From 16547260d9aa78a0005d6a6a9447dad6abaef237 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Sat, 1 Apr 2023 09:45:04 +0200
Subject: [PATCH] fix pep8 E303 in folders starting with m

---
 src/sage/manifolds/chart.py                           |  1 -
 .../differentiable/automorphismfield_group.py         |  2 --
 src/sage/manifolds/differentiable/chart.py            |  2 --
 src/sage/manifolds/differentiable/degenerate.py       |  1 -
 .../differentiable/degenerate_submanifold.py          |  1 -
 src/sage/manifolds/differentiable/diff_form.py        |  1 -
 src/sage/manifolds/differentiable/diff_map.py         |  1 -
 src/sage/manifolds/differentiable/integrated_curve.py |  9 ---------
 .../differentiable/levi_civita_connection.py          |  1 -
 src/sage/manifolds/differentiable/manifold.py         |  1 -
 src/sage/manifolds/differentiable/manifold_homset.py  |  2 --
 src/sage/manifolds/differentiable/metric.py           |  4 ----
 src/sage/manifolds/differentiable/scalarfield.py      |  1 -
 .../manifolds/differentiable/tensorfield_paral.py     |  3 ---
 src/sage/manifolds/differentiable/vectorfield.py      |  1 -
 .../manifolds/differentiable/vectorfield_module.py    |  1 -
 src/sage/manifolds/differentiable/vectorframe.py      |  2 --
 src/sage/manifolds/scalarfield.py                     |  1 -
 src/sage/manifolds/trivialization.py                  |  1 -
 src/sage/matrix/benchmark.py                          |  2 --
 src/sage/matrix/compute_J_ideal.py                    | 11 -----------
 src/sage/media/wav.py                                 |  1 -
 src/sage/misc/gperftools.py                           |  1 -
 src/sage/misc/sage_eval.py                            |  1 -
 src/sage/modular/quasimodform/element.py              |  1 -
 src/sage/modules/fg_pid/fgp_element.py                |  5 -----
 src/sage/modules/free_module.py                       |  1 -
 src/sage/modules/vector_space_morphism.py             |  1 -
 src/sage/modules/with_basis/morphism.py               |  1 -
 src/sage/modules/with_basis/representation.py         |  1 -
 src/sage/monoids/free_abelian_monoid.py               |  1 -
 31 files changed, 63 deletions(-)

diff --git a/src/sage/manifolds/chart.py b/src/sage/manifolds/chart.py
index d0ff3cea922..e48fe7c44fb 100644
--- a/src/sage/manifolds/chart.py
+++ b/src/sage/manifolds/chart.py
@@ -2317,7 +2317,6 @@ def _tighten_bounds(self):
         self._restrictions = new_restrictions
         self._fast_valid_coordinates = None
 
-
     def restrict(self, subset, restrictions=None):
         r"""
         Return the restriction of the chart to some open subset of its domain.
diff --git a/src/sage/manifolds/differentiable/automorphismfield_group.py b/src/sage/manifolds/differentiable/automorphismfield_group.py
index 0791f0b9f24..72955d48b3c 100644
--- a/src/sage/manifolds/differentiable/automorphismfield_group.py
+++ b/src/sage/manifolds/differentiable/automorphismfield_group.py
@@ -175,7 +175,6 @@ def __init__(self, vector_field_module):
         Parent.__init__(self, category=Groups())
         self._vmodule = vector_field_module
 
-
     #### Parent methods ####
 
     def _element_constructor_(self, comp=[], frame=None, name=None,
@@ -266,7 +265,6 @@ def _an_element_(self):
 
     #### End of parent methods ####
 
-
     #### Monoid methods ####
 
     @cached_method
diff --git a/src/sage/manifolds/differentiable/chart.py b/src/sage/manifolds/differentiable/chart.py
index 098f85516bf..6ea06b662ed 100644
--- a/src/sage/manifolds/differentiable/chart.py
+++ b/src/sage/manifolds/differentiable/chart.py
@@ -679,7 +679,6 @@ def symbolic_velocities(self, left='D', right=None):
         return list(var(list_strings_velocities))
 
 
-
 #*****************************************************************************
 
 class RealDiffChart(DiffChart, RealChart):
@@ -1001,7 +1000,6 @@ def __init__(self, domain, coordinates, calc_method=None,
         self._frame = CoordFrame(self)
         self._coframe = self._frame._coframe
 
-
     def restrict(self, subset, restrictions=None):
         r"""
         Return the restriction of the chart to some subset.
diff --git a/src/sage/manifolds/differentiable/degenerate.py b/src/sage/manifolds/differentiable/degenerate.py
index 0fddd642e17..30846aa6891 100644
--- a/src/sage/manifolds/differentiable/degenerate.py
+++ b/src/sage/manifolds/differentiable/degenerate.py
@@ -368,7 +368,6 @@ def open_subset(self, name, latex_name=None, coord_def={}):
         return resu
 
 
-
 #*******************************************************************************************
 
 from sage.manifolds.differentiable.tensorfield_paral import TensorFieldParal
diff --git a/src/sage/manifolds/differentiable/degenerate_submanifold.py b/src/sage/manifolds/differentiable/degenerate_submanifold.py
index 5d5ebb3de0f..67d5228f2d9 100644
--- a/src/sage/manifolds/differentiable/degenerate_submanifold.py
+++ b/src/sage/manifolds/differentiable/degenerate_submanifold.py
@@ -1323,7 +1323,6 @@ def principal_directions(self, screen=None):
         self._principal_directions[screen._name] = res
         return res
 
-
     def mean_curvature(self, screen=None):
         r"""
 
diff --git a/src/sage/manifolds/differentiable/diff_form.py b/src/sage/manifolds/differentiable/diff_form.py
index ec6a8d353f3..dc682328e55 100644
--- a/src/sage/manifolds/differentiable/diff_form.py
+++ b/src/sage/manifolds/differentiable/diff_form.py
@@ -1556,7 +1556,6 @@ def wedge(self, other):
         other_r = other.restrict(dom_resu)
         return FreeModuleAltForm.wedge(self_r, other_r)
 
-
     def interior_product(self, qvect):
         r"""
         Interior product with a multivector field.
diff --git a/src/sage/manifolds/differentiable/diff_map.py b/src/sage/manifolds/differentiable/diff_map.py
index 4260f233e40..ded6843afb3 100644
--- a/src/sage/manifolds/differentiable/diff_map.py
+++ b/src/sage/manifolds/differentiable/diff_map.py
@@ -1144,7 +1144,6 @@ def paral_comp(tcomp, chart1, chart2, coord2_1, jacob,
                             resu._components[frame] = comp
         return resu
 
-
     def pushforward(self, tensor):
         r"""
         Pushforward operator associated with ``self``.
diff --git a/src/sage/manifolds/differentiable/integrated_curve.py b/src/sage/manifolds/differentiable/integrated_curve.py
index 8b62aab4f39..74f76ab3e33 100644
--- a/src/sage/manifolds/differentiable/integrated_curve.py
+++ b/src/sage/manifolds/differentiable/integrated_curve.py
@@ -579,7 +579,6 @@ def fast_CoF(pos, vel, M=M):
                                for f in transf]
                 self._fast_changes_of_chart[CoC] = fast_transf
 
-
         self._velocities = list(velocities) # converts to list
         # since might not already be a list (which is later required)
         self._curve_parameter = curve_parameter
@@ -1376,13 +1375,11 @@ def jacobian(t,y):
         # 'tangent_vector_eval_at', and in 'plot' when plotting the
         # tangent vectors.)
 
-
         if isinstance(sol, list):
             coords_sol = [point[0:dim + 1] for point in sol]
         else:
             coords_sol = sol[:, 0:dim + 1].tolist() # far faster in numpy
 
-
         if verbose:
             print("Numerical integration completed.\n\n" +
                   "Checking all points are in the chart domain...")
@@ -1779,7 +1776,6 @@ def solve_across_charts(self, charts=None, step=None, solution_key=None,
                             new_vel = self._fast_changes_of_frame[(new_chart.frame().restrict(inter),
                                chart.frame().restrict(inter))](last_pts, last_vel)
 
-
                             ics = new_pts + new_vel
                             chart = new_chart
 
@@ -2434,7 +2430,6 @@ def plot_integrated(self, chart=None, ambient_coords=None,
         thickness = kwds.pop('thickness')
         aspect_ratio = kwds.pop('aspect_ratio')
 
-
         #
         # The mapping, if present, and the chart with respect to which the curve
         # is plotted
@@ -3425,7 +3420,6 @@ def __init__(self, parent, affine_connection, curve_parameter,
 
         velocities = chart.symbolic_velocities()
 
-
         dim = parent.codomain().dim()
         i0 = parent.codomain().start_index()
 
@@ -3470,7 +3464,6 @@ def __init__(self, parent, affine_connection, curve_parameter,
                     equations_rhs_chart += [rhs.simplify_full()]
                 equations_rhs[chart] = equations_rhs_chart
 
-
         IntegratedCurve.__init__(self, parent, equations_rhs,
                                  velocities, curve_parameter,
                                  initial_tangent_vector, chart=chart,
@@ -3479,7 +3472,6 @@ def __init__(self, parent, affine_connection, curve_parameter,
 
         self._affine_connection = affine_connection
 
-
     def _repr_(self):
         r"""
         Return a string representation of ``self``.
@@ -3825,7 +3817,6 @@ class IntegratedGeodesic(IntegratedAutoparallelCurve):
     def __init__(self, parent, metric, curve_parameter,
                  initial_tangent_vector, chart=None, name=None,
                  latex_name=None, verbose=False, across_charts=False):
-
         r"""
         Construct a geodesic curve with respect to the given metric with the
         given initial tangent vector.
diff --git a/src/sage/manifolds/differentiable/levi_civita_connection.py b/src/sage/manifolds/differentiable/levi_civita_connection.py
index 3b8095004e3..7ff2643e32b 100644
--- a/src/sage/manifolds/differentiable/levi_civita_connection.py
+++ b/src/sage/manifolds/differentiable/levi_civita_connection.py
@@ -387,7 +387,6 @@ def _new_coef(self, frame):
                               start_index=self._domain._sindex,
                               output_formatter=DiffScalarField.coord_function)
 
-
     def coef(self, frame=None):
         r"""
         Return the connection coefficients relative to the given frame.
diff --git a/src/sage/manifolds/differentiable/manifold.py b/src/sage/manifolds/differentiable/manifold.py
index e674ad8db05..e216a42ada3 100644
--- a/src/sage/manifolds/differentiable/manifold.py
+++ b/src/sage/manifolds/differentiable/manifold.py
@@ -2977,7 +2977,6 @@ def change_of_frame(self, frame1, frame2):
                              " has not been defined on the {}".format(self))
         return self._frame_changes[(frame1, frame2)]
 
-
     def set_change_of_frame(self, frame1, frame2, change_of_frame,
                          compute_inverse=True):
         r"""
diff --git a/src/sage/manifolds/differentiable/manifold_homset.py b/src/sage/manifolds/differentiable/manifold_homset.py
index 7152774ec75..2d35505f63c 100644
--- a/src/sage/manifolds/differentiable/manifold_homset.py
+++ b/src/sage/manifolds/differentiable/manifold_homset.py
@@ -777,7 +777,6 @@ def _repr_(self):
         description += "which actually are integrated curves"
         return description
 
-
     def _element_constructor_(self, equations_rhs, velocities,
                  curve_parameter, initial_tangent_vector, chart=None,
                  name=None, latex_name=None, verbose=False, across_charts=False):
@@ -1221,7 +1220,6 @@ def _repr_(self):
         description += "curves with respect to a certain affine connection"
         return description
 
-
     def _element_constructor_(self, affine_connection, curve_parameter,
                     initial_tangent_vector, chart=None, name=None,
                     latex_name=None, verbose=False, across_charts=False):
diff --git a/src/sage/manifolds/differentiable/metric.py b/src/sage/manifolds/differentiable/metric.py
index 6dece42f0fe..5da567945a3 100644
--- a/src/sage/manifolds/differentiable/metric.py
+++ b/src/sage/manifolds/differentiable/metric.py
@@ -662,7 +662,6 @@ def set(self, symbiform):
                 rst = self.restrict(dom)
                 rst.set(symbiform_rst)
 
-
     def inverse(self, expansion_symbol=None, order=1):
         r"""
         Return the inverse metric.
@@ -879,7 +878,6 @@ def christoffel_symbols(self, chart=None):
             frame = chart._frame
         return self.connection().coef(frame)
 
-
     def christoffel_symbols_display(self, chart=None, symbol=None,
                 latex_symbol=None, index_labels=None, index_latex_labels=None,
                 coordinate_labels=True, only_nonzero=True,
@@ -1069,7 +1067,6 @@ def riemann(self, name=None, latex_name=None):
         """
         return self.connection().riemann(name, latex_name)
 
-
     def ricci(self, name=None, latex_name=None):
         r"""
         Return the Ricci tensor associated with the metric.
@@ -2271,7 +2268,6 @@ def restrict(self, subdomain, dest_map=None):
             self._restrictions[subdomain] = resu
         return self._restrictions[subdomain]
 
-
     def set(self, symbiform):
         r"""
         Define the metric from a field of symmetric bilinear forms.
diff --git a/src/sage/manifolds/differentiable/scalarfield.py b/src/sage/manifolds/differentiable/scalarfield.py
index 1b9a3c2ae2d..ba5c5d70f2c 100644
--- a/src/sage/manifolds/differentiable/scalarfield.py
+++ b/src/sage/manifolds/differentiable/scalarfield.py
@@ -819,7 +819,6 @@ def differential(self) -> DiffForm:
     derivative = differential  # allows one to use functional notation,
                                # e.g. diff(f) for f.differential()
 
-
     def lie_derivative(self, vector):
         r"""
         Compute the Lie derivative with respect to a vector field.
diff --git a/src/sage/manifolds/differentiable/tensorfield_paral.py b/src/sage/manifolds/differentiable/tensorfield_paral.py
index eb517832382..065a5e9e5ec 100644
--- a/src/sage/manifolds/differentiable/tensorfield_paral.py
+++ b/src/sage/manifolds/differentiable/tensorfield_paral.py
@@ -657,7 +657,6 @@ def __init__(self, vector_field_module, tensor_type, name=None,
         # Initialization of derived quantities:
         self._init_derived()
 
-
     def _repr_(self):
         r"""
         String representation of ``self``.
@@ -769,7 +768,6 @@ def _preparse_display(self, basis=None, format_spec=None):
             basis = basis.frame()
         return (basis, format_spec)
 
-
     def _set_comp_unsafe(self, basis=None):
         r"""
         Return the components of the tensor field in a given vector frame
@@ -1511,7 +1509,6 @@ def paral_lie_deriv(a, b , coord_frame, chart_cp, local_list_ind):
                                     vc[[i]].coord_function(chart).diff(ind[k])
                     resc[[ind]] = rsum.scalar_field()
 
-
             #
             # 3/ Final result (the tensor)
             res = vf_module.tensor_from_comp(self._tensor_type, resc)
diff --git a/src/sage/manifolds/differentiable/vectorfield.py b/src/sage/manifolds/differentiable/vectorfield.py
index ecd41a9882f..01a9c52d93c 100644
--- a/src/sage/manifolds/differentiable/vectorfield.py
+++ b/src/sage/manifolds/differentiable/vectorfield.py
@@ -359,7 +359,6 @@ def __call__(self, scalar):
             resu.set_name(name=name, latex_name=latex_name)
         return resu
 
-
     @options(max_range=8, scale=1, color='blue')
     def plot(self, chart=None, ambient_coords=None, mapping=None,
              chart_domain=None, fixed_coords=None, ranges=None,
diff --git a/src/sage/manifolds/differentiable/vectorfield_module.py b/src/sage/manifolds/differentiable/vectorfield_module.py
index 12060175278..5a3791409af 100644
--- a/src/sage/manifolds/differentiable/vectorfield_module.py
+++ b/src/sage/manifolds/differentiable/vectorfield_module.py
@@ -1206,7 +1206,6 @@ def metric(self, name: str, signature: Optional[int] = None, latex_name: Optiona
         return PseudoRiemannianMetric(self, name, signature=signature[0]-signature[1],
                                       latex_name=latex_name)
 
-
     def symplectic_form(
         self, name: Optional[str] = None, latex_name: Optional[str] = None
     ):
diff --git a/src/sage/manifolds/differentiable/vectorframe.py b/src/sage/manifolds/differentiable/vectorframe.py
index 8f8c26c0c61..a02d69da5d0 100644
--- a/src/sage/manifolds/differentiable/vectorframe.py
+++ b/src/sage/manifolds/differentiable/vectorframe.py
@@ -764,7 +764,6 @@ def __init__(self, vector_field_module, symbol, latex_symbol=None,
         # NB: set(self._restrictions.values()) is identical to
         #     self._subframes
 
-
     ###### Methods that must be redefined by derived classes of ######
     ###### FreeModuleBasis                                      ######
 
@@ -1777,7 +1776,6 @@ def __init__(self, chart):
         # - force_free=True ensures that a free module is constructed in case
         #   it is the first call to the vector field module on chart.domain()
 
-
     ###### Methods that must be redefined by derived classes of ######
     ###### FreeModuleBasis                                      ######
 
diff --git a/src/sage/manifolds/scalarfield.py b/src/sage/manifolds/scalarfield.py
index 4b43a9dca14..458312279b7 100644
--- a/src/sage/manifolds/scalarfield.py
+++ b/src/sage/manifolds/scalarfield.py
@@ -2652,7 +2652,6 @@ def __neg__(self):
             result._latex_name = '-' + self._latex_name
         return result
 
-
     #########  CommutativeAlgebraElement arithmetic operators ########
 
     def _add_(self, other):
diff --git a/src/sage/manifolds/trivialization.py b/src/sage/manifolds/trivialization.py
index dcdaad390d9..ed3a8b4ed9f 100644
--- a/src/sage/manifolds/trivialization.py
+++ b/src/sage/manifolds/trivialization.py
@@ -693,7 +693,6 @@ def matrix(self):
         """
         return self._automorphism.matrix(self._frame1)
 
-
     def __eq__(self, other):
         r"""
         Equality operator.
diff --git a/src/sage/matrix/benchmark.py b/src/sage/matrix/benchmark.py
index 811a1cbfc98..751b89c5cc3 100644
--- a/src/sage/matrix/benchmark.py
+++ b/src/sage/matrix/benchmark.py
@@ -562,7 +562,6 @@ def vecmat_ZZ(n=300, min=-9, max=9, system='sage', times=200):
         raise ValueError('unknown system "%s"'%system)
 
 
-
 #######################################################################
 # Dense Benchmarks over GF(p), for small p.
 #######################################################################
@@ -721,7 +720,6 @@ def matrix_add_GF(n=1000, p=16411, system='sage',times=100):
         raise ValueError('unknown system "%s"'%system)
 
 
-
 # Matrix multiplication over GF(p)
 
 def matrix_multiply_GF(n=100, p=16411, system='sage', times=3):
diff --git a/src/sage/matrix/compute_J_ideal.py b/src/sage/matrix/compute_J_ideal.py
index 7c31c0160f1..55dcb5e7072 100644
--- a/src/sage/matrix/compute_J_ideal.py
+++ b/src/sage/matrix/compute_J_ideal.py
@@ -190,7 +190,6 @@ def lifting(p, t, A, G):
     """
     from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
-
     DX = A.parent().base()
     (X,) = DX.variable_names()
     D = DX.base_ring()
@@ -203,7 +202,6 @@ def lifting(p, t, A, G):
     if not (A*G % p**(t-1)).is_zero():
         raise ValueError("A*G not zero mod %s^%s" % (p, t-1))
 
-
     R = A*G/p**(t-1)
     R.change_ring(DX)
 
@@ -351,7 +349,6 @@ def __init__(self, B):
         self._DX = X.parent()
         self._cache = {}
 
-
     def find_monic_replacements(self, p, t, pt_generators, prev_nu):
         r"""
         Replace possibly non-monic generators of `N_{(p^t)}(B)` by monic
@@ -432,7 +429,6 @@ def find_monic_replacements(self, p, t, pt_generators, prev_nu):
 
         return replacements
 
-
     def current_nu(self, p, t, pt_generators, prev_nu):
         r"""
         Compute `(p^t)`-minimal polynomial of `B`.
@@ -482,7 +478,6 @@ def current_nu(self, p, t, pt_generators, prev_nu):
 
         from sage.misc.verbose import verbose
 
-
         if not all((g(self._B) % p**t).is_zero()
                    for g in pt_generators):
             raise ValueError("%s not in N_{(%s^%s)}(B)" %
@@ -519,7 +514,6 @@ def current_nu(self, p, t, pt_generators, prev_nu):
 
         return g
 
-
     def mccoy_column(self, p, t, nu):
         r"""
         Compute matrix for McCoy's criterion.
@@ -577,7 +571,6 @@ def mccoy_column(self, p, t, nu):
 
         return column
 
-
     def p_minimal_polynomials(self, p, s_max=None):
         r"""
         Compute `(p^s)`-minimal polynomials `\nu_s` of `B`.
@@ -768,7 +761,6 @@ def p_minimal_polynomials(self, p, s_max=None):
             d = self._A.ncols()
             G = matrix(self._DX, d, 0)
 
-
         while t < s_max:
             deg_prev_nu = nu.degree()
             t += 1
@@ -812,7 +804,6 @@ def p_minimal_polynomials(self, p, s_max=None):
 
         return p_min_polys
 
-
     def null_ideal(self, b=0):
         r"""
         Return the `(b)`-ideal `N_{(b)}(B)=\{f\in D[X] \mid f(B)\in M_n(bD)\}`.
@@ -877,7 +868,6 @@ def null_ideal(self, b=0):
 
         return self._DX.ideal(generators)
 
-
     def prime_candidates(self):
         r"""
         Determine those primes `p` where `\mu_B` might not be a
@@ -910,7 +900,6 @@ def prime_candidates(self):
 
         return [p for (p, t) in factor(T.det())]
 
-
     def integer_valued_polynomials_generators(self):
         r"""
         Determine the generators of the ring of integer valued polynomials on `B`.
diff --git a/src/sage/media/wav.py b/src/sage/media/wav.py
index c847754f2e5..9e9664595b3 100644
--- a/src/sage/media/wav.py
+++ b/src/sage/media/wav.py
@@ -102,7 +102,6 @@ def __init__(self, data=None, **kwds):
         else:
             raise ValueError("Must give a filename")
 
-
     def save(self, filename='sage.wav'):
         r"""
         Save this wave file to disk, either as a Sage sobj or as a .wav file.
diff --git a/src/sage/misc/gperftools.py b/src/sage/misc/gperftools.py
index 55ee572b8c4..d6e8123e8b2 100644
--- a/src/sage/misc/gperftools.py
+++ b/src/sage/misc/gperftools.py
@@ -47,7 +47,6 @@
 libprofiler = None
 
 
-
 class Profiler(SageObject):
 
     def __init__(self, filename=None):
diff --git a/src/sage/misc/sage_eval.py b/src/sage/misc/sage_eval.py
index 4e2a9968f24..8d0416a4cfd 100644
--- a/src/sage/misc/sage_eval.py
+++ b/src/sage/misc/sage_eval.py
@@ -198,7 +198,6 @@ def sage_eval(source, locals=None, cmds='', preparse=True):
         return eval(source, sage.all.__dict__, locals)
 
 
-
 def sageobj(x, vars=None):
     """
     Return a native Sage object associated to ``x``, if possible and
diff --git a/src/sage/modular/quasimodform/element.py b/src/sage/modular/quasimodform/element.py
index 24a6b7ebfad..b92c31722ac 100644
--- a/src/sage/modular/quasimodform/element.py
+++ b/src/sage/modular/quasimodform/element.py
@@ -622,7 +622,6 @@ def __getitem__(self, weight):
 
     homogeneous_component = __getitem__  # alias
 
-
     def serre_derivative(self):
         r"""
         Return the Serre derivative of the given quasimodular form.
diff --git a/src/sage/modules/fg_pid/fgp_element.py b/src/sage/modules/fg_pid/fgp_element.py
index dbaeaf8c3e0..0a0f435d779 100644
--- a/src/sage/modules/fg_pid/fgp_element.py
+++ b/src/sage/modules/fg_pid/fgp_element.py
@@ -120,7 +120,6 @@ def lift(self):
         """
         return self._x
 
-
     def __neg__(self):
         """
         EXAMPLES::
@@ -135,7 +134,6 @@ def __neg__(self):
         P = self.parent()
         return P.element_class(P, -self._x)
 
-
     def _add_(self, other):
         """
         EXAMPLES::
@@ -170,7 +168,6 @@ def _add_(self, other):
         P = self.parent()
         return P.element_class(P, self._x + other._x)
 
-
     def _sub_(self, other):
         """
         EXAMPLES::
@@ -190,7 +187,6 @@ def _sub_(self, other):
         P = self.parent()
         return P.element_class(P, self._x - other._x)
 
-
     def _rmul_(self, c):
         """
         Multiplication by a scalar from the left (``self`` is on the right).
@@ -293,7 +289,6 @@ def _repr_(self):
         """
         return repr(self.vector())
 
-
     def __getitem__(self, *args):
         """
         EXAMPLES::
diff --git a/src/sage/modules/free_module.py b/src/sage/modules/free_module.py
index 41bd5633503..b7618475111 100644
--- a/src/sage/modules/free_module.py
+++ b/src/sage/modules/free_module.py
@@ -1830,7 +1830,6 @@ def free_resolution(self, *args, **kwds):
         raise NotImplementedError("the module must be a free module or "
                                   "have the base ring be a polynomial ring using Singular")
 
-
     def graded_free_resolution(self, *args, **kwds):
         r"""
         Return a graded free resolution of ``self``.
diff --git a/src/sage/modules/vector_space_morphism.py b/src/sage/modules/vector_space_morphism.py
index b0e0846a163..8044ed8dd4c 100644
--- a/src/sage/modules/vector_space_morphism.py
+++ b/src/sage/modules/vector_space_morphism.py
@@ -866,7 +866,6 @@ def __init__(self, homspace, A, side="left"):
             if homspace.domain().dimension() != A.ncols():
                 raise TypeError('codomain dimension is incompatible with matrix size')
 
-
         A = homspace._matrix_space(side)(A)
         free_module_morphism.FreeModuleMorphism.__init__(self, homspace, A, side)
 
diff --git a/src/sage/modules/with_basis/morphism.py b/src/sage/modules/with_basis/morphism.py
index 6a43cab1461..0a38d7903d0 100644
--- a/src/sage/modules/with_basis/morphism.py
+++ b/src/sage/modules/with_basis/morphism.py
@@ -690,7 +690,6 @@ def __init__(self, triangular="upper", unitriangular=False,
 
         self._inverse_on_support = inverse_on_support
 
-
         if invertible is None and (domain.basis().keys() == codomain.basis().keys()) and \
            (self._inverse_on_support==identity or domain in Modules.FiniteDimensional):
             invertible = True
diff --git a/src/sage/modules/with_basis/representation.py b/src/sage/modules/with_basis/representation.py
index 815871e038d..44b9f6115e2 100644
--- a/src/sage/modules/with_basis/representation.py
+++ b/src/sage/modules/with_basis/representation.py
@@ -494,7 +494,6 @@ def side(self):
         """
         return "left" if self._left_repr else "right"
 
-
     class Element(CombinatorialFreeModule.Element):
         def _acted_upon_(self, scalar, self_on_left=False):
             """
diff --git a/src/sage/monoids/free_abelian_monoid.py b/src/sage/monoids/free_abelian_monoid.py
index 54771b247e4..aa0581c2c0e 100644
--- a/src/sage/monoids/free_abelian_monoid.py
+++ b/src/sage/monoids/free_abelian_monoid.py
@@ -220,7 +220,6 @@ def __call__(self, x):
             return x
         return self.element_class(self, x)
 
-
     def __contains__(self, x):
         """
         Return True if `x` is an element of this abelian monoid.