
+
 class CoordChange(SageObject):
     r"""
     Transition map between two charts of a topological manifold.
diff --git a/src/sage/manifolds/chart_func.py b/src/sage/manifolds/chart_func.py
index fed078a2baa..aae7a2b1fff 100644
--- a/src/sage/manifolds/chart_func.py
+++ b/src/sage/manifolds/chart_func.py
@@ -2613,6 +2613,7 @@ def collect_common_factors(self):
         self._del_derived()
         return self
 
+
 class ChartFunctionRing(Parent, UniqueRepresentation):
     """
     Ring of all chart functions on a chart.
diff --git a/src/sage/manifolds/continuous_map.py b/src/sage/manifolds/continuous_map.py
index f715d2e5738..88a880b922f 100644
--- a/src/sage/manifolds/continuous_map.py
+++ b/src/sage/manifolds/continuous_map.py
@@ -34,6 +34,7 @@
 from sage.categories.homset import Hom
 from sage.categories.morphism import Morphism
 
+
 class ContinuousMap(Morphism):
     r"""
     Continuous map between two topological manifolds.
diff --git a/src/sage/manifolds/continuous_map_image.py b/src/sage/manifolds/continuous_map_image.py
index cf3b073e875..bbcfa672a5a 100644
--- a/src/sage/manifolds/continuous_map_image.py
+++ b/src/sage/manifolds/continuous_map_image.py
@@ -19,6 +19,7 @@
 
 from sage.manifolds.subset import ManifoldSubset
 
+
 class ImageManifoldSubset(ManifoldSubset):
     r"""
     Subset of a topological manifold that is a continuous image of a manifold subset.
diff --git a/src/sage/manifolds/differentiable/affine_connection.py b/src/sage/manifolds/differentiable/affine_connection.py
index 2c24b7c3ba9..d1e25cc3e31 100644
--- a/src/sage/manifolds/differentiable/affine_connection.py
+++ b/src/sage/manifolds/differentiable/affine_connection.py
@@ -35,6 +35,7 @@
 from sage.parallel.decorate import parallel
 from sage.parallel.parallelism import Parallelism
 
+
 class AffineConnection(SageObject):
     r"""
     Affine connection on a smooth manifold.
diff --git a/src/sage/manifolds/differentiable/automorphismfield.py b/src/sage/manifolds/differentiable/automorphismfield.py
index 4143e29228a..3556fc56e95 100644
--- a/src/sage/manifolds/differentiable/automorphismfield.py
+++ b/src/sage/manifolds/differentiable/automorphismfield.py
@@ -28,6 +28,7 @@
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
 
+
 class AutomorphismField(TensorField):
     r"""
     Field of automorphisms of tangent spaces to a generic (a priori
diff --git a/src/sage/manifolds/differentiable/automorphismfield_group.py b/src/sage/manifolds/differentiable/automorphismfield_group.py
index 78a906466b3..c6315670c9e 100644
--- a/src/sage/manifolds/differentiable/automorphismfield_group.py
+++ b/src/sage/manifolds/differentiable/automorphismfield_group.py
@@ -48,6 +48,7 @@
 from sage.manifolds.differentiable.automorphismfield import (AutomorphismField,
                                                              AutomorphismFieldParal)
 
+
 class AutomorphismFieldGroup(UniqueRepresentation, Parent):
     r"""
     General linear group of the module of vector fields along a differentiable
diff --git a/src/sage/manifolds/differentiable/chart.py b/src/sage/manifolds/differentiable/chart.py
index af74ac85669..bcfa37dc237 100644
--- a/src/sage/manifolds/differentiable/chart.py
+++ b/src/sage/manifolds/differentiable/chart.py
@@ -1069,6 +1069,7 @@ def restrict(self, subset, restrictions=None):
 
 #******************************************************************************
 
+
 class DiffCoordChange(CoordChange):
     r"""
     Transition map between two charts of a differentiable manifold.
diff --git a/src/sage/manifolds/differentiable/curve.py b/src/sage/manifolds/differentiable/curve.py
index 8b88a0351eb..e28e44b8adb 100644
--- a/src/sage/manifolds/differentiable/curve.py
+++ b/src/sage/manifolds/differentiable/curve.py
@@ -37,6 +37,7 @@
 from sage.manifolds.point import ManifoldPoint
 from sage.manifolds.differentiable.diff_map import DiffMap
 
+
 class DifferentiableCurve(DiffMap):
     r"""
     Curve in a differentiable manifold.
diff --git a/src/sage/manifolds/differentiable/de_rham_cohomology.py b/src/sage/manifolds/differentiable/de_rham_cohomology.py
index 53a5b50aaa0..9bc766f5a78 100644
--- a/src/sage/manifolds/differentiable/de_rham_cohomology.py
+++ b/src/sage/manifolds/differentiable/de_rham_cohomology.py
@@ -53,6 +53,7 @@
 from .characteristic_cohomology_class import (CharacteristicCohomologyClassRing,
                                               CharacteristicCohomologyClassRingElement)
 
+
 class DeRhamCohomologyClass(AlgebraElement):
     r"""
     Define a cohomology class in the de Rham cohomology ring.
@@ -298,6 +299,7 @@ def __eq__(self, other):
                 return True
         raise NotImplementedError('comparison via exact forms is currently not supported')
 
+
 class DeRhamCohomologyRing(Parent, UniqueRepresentation):
     r"""
     The de Rham cohomology ring of a de Rham complex.
diff --git a/src/sage/manifolds/differentiable/degenerate.py b/src/sage/manifolds/differentiable/degenerate.py
index da83139ed6e..b34fefc3a89 100644
--- a/src/sage/manifolds/differentiable/degenerate.py
+++ b/src/sage/manifolds/differentiable/degenerate.py
@@ -22,6 +22,7 @@
 
 ###############################################################################
 
+
 class DegenerateManifold(DifferentiableManifold):
     r"""
 
@@ -370,6 +371,7 @@ def open_subset(self, name, latex_name=None, coord_def={}):
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
 from sage.manifolds.differentiable.tensorfield import TensorField
 
+
 class TangentTensor(TensorFieldParal):
     r"""
     Let ``S`` be a lightlike submanifold embedded in a pseudo-Riemannian
diff --git a/src/sage/manifolds/differentiable/degenerate_submanifold.py b/src/sage/manifolds/differentiable/degenerate_submanifold.py
index 7608c97612b..a119fb57802 100644
--- a/src/sage/manifolds/differentiable/degenerate_submanifold.py
+++ b/src/sage/manifolds/differentiable/degenerate_submanifold.py
@@ -172,6 +172,7 @@
 if TYPE_CHECKING:
     from sage.manifolds.differentiable.metric import DegenerateMetric
 
+
 class DegenerateSubmanifold(DegenerateManifold, DifferentiableSubmanifold):
     r"""
     Degenerate submanifolds.
diff --git a/src/sage/manifolds/differentiable/diff_form_module.py b/src/sage/manifolds/differentiable/diff_form_module.py
index 291893b6cc9..ee0dd856697 100644
--- a/src/sage/manifolds/differentiable/diff_form_module.py
+++ b/src/sage/manifolds/differentiable/diff_form_module.py
@@ -570,6 +570,7 @@ def degree(self):
 
 # *****************************************************************************
 
+
 class DiffFormFreeModule(ExtPowerDualFreeModule):
     r"""
     Free module of differential forms of a given degree `p` (`p`-forms) along
diff --git a/src/sage/manifolds/differentiable/diff_map.py b/src/sage/manifolds/differentiable/diff_map.py
index ac9a7f74e99..6ac44fa7fb6 100644
--- a/src/sage/manifolds/differentiable/diff_map.py
+++ b/src/sage/manifolds/differentiable/diff_map.py
@@ -43,6 +43,7 @@
     from sage.manifolds.point import ManifoldPoint
     from sage.tensor.modules.free_module_morphism import FiniteRankFreeModuleMorphism
 
+
 class DiffMap(ContinuousMap):
     r"""
     Differentiable map between two differentiable manifolds.
diff --git a/src/sage/manifolds/differentiable/examples/euclidean.py b/src/sage/manifolds/differentiable/examples/euclidean.py
index 08fef01cbda..ec0f30be82c 100644
--- a/src/sage/manifolds/differentiable/examples/euclidean.py
+++ b/src/sage/manifolds/differentiable/examples/euclidean.py
@@ -419,6 +419,7 @@
 
 ###############################################################################
 
+
 class EuclideanSpace(PseudoRiemannianManifold):
     r"""
     Euclidean space.
@@ -1041,6 +1042,7 @@ def sphere(self, radius=1, center=None, name=None, latex_name=None,
 
 ###############################################################################
 
+
 class EuclideanPlane(EuclideanSpace):
     r"""
     Euclidean plane.
diff --git a/src/sage/manifolds/differentiable/examples/real_line.py b/src/sage/manifolds/differentiable/examples/real_line.py
index 746bae34c91..52b3dfad182 100644
--- a/src/sage/manifolds/differentiable/examples/real_line.py
+++ b/src/sage/manifolds/differentiable/examples/real_line.py
@@ -33,6 +33,7 @@
 from sage.manifolds.structure import RealDifferentialStructure
 from sage.categories.manifolds import Manifolds
 
+
 class OpenInterval(DifferentiableManifold):
     r"""
     Open interval as a 1-dimensional differentiable manifold over `\RR`.
diff --git a/src/sage/manifolds/differentiable/examples/sphere.py b/src/sage/manifolds/differentiable/examples/sphere.py
index ceb9ad849e1..43956a3ba1a 100644
--- a/src/sage/manifolds/differentiable/examples/sphere.py
+++ b/src/sage/manifolds/differentiable/examples/sphere.py
@@ -173,6 +173,7 @@
 from sage.rings.real_mpfr import RR
 from sage.manifolds.differentiable.examples.euclidean import EuclideanSpace
 
+
 class Sphere(PseudoRiemannianSubmanifold):
     r"""
     Sphere smoothly embedded in Euclidean Space.
diff --git a/src/sage/manifolds/differentiable/integrated_curve.py b/src/sage/manifolds/differentiable/integrated_curve.py
index 2ce087ba3e8..135e6d53d32 100644
--- a/src/sage/manifolds/differentiable/integrated_curve.py
+++ b/src/sage/manifolds/differentiable/integrated_curve.py
@@ -2864,6 +2864,7 @@ def plot_integrated(self, chart=None, ambient_coords=None,
                              aspect_ratio=aspect_ratio, color=color,
                              style=style, label_axes=label_axes)
 
+
 class IntegratedAutoparallelCurve(IntegratedCurve):
     r"""
     Autoparallel curve on the manifold with respect to a given
@@ -3648,6 +3649,7 @@ def system(self, verbose=False):
 
         return [self._equations_rhs, v0, chart]
 
+
 class IntegratedGeodesic(IntegratedAutoparallelCurve):
     r"""
     Geodesic on the manifold with respect to a given metric.
diff --git a/src/sage/manifolds/differentiable/levi_civita_connection.py b/src/sage/manifolds/differentiable/levi_civita_connection.py
index a995cf804cd..55c4aca9416 100644
--- a/src/sage/manifolds/differentiable/levi_civita_connection.py
+++ b/src/sage/manifolds/differentiable/levi_civita_connection.py
@@ -34,6 +34,7 @@
 from sage.manifolds.differentiable.affine_connection import AffineConnection
 from sage.manifolds.differentiable.vectorframe import CoordFrame
 
+
 class LeviCivitaConnection(AffineConnection):
     r"""
     Levi-Civita connection on a pseudo-Riemannian manifold.
diff --git a/src/sage/manifolds/differentiable/manifold_homset.py b/src/sage/manifolds/differentiable/manifold_homset.py
index 52a75ac61ad..d26e1cfea91 100644
--- a/src/sage/manifolds/differentiable/manifold_homset.py
+++ b/src/sage/manifolds/differentiable/manifold_homset.py
@@ -49,6 +49,7 @@
 from sage.manifolds.differentiable.integrated_curve import IntegratedAutoparallelCurve
 from sage.manifolds.differentiable.integrated_curve import IntegratedGeodesic
 
+
 class DifferentiableManifoldHomset(TopologicalManifoldHomset):
     r"""
     Set of differentiable maps between two differentiable manifolds.
@@ -508,6 +509,7 @@ def _an_element_(self):
 
 #******************************************************************************
 
+
 class IntegratedCurveSet(DifferentiableCurveSet):
     r"""
     Set of integrated curves in a differentiable manifold.
@@ -962,6 +964,7 @@ def one(self):
 
 #******************************************************************************
 
+
 class IntegratedAutoparallelCurveSet(IntegratedCurveSet):
     r"""
     Set of integrated autoparallel curves in a differentiable manifold.
@@ -1415,6 +1418,7 @@ def _an_element_(self):
 
 #******************************************************************************
 
+
 class IntegratedGeodesicSet(IntegratedAutoparallelCurveSet):
     r"""
     Set of integrated geodesic in a differentiable manifold.
diff --git a/src/sage/manifolds/differentiable/mixed_form_algebra.py b/src/sage/manifolds/differentiable/mixed_form_algebra.py
index c3ab8bbbbe9..26339c0d6ad 100644
--- a/src/sage/manifolds/differentiable/mixed_form_algebra.py
+++ b/src/sage/manifolds/differentiable/mixed_form_algebra.py
@@ -37,6 +37,7 @@
 from sage.symbolic.ring import SR
 from sage.manifolds.differentiable.mixed_form import MixedForm
 
+
 class MixedFormAlgebra(Parent, UniqueRepresentation):
     r"""
     An instance of this class represents the graded algebra of mixed forms.
diff --git a/src/sage/manifolds/differentiable/multivector_module.py b/src/sage/manifolds/differentiable/multivector_module.py
index 2dc036a878c..fa2d5fce099 100644
--- a/src/sage/manifolds/differentiable/multivector_module.py
+++ b/src/sage/manifolds/differentiable/multivector_module.py
@@ -489,6 +489,7 @@ def degree(self):
 
 #***********************************************************************
 
+
 class MultivectorFreeModule(ExtPowerFreeModule):
     r"""
     Free module of multivector fields of a given degree `p` (`p`-vector
diff --git a/src/sage/manifolds/differentiable/multivectorfield.py b/src/sage/manifolds/differentiable/multivectorfield.py
index 08b6d4d75a8..1e739dfdd17 100644
--- a/src/sage/manifolds/differentiable/multivectorfield.py
+++ b/src/sage/manifolds/differentiable/multivectorfield.py
@@ -40,6 +40,7 @@
 from sage.manifolds.differentiable.tensorfield import TensorField
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
 
+
 class MultivectorField(TensorField):
     r"""
     Multivector field with values on a generic (i.e. a priori not
diff --git a/src/sage/manifolds/differentiable/pseudo_riemannian.py b/src/sage/manifolds/differentiable/pseudo_riemannian.py
index 3ad49659de8..505900ad0df 100644
--- a/src/sage/manifolds/differentiable/pseudo_riemannian.py
+++ b/src/sage/manifolds/differentiable/pseudo_riemannian.py
@@ -274,6 +274,7 @@
 
 ###############################################################################
 
+
 class PseudoRiemannianManifold(DifferentiableManifold):
     r"""
     PseudoRiemannian manifold.
diff --git a/src/sage/manifolds/differentiable/scalarfield_algebra.py b/src/sage/manifolds/differentiable/scalarfield_algebra.py
index 205f8cef841..fc716f5fcc4 100644
--- a/src/sage/manifolds/differentiable/scalarfield_algebra.py
+++ b/src/sage/manifolds/differentiable/scalarfield_algebra.py
@@ -35,6 +35,7 @@ class `C^k` over a topological field `K` (in
 from sage.manifolds.scalarfield_algebra import ScalarFieldAlgebra
 from sage.manifolds.differentiable.scalarfield import DiffScalarField
 
+
 class DiffScalarFieldAlgebra(ScalarFieldAlgebra):
     r"""
     Commutative algebra of differentiable scalar fields on a differentiable
diff --git a/src/sage/manifolds/differentiable/symplectic_form_test.py b/src/sage/manifolds/differentiable/symplectic_form_test.py
index c38feb90cef..804c8956b6e 100644
--- a/src/sage/manifolds/differentiable/symplectic_form_test.py
+++ b/src/sage/manifolds/differentiable/symplectic_form_test.py
@@ -158,6 +158,7 @@ def test_omega_on_one_forms_is_omega_on_dual_vectors(
         b = M.one_form(3,4)
         assert omega.on_forms(a, b) == omega(a.up(omega), b.up(omega))
 
+
 def generic_scalar_field(M: DifferentiableManifold, name: str) -> DiffScalarField:
     chart_functions = {chart: function(name)(*chart[:]) for chart in M.atlas()}
     return M.scalar_field(chart_functions, name=name)
diff --git a/src/sage/manifolds/differentiable/tangent_space.py b/src/sage/manifolds/differentiable/tangent_space.py
index fd2576f8917..0320b70bb93 100644
--- a/src/sage/manifolds/differentiable/tangent_space.py
+++ b/src/sage/manifolds/differentiable/tangent_space.py
@@ -34,6 +34,7 @@
 if TYPE_CHECKING:
     from sage.manifolds.point import ManifoldPoint
 
+
 class TangentSpace(FiniteRankFreeModule):
     r"""
     Tangent space to a differentiable manifold at a given point.
diff --git a/src/sage/manifolds/differentiable/tensorfield_module.py b/src/sage/manifolds/differentiable/tensorfield_module.py
index fcdd93a9f0f..22d42050b89 100644
--- a/src/sage/manifolds/differentiable/tensorfield_module.py
+++ b/src/sage/manifolds/differentiable/tensorfield_module.py
@@ -587,6 +587,7 @@ def zero(self):
 
 #***********************************************************************
 
+
 class TensorFieldFreeModule(TensorFreeModule):
     r"""
     Free module of tensor fields of a given type `(k,l)` along a
diff --git a/src/sage/manifolds/differentiable/vector_bundle.py b/src/sage/manifolds/differentiable/vector_bundle.py
index f65bba7a79d..79e940a19e6 100644
--- a/src/sage/manifolds/differentiable/vector_bundle.py
+++ b/src/sage/manifolds/differentiable/vector_bundle.py
@@ -37,6 +37,7 @@
 from sage.misc.superseded import deprecated_function_alias
 from sage.rings.rational_field import QQ
 
+
 class DifferentiableVectorBundle(TopologicalVectorBundle):
     r"""
     An instance of this class represents a differentiable vector bundle
@@ -333,6 +334,7 @@ def total_space(self):
 
 # *****************************************************************************
 
+
 class TensorBundle(DifferentiableVectorBundle):
     r"""
     Tensor bundle over a differentiable manifold along a differentiable map.
diff --git a/src/sage/manifolds/differentiable/vectorfield.py b/src/sage/manifolds/differentiable/vectorfield.py
index 6b0b51582a3..44ae84089de 100644
--- a/src/sage/manifolds/differentiable/vectorfield.py
+++ b/src/sage/manifolds/differentiable/vectorfield.py
@@ -1376,6 +1376,7 @@ def cross_product(self, other, metric=None):
 
 #******************************************************************************
 
+
 class VectorFieldParal(FiniteRankFreeModuleElement, MultivectorFieldParal,
                        VectorField):
     r"""
diff --git a/src/sage/manifolds/differentiable/vectorframe.py b/src/sage/manifolds/differentiable/vectorframe.py
index a284c6487b6..594d2e9a729 100644
--- a/src/sage/manifolds/differentiable/vectorframe.py
+++ b/src/sage/manifolds/differentiable/vectorframe.py
@@ -1554,6 +1554,7 @@ def set_name(self, symbol, latex_symbol=None, indices=None,
 
 #******************************************************************************
 
+
 class CoordCoFrame(CoFrame):
     r"""
     Coordinate coframe on a differentiable manifold.
@@ -1667,6 +1668,7 @@ def _repr_(self):
 
 #******************************************************************************
 
+
 class CoordFrame(VectorFrame):
     r"""
     Coordinate frame on a differentiable manifold.
diff --git a/src/sage/manifolds/family.py b/src/sage/manifolds/family.py
index f9c3404535e..565fa2401cc 100644
--- a/src/sage/manifolds/family.py
+++ b/src/sage/manifolds/family.py
@@ -28,6 +28,7 @@
 from functools import total_ordering
 from sage.sets.family import FiniteFamily
 
+
 @total_ordering
 class ManifoldObjectFiniteFamily(FiniteFamily):
 
@@ -181,6 +182,7 @@ def _latex_(self):
         """
         return self._latex_name
 
+
 class ManifoldSubsetFiniteFamily(ManifoldObjectFiniteFamily):
 
     r"""
diff --git a/src/sage/manifolds/local_frame.py b/src/sage/manifolds/local_frame.py
index 99fcbe4acff..42e1579640d 100644
--- a/src/sage/manifolds/local_frame.py
+++ b/src/sage/manifolds/local_frame.py
@@ -408,6 +408,7 @@ def set_name(self, symbol, latex_symbol=None, indices=None,
 
 #******************************************************************************
 
+
 class LocalFrame(FreeModuleBasis):
     r"""
     Local frame on a vector bundle.
@@ -1232,6 +1233,7 @@ def set_name(self, symbol, latex_symbol=None, indices=None,
 
 #******************************************************************************
 
+
 class TrivializationCoFrame(LocalCoFrame):
     r"""
     Trivialization coframe on a vector bundle.
@@ -1364,6 +1366,7 @@ def _repr_(self):
 
 #******************************************************************************
 
+
 class TrivializationFrame(LocalFrame):
     r"""
     Trivialization frame on a topological vector bundle.
diff --git a/src/sage/manifolds/manifold_homset.py b/src/sage/manifolds/manifold_homset.py
index 78c9bc9984c..c390233ca55 100644
--- a/src/sage/manifolds/manifold_homset.py
+++ b/src/sage/manifolds/manifold_homset.py
@@ -33,6 +33,7 @@
 from sage.manifolds.continuous_map import ContinuousMap
 from sage.misc.cachefunc import cached_method
 
+
 class TopologicalManifoldHomset(UniqueRepresentation, Homset):
     r"""
     Set of continuous maps between two topological manifolds.
diff --git a/src/sage/manifolds/operators.py b/src/sage/manifolds/operators.py
index 636c11db149..eed5df22eb5 100644
--- a/src/sage/manifolds/operators.py
+++ b/src/sage/manifolds/operators.py
@@ -43,6 +43,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+
 def grad(scalar):
     r"""
     Gradient operator.
@@ -94,6 +95,7 @@ def grad(scalar):
     """
     return scalar.gradient()
 
+
 def div(tensor):
     r"""
     Divergence operator.
@@ -167,6 +169,7 @@ def div(tensor):
     """
     return tensor.divergence()
 
+
 def curl(vector):
     r"""
     Curl operator.
@@ -234,6 +237,7 @@ def curl(vector):
     """
     return vector.curl()
 
+
 def laplacian(field):
     r"""
     Laplace-Beltrami operator.
@@ -294,6 +298,7 @@ def laplacian(field):
     """
     return field.laplacian()
 
+
 def dalembertian(field):
     r"""
     d'Alembert operator.
diff --git a/src/sage/manifolds/point.py b/src/sage/manifolds/point.py
index f50ae75f553..b3647cc1447 100644
--- a/src/sage/manifolds/point.py
+++ b/src/sage/manifolds/point.py
@@ -92,6 +92,7 @@
 from sage.symbolic.expression import Expression
 from sage.rings.integer_ring import ZZ
 
+
 class ManifoldPoint(Element):
     r"""
     Point of a topological manifold.
diff --git a/src/sage/manifolds/scalarfield_algebra.py b/src/sage/manifolds/scalarfield_algebra.py
index 311f749adf3..960b4514387 100644
--- a/src/sage/manifolds/scalarfield_algebra.py
+++ b/src/sage/manifolds/scalarfield_algebra.py
@@ -38,6 +38,7 @@
 from sage.symbolic.ring import SymbolicRing, SR
 from sage.manifolds.scalarfield import ScalarField
 
+
 class ScalarFieldAlgebra(UniqueRepresentation, Parent):
     r"""
     Commutative algebra of scalar fields on a topological manifold.
diff --git a/src/sage/manifolds/section.py b/src/sage/manifolds/section.py
index 50ab4531cb6..75af42a57e5 100644
--- a/src/sage/manifolds/section.py
+++ b/src/sage/manifolds/section.py
@@ -25,6 +25,7 @@
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 
+
 class Section(ModuleElementWithMutability):
     r"""
     Section in a vector bundle.
@@ -2250,6 +2251,7 @@ def set_immutable(self):
 
 #******************************************************************************
 
+
 class TrivialSection(FiniteRankFreeModuleElement, Section):
     r"""
     Section in a trivial vector bundle.
diff --git a/src/sage/manifolds/section_module.py b/src/sage/manifolds/section_module.py
index 5c654762977..6192045f45a 100644
--- a/src/sage/manifolds/section_module.py
+++ b/src/sage/manifolds/section_module.py
@@ -34,6 +34,7 @@
 from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule
 from sage.manifolds.section import Section, TrivialSection
 
+
 class SectionModule(UniqueRepresentation, Parent):
     r"""
     Module of sections over a vector bundle `E \to M` of class `C^k` on a domain
@@ -476,6 +477,7 @@ def set_default_frame(self, basis):
 
 #******************************************************************************
 
+
 class SectionFreeModule(FiniteRankFreeModule):
     r"""
     Free module of sections over a vector bundle `E \to M` of class `C^k` on a
diff --git a/src/sage/manifolds/structure.py b/src/sage/manifolds/structure.py
index cf6a9466f9a..ed166b6438a 100644
--- a/src/sage/manifolds/structure.py
+++ b/src/sage/manifolds/structure.py
@@ -35,6 +35,8 @@
 
 # This is a slight abuse by making this a Singleton, but there is no
 #    need to have different copies of this object.
+
+
 class TopologicalStructure(Singleton):
     """
     The structure of a topological manifold over a general topological field.
@@ -82,6 +84,7 @@ def subcategory(self, cat):
         """
         return cat
 
+
 class DifferentialStructure(Singleton):
     """
     The structure of a differentiable manifold over a general topological
@@ -130,6 +133,7 @@ def subcategory(self, cat):
         """
         return cat
 
+
 class PseudoRiemannianStructure(Singleton):
     """
     The structure of a pseudo-Riemannian manifold.
@@ -153,6 +157,7 @@ def subcategory(self, cat):
         """
         return cat
 
+
 class RiemannianStructure(Singleton):
     """
     The structure of a Riemannian manifold.
@@ -176,6 +181,7 @@ def subcategory(self, cat):
         """
         return cat
 
+
 class LorentzianStructure(Singleton):
     """
     The structure of a Lorentzian manifold.
@@ -199,6 +205,7 @@ def subcategory(self, cat):
         """
         return cat
 
+
 class DegenerateStructure(Singleton):
     """
     The structure of a degenerate manifold.
diff --git a/src/sage/manifolds/subset.py b/src/sage/manifolds/subset.py
index 5a3f9238a9a..453fa02de2f 100644
--- a/src/sage/manifolds/subset.py
+++ b/src/sage/manifolds/subset.py
@@ -75,6 +75,7 @@
 from sage.manifolds.family import ManifoldObjectFiniteFamily, ManifoldSubsetFiniteFamily
 from sage.manifolds.point import ManifoldPoint
 
+
 class ManifoldSubset(UniqueRepresentation, Parent):
     r"""
     Subset of a topological manifold.
diff --git a/src/sage/manifolds/subsets/closure.py b/src/sage/manifolds/subsets/closure.py
index 9be9f7f9939..b1eb8d37835 100644
--- a/src/sage/manifolds/subsets/closure.py
+++ b/src/sage/manifolds/subsets/closure.py
@@ -17,6 +17,7 @@
 
 from sage.manifolds.subset import ManifoldSubset
 
+
 class ManifoldSubsetClosure(ManifoldSubset):
 
     r"""
diff --git a/src/sage/manifolds/trivialization.py b/src/sage/manifolds/trivialization.py
index 940ce857132..4c718db8ffe 100644
--- a/src/sage/manifolds/trivialization.py
+++ b/src/sage/manifolds/trivialization.py
@@ -24,6 +24,7 @@
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.manifolds.local_frame import TrivializationFrame
 
+
 class Trivialization(UniqueRepresentation, SageObject):
     r"""
     A local trivialization of a given vector bundle.
@@ -302,6 +303,7 @@ def coframe(self):
 
 # *****************************************************************************
 
+
 class TransitionMap(SageObject):
     r"""
     Transition map between two trivializations.
diff --git a/src/sage/manifolds/utilities.py b/src/sage/manifolds/utilities.py
index b51b7ace03d..190213eeb41 100644
--- a/src/sage/manifolds/utilities.py
+++ b/src/sage/manifolds/utilities.py
@@ -672,6 +672,7 @@ def simplify_chain_generic(expr):
     expr = expr.expand_sum()
     return expr
 
+
 def simplify_chain_generic_sympy(expr):
     r"""
     Apply a chain of simplifications to a sympy expression.
@@ -731,6 +732,7 @@ def simplify_chain_generic_sympy(expr):
     expr = expr.simplify()
     return expr
 
+
 def simplify_chain_real_sympy(expr):
     r"""
     Apply a chain of simplifications to a sympy expression, assuming the
@@ -804,6 +806,7 @@ def simplify_chain_real_sympy(expr):
 
 #******************************************************************************
 
+
 class ExpressionNice(Expression):
     r"""
     Subclass of :class:`~sage.symbolic.expression.Expression` for a
@@ -1229,6 +1232,7 @@ def _list_functions(ex, list_f):
 
 #******************************************************************************
 
+
 def set_axes_labels(graph, xlabel, ylabel, zlabel, **kwds):
     r"""
     Set axes labels for a 3D graphics object ``graph``.
@@ -1278,6 +1282,7 @@ def set_axes_labels(graph, xlabel, ylabel, zlabel, **kwds):
     graph += text3d('  ' + zlabel, (xmin1, ymin1, z1), **kwds)
     return graph
 
+
 def exterior_derivative(form):
     r"""
     Exterior derivative of a differential form.
diff --git a/src/sage/manifolds/vector_bundle.py b/src/sage/manifolds/vector_bundle.py
index fa2d277d012..ad830d68469 100644
--- a/src/sage/manifolds/vector_bundle.py
+++ b/src/sage/manifolds/vector_bundle.py
@@ -41,6 +41,7 @@
 from sage.rings.integer import Integer
 from sage.manifolds.vector_bundle_fiber import VectorBundleFiber
 
+
 class TopologicalVectorBundle(CategoryObject, UniqueRepresentation):
     r"""
     An instance of this class is a topological vector bundle `E \to B` over a
diff --git a/src/sage/manifolds/vector_bundle_fiber.py b/src/sage/manifolds/vector_bundle_fiber.py
index da255d46fd7..325ac1582b2 100644
--- a/src/sage/manifolds/vector_bundle_fiber.py
+++ b/src/sage/manifolds/vector_bundle_fiber.py
@@ -21,6 +21,7 @@
 from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule
 from sage.manifolds.vector_bundle_fiber_element import VectorBundleFiberElement
 
+
 class VectorBundleFiber(FiniteRankFreeModule):
     r"""
     Fiber of a given vector bundle at a given point.
diff --git a/src/sage/manifolds/vector_bundle_fiber_element.py b/src/sage/manifolds/vector_bundle_fiber_element.py
index 19eaf08bb77..39f18691463 100644
--- a/src/sage/manifolds/vector_bundle_fiber_element.py
+++ b/src/sage/manifolds/vector_bundle_fiber_element.py
@@ -20,6 +20,7 @@
 
 from sage.tensor.modules.free_module_element import FiniteRankFreeModuleElement
 
+
 class VectorBundleFiberElement(FiniteRankFreeModuleElement):
     r"""
     Vector in a fiber of a vector bundle at the given point.