sagemathgh-38816: fix all pep E302 in manifolds and geometry

this is about fixing the warning

E302 expected 2 blank lines, found 1

in the `manifolds` and `geometry` folders.

Purely scripted using `autopep8`

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

URL: sagemath#38816
Reported by: Frédéric Chapoton
Reviewer(s): Vincent Macri

build/pkgs/configure/checksums.ini

@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=978eb775a20fea3ed9b88f0d67ecd84a3d9cd6ea
-sha256=c3987bb0f8aca81e112a17d8904ef2353a706159d43250305dc2bcac4ca2e33a
+sha1=869b8dcff3ad88d00ad0212c4f1727a1c0d0a078
+sha256=7880976e0ba4561e205467391ccdfd966789e8d09d2ca5a442767b634beb671e

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-4326d0d9422011034a230ab3c1445fafeb2ac444
+1c867dde3c7e7b486606afcfe479bb96d18f6b0b

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.

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

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

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.

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

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``.

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

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.

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.

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.

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.

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`.

src/sage/geometry/polyhedron/base5.py

@@ -42,6 +42,7 @@
 
 from .base4 import Polyhedron_base4
 
+
 class Polyhedron_base5(Polyhedron_base4):
     """
     Methods constructing new polyhedra

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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