From 471d5551e74dc86c02051def347433f77634b72f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Sat, 26 Oct 2024 21:41:12 +0200
Subject: [PATCH] autopep8 fixes for E302 in matrix,rings,groups,dynamics

---
 .../dynamics/arithmetic_dynamics/affine_ds.py     |  2 ++
 .../dynamics/arithmetic_dynamics/berkovich_ds.py  |  1 +
 .../endPN_automorphism_group.py                   | 14 ++++++++++++++
 .../arithmetic_dynamics/endPN_minimal_model.py    |  9 +++++++++
 .../dynamics/arithmetic_dynamics/projective_ds.py |  2 ++
 src/sage/dynamics/cellular_automata/elementary.py |  1 +
 src/sage/dynamics/cellular_automata/glca.py       |  1 +
 .../dynamics/complex_dynamics/mandel_julia.py     |  2 ++
 src/sage/dynamics/finite_dynamical_system.py      |  3 +++
 .../dynamics/finite_dynamical_system_catalog.py   |  3 +++
 src/sage/dynamics/surface_dynamics_deprecation.py |  1 +
 src/sage/groups/abelian_gps/abelian_aut.py        |  3 +++
 src/sage/groups/abelian_gps/abelian_group_gap.py  |  6 ++++++
 src/sage/groups/finitely_presented_named.py       |  6 ++++++
 src/sage/groups/fqf_orthogonal.py                 |  1 +
 src/sage/groups/indexed_free_group.py             |  2 ++
 src/sage/groups/libgap_group.py                   |  1 +
 .../groups/matrix_gps/finitely_generated_gap.py   |  1 +
 src/sage/groups/matrix_gps/heisenberg.py          |  1 +
 src/sage/groups/matrix_gps/homset.py              |  1 +
 src/sage/groups/matrix_gps/morphism.py            |  1 +
 src/sage/groups/matrix_gps/named_group_gap.py     |  1 +
 src/sage/groups/perm_gps/cubegroup.py             |  2 ++
 src/sage/matrix/benchmark.py                      | 15 +++++++++++++++
 .../matrix/matrix_integer_dense_saturation.py     |  3 +++
 src/sage/matrix/matrix_space.py                   |  1 +
 src/sage/rings/asymptotic/growth_group.py         |  1 +
 .../rings/asymptotic/growth_group_cartesian.py    |  2 ++
 src/sage/rings/complex_interval_field.py          |  2 ++
 src/sage/rings/finite_rings/conway_polynomials.py |  4 ++++
 .../rings/finite_rings/finite_field_pari_ffelt.py |  1 +
 src/sage/rings/finite_rings/galois_group.py       |  2 ++
 src/sage/rings/finite_rings/homset.py             |  1 +
 src/sage/rings/finite_rings/maps_finite_field.py  |  3 +++
 src/sage/rings/function_field/constructor.py      |  1 +
 src/sage/rings/function_field/divisor.py          |  2 ++
 .../drinfeld_modules/charzero_drinfeld_module.py  |  1 +
 .../drinfeld_modules/drinfeld_module.py           |  1 +
 src/sage/rings/function_field/valuation.py        |  1 +
 src/sage/rings/function_field/valuation_ring.py   |  1 +
 src/sage/rings/ideal.py                           |  5 +++++
 src/sage/rings/lazy_series.py                     |  3 +++
 src/sage/rings/lazy_series_ring.py                |  4 ++++
 src/sage/rings/monomials.py                       |  1 +
 src/sage/rings/polynomial/complex_roots.py        |  1 +
 src/sage/rings/polynomial/ideal.py                |  1 +
 .../rings/polynomial/laurent_polynomial_ideal.py  |  1 +
 .../rings/polynomial/laurent_polynomial_ring.py   |  5 +++++
 .../polynomial/laurent_polynomial_ring_base.py    |  1 +
 src/sage/rings/polynomial/msolve.py               |  3 +++
 .../rings/polynomial/multi_polynomial_ideal.py    |  2 ++
 .../rings/polynomial/multi_polynomial_sequence.py |  2 ++
 src/sage/rings/polynomial/ore_function_element.py |  1 +
 .../polynomial/polynomial_element_generic.py      |  3 +++
 .../rings/polynomial/polynomial_quotient_ring.py  |  1 +
 src/sage/rings/polynomial/term_order.py           |  1 +
 src/sage/rings/qqbar_decorators.py                |  1 +
 src/sage/rings/quotient_ring.py                   |  1 +
 src/sage/rings/ring_extension_homset.py           |  1 +
 59 files changed, 145 insertions(+)

diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
index c2ad0f04cea..2096d734c85 100644
--- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
@@ -884,6 +884,7 @@ def degree(self):
         """
         return self.as_scheme_morphism().degree()
 
+
 class DynamicalSystem_affine_field(DynamicalSystem_affine,
                                    SchemeMorphism_polynomial_affine_space_field):
     @cached_method
@@ -985,6 +986,7 @@ def reduce_base_field(self):
         """
         return self.as_scheme_morphism().reduce_base_field().as_dynamical_system()
 
+
 class DynamicalSystem_affine_finite_field(DynamicalSystem_affine_field,
                                     SchemeMorphism_polynomial_affine_space_finite_field):
 
diff --git a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
index 0c27d8e2bde..f84ab7e94ed 100644
--- a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
@@ -960,6 +960,7 @@ def __call__(self, x, type_3_pole_check=True):
                 new_radius = max(new_radius, p**(-valuation/prime.absolute_ramification_index())*r**i)
         return self.domain()(new_center, new_radius)
 
+
 class DynamicalSystem_Berkovich_affine(DynamicalSystem_Berkovich):
     r"""
     A dynamical system of the affine Berkovich line over `\CC_p`.
diff --git a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
index 76ba5864fe6..196da8a081a 100644
--- a/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
+++ b/src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py
@@ -335,6 +335,7 @@ def height_bound(polynomial):
 
     return (6*(L2norm_sq)**3)
 
+
 def PGL_repn(rational_function):
     r"""
     Take a linear fraction transformation and represent it as a 2x2 matrix.
@@ -365,6 +366,7 @@ def PGL_repn(rational_function):
         g = rational_function.denominator()
         return matrix(F, 2, [f[1], f[0], g[1], g[0]])
 
+
 def PGL_order(A):
     r"""
     Find the multiplicative order of a linear fractional transformation that
@@ -402,6 +404,7 @@ def PGL_order(A):
 
     return n
 
+
 def CRT_helper(automorphisms, moduli):
     r"""
     Lift the given list of automorphisms to `Zmod(M)`.
@@ -449,6 +452,7 @@ def CRT_helper(automorphisms, moduli):
 
     return autos, modulus*moduli[0]
 
+
 def CRT_automorphisms(automorphisms, order_elts, degree, moduli):
     r"""
     Compute a maximal list of automorphisms over `Zmod(M)`.
@@ -495,6 +499,7 @@ def CRT_automorphisms(automorphisms, order_elts, degree, moduli):
     # get list of CRT'ed automorphisms
     return CRT_helper(degree_d_autos, moduli)
 
+
 def valid_automorphisms(automorphisms_CRT, rational_function, ht_bound, M,
                         return_functions=False):
     r"""
@@ -904,6 +909,7 @@ def automorphism_group_FF(rational_function, absolute=False, iso_type=False, ret
     else:
         return G, which_group(G[1])
 
+
 def field_descent(sigma, y):
     r"""
     Function for descending an element in a field `E` to a subfield `F`.
@@ -961,6 +967,7 @@ def field_descent(sigma, y):
 
     return x + F(quotient)*a**(steps)
 
+
 def rational_function_coefficient_descent(rational_function, sigma, poly_ring):
     r"""
     Function for descending the coefficients of a rational function from field `E`
@@ -1059,6 +1066,7 @@ def rational_function_coerce(rational_function, sigma, S_polys):
     else:
         return S_polys([sigma(a) for a in f]) / S_polys([sigma(b) for b in g])
 
+
 def rational_function_reduce(rational_function):
     r"""
     Force Sage to divide out common factors in numerator and denominator
@@ -1084,6 +1092,7 @@ def rational_function_reduce(rational_function):
     comm_factor = gcd(F,G)
     return (F.quo_rem(comm_factor)[0]) / (G.quo_rem(comm_factor)[0])
 
+
 def three_stable_points(rational_function, invariant_list):
     r"""
     Implementation of Algorithm 1 for automorphism groups from
@@ -1157,6 +1166,7 @@ def three_stable_points(rational_function, invariant_list):
                 automorphisms.append(s)
     return automorphisms
 
+
 def automorphism_group_FF_alg2(rational_function):
     r"""
     Implementation of algorithm for determining the absolute automorphism
@@ -1455,6 +1465,7 @@ def order_p_automorphisms(rational_function, pre_image):
 
     return automorphisms_p
 
+
 def automorphisms_fixing_pair(rational_function, pair, quad):
     r"""
     Compute the set of automorphisms with order prime to the characteristic
@@ -1535,6 +1546,7 @@ def automorphisms_fixing_pair(rational_function, pair, quad):
 
     return list(set(automorphisms_prime_to_p))
 
+
 def automorphism_group_FF_alg3(rational_function):
     r"""
     Implementation of Algorithm 3 in the paper by Faber/Manes/Viray [FMV]_
@@ -2125,6 +2137,7 @@ def greedy_independence_check(P, repeated_mult, point_to_mult):
                 if len(source) == n+2:
                     return source, corresponding
 
+
 def conjugating_set_helper(f, g, num_cpus, source, possible_targets):
     r"""
     Return the set of elements in PGL over the base ring
@@ -2270,6 +2283,7 @@ def find_conjugations_arrangement(tuples):
         Conj = find_conjugations_subset(product(*subset_iterators))
     return Conj
 
+
 def is_conjugate_helper(f, g, num_cpus, source, possible_targets):
     r"""
     Return if ``f`` is conjugate to ``g``.
diff --git a/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py b/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
index c8528c4821f..902f83b55ae 100644
--- a/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
+++ b/src/sage/dynamics/arithmetic_dynamics/endPN_minimal_model.py
@@ -473,6 +473,8 @@ def Min(Fun, p, ubRes, conj, all_orbits=False):
 ###################################################
 
 #modification of Bruin-Molnar for all representatives
+
+
 def BM_all_minimal(vp, return_transformation=False, D=None):
     r"""
     Determine a representative in each `SL(2,\ZZ)` orbit with minimal
@@ -623,6 +625,8 @@ def BM_all_minimal(vp, return_transformation=False, D=None):
 ###################################################
 
 #find minimal model
+
+
 def HS_minimal(f, return_transformation=False, D=None):
     r"""
     Compute a minimal model for the given projective dynamical system.
@@ -713,6 +717,8 @@ def HS_minimal(f, return_transformation=False, D=None):
     return F
 
 #find all representatives of orbits for one prime
+
+
 def HS_all_minimal_p(p, f, m=None, return_transformation=False):
     r"""
     Find a representative in each distinct `SL(2,\ZZ)` orbit with
@@ -814,6 +820,8 @@ def HS_all_minimal_p(p, f, m=None, return_transformation=False):
         return [funct for funct, matr in reps]
 
 #find all representatives of orbits
+
+
 def HS_all_minimal(f, return_transformation=False, D=None):
     r"""
     Determine a representative in each `SL(2,\ZZ)` orbit with minimal resultant.
@@ -906,6 +914,7 @@ def HS_all_minimal(f, return_transformation=False, D=None):
 # Ben Hutz July 2018
 #####################################3
 
+
 def get_bound_dynamical(F, f, m=1, dynatomic=True, prec=53, emb=None):
     """
     The hyperbolic distance from `j` which must contain the smallest map.
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index a74efd9129a..8cd24f6611d 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -7026,6 +7026,7 @@ def Lattes_to_curve(self, return_conjugation=False, check_lattes=False):
             return (M, E)
         return E
 
+
 class DynamicalSystem_projective_field(DynamicalSystem_projective,
                                        SchemeMorphism_polynomial_projective_space_field):
 
@@ -9117,6 +9118,7 @@ def is_newton(self, return_conjugation=False):
         else:
             return Npoly.derivative(z) == (z - N_aff[0]).denominator()
 
+
 class DynamicalSystem_projective_finite_field(DynamicalSystem_projective_field,
                                               SchemeMorphism_polynomial_projective_space_finite_field):
 
diff --git a/src/sage/dynamics/cellular_automata/elementary.py b/src/sage/dynamics/cellular_automata/elementary.py
index 51f959ed237..1c91687db8c 100644
--- a/src/sage/dynamics/cellular_automata/elementary.py
+++ b/src/sage/dynamics/cellular_automata/elementary.py
@@ -25,6 +25,7 @@
 lazy_import("sage.plot.matrix_plot", "matrix_plot")
 from sage.misc.constant_function import ConstantFunction
 
+
 class ElementaryCellularAutomata(SageObject):
     r"""
     Elementary cellular automata.
diff --git a/src/sage/dynamics/cellular_automata/glca.py b/src/sage/dynamics/cellular_automata/glca.py
index ea84884755b..929f1131456 100644
--- a/src/sage/dynamics/cellular_automata/glca.py
+++ b/src/sage/dynamics/cellular_automata/glca.py
@@ -20,6 +20,7 @@
 from sage.typeset.ascii_art import AsciiArt
 from sage.typeset.unicode_art import UnicodeArt
 
+
 class GraftalLaceCellularAutomata(SageObject):
     r"""
     Graftal Lace Cellular Automata (GLCA).
diff --git a/src/sage/dynamics/complex_dynamics/mandel_julia.py b/src/sage/dynamics/complex_dynamics/mandel_julia.py
index f21ffca80e4..b95040c2da2 100644
--- a/src/sage/dynamics/complex_dynamics/mandel_julia.py
+++ b/src/sage/dynamics/complex_dynamics/mandel_julia.py
@@ -58,6 +58,7 @@
 
 EPS = 0.00001
 
+
 def mandelbrot_plot(f=None, **kwds):
     r"""
     Plot of the Mandelbrot set for a one parameter family of polynomial maps.
@@ -498,6 +499,7 @@ def kneading_sequence(theta):
         KS_str = ''.join(KS) + '*'
     return KS_str
 
+
 def julia_plot(f=None, **kwds):
     r"""
     Plots the Julia set of a given polynomial ``f``. Users can specify whether
diff --git a/src/sage/dynamics/finite_dynamical_system.py b/src/sage/dynamics/finite_dynamical_system.py
index d6cfc29feb7..441a498f608 100644
--- a/src/sage/dynamics/finite_dynamical_system.py
+++ b/src/sage/dynamics/finite_dynamical_system.py
@@ -678,6 +678,7 @@ def is_homomesic(self, h, average=None, find_average=False, elements=None):
             return True
         return orbavgs[0] == average
 
+
 class InvertibleDiscreteDynamicalSystem(DiscreteDynamicalSystem):
     r"""
     An invertible discrete dynamical system.
@@ -969,6 +970,7 @@ def inverse_evolution_default(self, x):
         """
         return self.orbit(x)[-1]
 
+
 class FiniteDynamicalSystem(DiscreteDynamicalSystem):
     r"""
     A finite discrete dynamical system.
@@ -1113,6 +1115,7 @@ def cycles(self):
                     break
         return cycs
 
+
 class InvertibleFiniteDynamicalSystem(InvertibleDiscreteDynamicalSystem, FiniteDynamicalSystem):
     r"""
     An invertible finite discrete dynamical system.
diff --git a/src/sage/dynamics/finite_dynamical_system_catalog.py b/src/sage/dynamics/finite_dynamical_system_catalog.py
index 74217178a29..c00083f56c4 100755
--- a/src/sage/dynamics/finite_dynamical_system_catalog.py
+++ b/src/sage/dynamics/finite_dynamical_system_catalog.py
@@ -28,6 +28,7 @@
         FiniteDynamicalSystem, InvertibleDiscreteDynamicalSystem, \
         InvertibleFiniteDynamicalSystem
 
+
 def permutation(pi, invertible=True):
     r"""
     Return the invertible finite discrete dynamical system
@@ -64,6 +65,7 @@ def permutation(pi, invertible=True):
     X = range(1, n+1)
     return InvertibleFiniteDynamicalSystem(X, pi, inverse=pi.inverse(), create_tuple=True)
 
+
 def one_line(xs):
     r"""
     Return the finite discrete dynamical system
@@ -148,6 +150,7 @@ def bitstring_rotation(n, ones=None):
         psi = lambda x: (x[-1],) + x[:-1]
     return InvertibleFiniteDynamicalSystem(X, phi, inverse=psi)
 
+
 def striker_sweep(E, predicate, elements, lazy=False):
     r"""
     Return the invertible finite discrete dynamical system
diff --git a/src/sage/dynamics/surface_dynamics_deprecation.py b/src/sage/dynamics/surface_dynamics_deprecation.py
index 9da8f1d0be3..8f6e37fe1b2 100644
--- a/src/sage/dynamics/surface_dynamics_deprecation.py
+++ b/src/sage/dynamics/surface_dynamics_deprecation.py
@@ -9,6 +9,7 @@
 "information at\n"                                                         \
 "    http://www.labri.fr/perso/vdelecro/surface-dynamics/latest/"
 
+
 def surface_dynamics_deprecation(name):
     r"""
     TESTS::
diff --git a/src/sage/groups/abelian_gps/abelian_aut.py b/src/sage/groups/abelian_gps/abelian_aut.py
index 7108f311a48..89551916589 100644
--- a/src/sage/groups/abelian_gps/abelian_aut.py
+++ b/src/sage/groups/abelian_gps/abelian_aut.py
@@ -205,6 +205,7 @@ def matrix(self):
         m.set_immutable()
         return m
 
+
 class AbelianGroupAutomorphismGroup_gap(CachedRepresentation,
                                         GroupMixinLibGAP,
                                         Group,
@@ -407,6 +408,7 @@ def is_subgroup_of(self, G):
             return False
         return G.gap().IsSubsemigroup(self).sage()
 
+
 class AbelianGroupAutomorphismGroup(AbelianGroupAutomorphismGroup_gap):
     r"""
     The full automorphism group of a finite abelian group.
@@ -467,6 +469,7 @@ def _repr_(self):
         """
         return "Full group of automorphisms of %s" % self.domain()
 
+
 class AbelianGroupAutomorphismGroup_subgroup(AbelianGroupAutomorphismGroup_gap):
     r"""
     Groups of automorphisms of abelian groups.
diff --git a/src/sage/groups/abelian_gps/abelian_group_gap.py b/src/sage/groups/abelian_gps/abelian_group_gap.py
index 199aa935f56..0c0d6a5f49b 100644
--- a/src/sage/groups/abelian_gps/abelian_group_gap.py
+++ b/src/sage/groups/abelian_gps/abelian_group_gap.py
@@ -39,6 +39,7 @@
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.categories.groups import Groups
 
+
 class AbelianGroupElement_gap(ElementLibGAP):
     r"""
     An element of an abelian group via libgap.
@@ -184,6 +185,7 @@ def order(self):
         """
         return self.gap().Order().sage()
 
+
 class AbelianGroupElement_polycyclic(AbelianGroupElement_gap):
     r"""
     An element of an abelian group using the GAP package ``Polycyclic``.
@@ -220,6 +222,7 @@ def exponents(self):
         """
         return tuple(self.gap().Exponents().sage())
 
+
 class AbelianGroup_gap(UniqueRepresentation, GroupMixinLibGAP, ParentLibGAP, AbelianGroupBase):
     r"""
     Finitely generated abelian groups implemented in GAP.
@@ -620,6 +623,7 @@ def subgroup(self, gens):
         gens = tuple([self(g) for g in gens])
         return AbelianGroupSubgroup_gap(self.ambient(), gens)
 
+
 class AbelianGroupGap(AbelianGroup_gap):
     r"""
     Abelian groups implemented using GAP.
@@ -730,6 +734,7 @@ def __reduce__(self):
         """
         return AbelianGroupGap, (self.gens_orders(),)
 
+
 class AbelianGroupSubgroup_gap(AbelianGroup_gap):
     r"""
     Subgroups of abelian groups with GAP.
@@ -879,6 +884,7 @@ def retract(self, x):
         """
         return self(x)
 
+
 class AbelianGroupQuotient_gap(AbelianGroup_gap):
     r"""
     Quotients of abelian groups by a subgroup.
diff --git a/src/sage/groups/finitely_presented_named.py b/src/sage/groups/finitely_presented_named.py
index 8b07c5af7df..940d761ef49 100644
--- a/src/sage/groups/finitely_presented_named.py
+++ b/src/sage/groups/finitely_presented_named.py
@@ -202,6 +202,7 @@ def FinitelyGeneratedAbelianPresentation(int_list):
     ret_rls = ret_rls + [x[0]**(-1)*x[1]**(-1)*x[0]*x[1] for x in gen_pairs]
     return FinitelyPresentedGroup(F, tuple(ret_rls))
 
+
 def FinitelyGeneratedHeisenbergPresentation(n=1, p=0):
     r"""
     Return a finite presentation of the Heisenberg group.
@@ -292,6 +293,7 @@ def commutator(a, b):
         rls += [w**p for w in F.gens()]
     return FinitelyPresentedGroup(F, tuple(rls))
 
+
 def DihedralPresentation(n):
     r"""
     Build the Dihedral group of order `2n` as a finitely presented group.
@@ -327,6 +329,7 @@ def DihedralPresentation(n):
     rls = F([1])**n, F([2])**2, (F([1])*F([2]))**2
     return FinitelyPresentedGroup( F, rls )
 
+
 def DiCyclicPresentation(n):
     r"""
     Build the dicyclic group of order `4n`, for `n \geq 2`, as a finitely
@@ -455,6 +458,7 @@ def QuaternionPresentation():
     rls = F([1])**4, F([2,2,-1,-1]), F([1,2,1,-2])
     return FinitelyPresentedGroup(F, rls)
 
+
 def AlternatingPresentation(n):
     r"""
     Build the Alternating group of order `n!/2` as a finitely presented group.
@@ -521,6 +525,7 @@ def KleinFourPresentation():
     rls = F([1])**2, F([2])**2, F([-1])*F([-2])*F([1])*F([2])
     return FinitelyPresentedGroup(F, rls)
 
+
 def BinaryDihedralPresentation(n):
     r"""
     Build a binary dihedral group of order `4n` as a finitely presented group.
@@ -561,6 +566,7 @@ def BinaryDihedralPresentation(n):
     rls = (x**-2 * y**2, x**-2 * z**n, x**-2 * x*y*z)
     return FinitelyPresentedGroup(F, rls)
 
+
 def CactusPresentation(n):
     r"""
     Build the `n`-fruit cactus group as a finitely presented group.
diff --git a/src/sage/groups/fqf_orthogonal.py b/src/sage/groups/fqf_orthogonal.py
index 5da64f03212..e5ebd06ccdb 100644
--- a/src/sage/groups/fqf_orthogonal.py
+++ b/src/sage/groups/fqf_orthogonal.py
@@ -381,6 +381,7 @@ def _repr_(self):
         """
         return "Group of isometries of \n%s\ngenerated by %s elements" % (self.invariant_form(), len(self.gens()))
 
+
 class ActionOnFqf(Action):
     r"""
     Action on a finite quadratic module.
diff --git a/src/sage/groups/indexed_free_group.py b/src/sage/groups/indexed_free_group.py
index ad484532f13..67a3308d787 100644
--- a/src/sage/groups/indexed_free_group.py
+++ b/src/sage/groups/indexed_free_group.py
@@ -137,6 +137,7 @@ def group_generators(self):
 
     gens = group_generators
 
+
 class IndexedFreeGroup(IndexedGroup, Group):
     """
     An indexed free group.
@@ -297,6 +298,7 @@ def to_word_list(self):
             return [ (k, sign(e)) for k,e in self._sorted_items()
                      for dummy in range(abs(e))]
 
+
 class IndexedFreeAbelianGroup(IndexedGroup, AbelianGroup):
     """
     An indexed free abelian group.
diff --git a/src/sage/groups/libgap_group.py b/src/sage/groups/libgap_group.py
index 09889de4af5..81c7b9dd1df 100644
--- a/src/sage/groups/libgap_group.py
+++ b/src/sage/groups/libgap_group.py
@@ -36,6 +36,7 @@
 from sage.groups.libgap_wrapper import ParentLibGAP, ElementLibGAP
 from sage.groups.libgap_mixin import GroupMixinLibGAP
 
+
 class GroupLibGAP(GroupMixinLibGAP, Group, ParentLibGAP):
 
     Element = ElementLibGAP
diff --git a/src/sage/groups/matrix_gps/finitely_generated_gap.py b/src/sage/groups/matrix_gps/finitely_generated_gap.py
index d3403f22f40..70f409b2b54 100644
--- a/src/sage/groups/matrix_gps/finitely_generated_gap.py
+++ b/src/sage/groups/matrix_gps/finitely_generated_gap.py
@@ -924,6 +924,7 @@ def invariants_of_degree(self, deg, chi=None, R=None):
                     break
         return list(inv)
 
+
 def _new_invariant_is_linearly_independent(F, invariants):
     """
     EXAMPLES::
diff --git a/src/sage/groups/matrix_gps/heisenberg.py b/src/sage/groups/matrix_gps/heisenberg.py
index f101c27153b..ed71925c5ed 100644
--- a/src/sage/groups/matrix_gps/heisenberg.py
+++ b/src/sage/groups/matrix_gps/heisenberg.py
@@ -26,6 +26,7 @@
 from sage.rings.integer_ring import ZZ
 from copy import copy
 
+
 class HeisenbergGroup(UniqueRepresentation, FinitelyGeneratedMatrixGroup_gap):
     r"""
     The Heisenberg group of degree `n`.
diff --git a/src/sage/groups/matrix_gps/homset.py b/src/sage/groups/matrix_gps/homset.py
index b9d25ae0727..02818275424 100644
--- a/src/sage/groups/matrix_gps/homset.py
+++ b/src/sage/groups/matrix_gps/homset.py
@@ -21,6 +21,7 @@
 from sage.misc.lazy_import import lazy_import
 from sage.misc.superseded import deprecation
 
+
 def is_MatrixGroupHomset(x):
     r"""
     Test whether ``x`` is a matrix group homset.
diff --git a/src/sage/groups/matrix_gps/morphism.py b/src/sage/groups/matrix_gps/morphism.py
index e2fc2e0fd59..e73ba7e945a 100644
--- a/src/sage/groups/matrix_gps/morphism.py
+++ b/src/sage/groups/matrix_gps/morphism.py
@@ -15,6 +15,7 @@
 
 from sage.misc.lazy_import import lazy_import
 
+
 def to_libgap(x):
     """
     Helper to convert ``x`` to a LibGAP matrix or matrix group
diff --git a/src/sage/groups/matrix_gps/named_group_gap.py b/src/sage/groups/matrix_gps/named_group_gap.py
index 699e351f06d..926ae0649a0 100644
--- a/src/sage/groups/matrix_gps/named_group_gap.py
+++ b/src/sage/groups/matrix_gps/named_group_gap.py
@@ -18,6 +18,7 @@
 from sage.groups.matrix_gps.matrix_group_gap import MatrixGroup_gap
 from sage.groups.matrix_gps.named_group import NamedMatrixGroup_generic
 
+
 class NamedMatrixGroup_gap(NamedMatrixGroup_generic, MatrixGroup_gap):
 
     def __init__(self, degree, base_ring, special, sage_name, latex_string,
diff --git a/src/sage/groups/perm_gps/cubegroup.py b/src/sage/groups/perm_gps/cubegroup.py
index 8eadbac39f1..7603da471f9 100644
--- a/src/sage/groups/perm_gps/cubegroup.py
+++ b/src/sage/groups/perm_gps/cubegroup.py
@@ -128,6 +128,7 @@
 #########################################################
 # written by Tom Boothby, placed in the public domain
 
+
 def xproj(x, y, z, r):
     r"""
     Return the `x`-projection of `(x,y,z)` rotated by `r`.
@@ -347,6 +348,7 @@ def create_poly(face, color):
     32: "rbd",
 }
 
+
 def index2singmaster(facet):
     """
     Translate index used (eg, 43) to Singmaster facet notation (eg,
diff --git a/src/sage/matrix/benchmark.py b/src/sage/matrix/benchmark.py
index 8567f869511..b411de7d119 100644
--- a/src/sage/matrix/benchmark.py
+++ b/src/sage/matrix/benchmark.py
@@ -121,6 +121,7 @@ def report_ZZ(**kwds):
 
 # Integer Nullspace
 
+
 def nullspace_ZZ(n=200, min=0, max=2**32, system='sage'):
     """
     Nullspace over ZZ:
@@ -240,6 +241,7 @@ def rank_ZZ(n=700, min=0, max=9, system='sage'):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def rank2_ZZ(n=400, min=0, max=2**64, system='sage'):
     """
     Rank 2 over ZZ:
@@ -281,6 +283,7 @@ def rank2_ZZ(n=400, min=0, max=2**64, system='sage'):
 
 # Smith Form
 
+
 def smithform_ZZ(n=128, min=0, max=9, system='sage'):
     """
     Smith Form over ZZ:
@@ -366,6 +369,7 @@ def matrix_multiply_ZZ(n=300, min=-9, max=9, system='sage', times=1):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def matrix_add_ZZ(n=200, min=-9, max=9, system='sage', times=50):
     """
     Matrix addition over ZZ
@@ -413,6 +417,7 @@ def matrix_add_ZZ(n=200, min=-9, max=9, system='sage', times=50):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def matrix_add_ZZ_2(n=200, bits=16, system='sage', times=50):
     """
     Matrix addition over ZZ.
@@ -435,6 +440,7 @@ def matrix_add_ZZ_2(n=200, bits=16, system='sage', times=50):
     b = 2**bits
     return matrix_add_ZZ(n=n, min=-b, max=b,system=system, times=times)
 
+
 def det_ZZ(n=200, min=1, max=100, system='sage'):
     """
     Dense integer determinant over ZZ.
@@ -602,6 +608,7 @@ def report_GF(p=16411, **kwds):
 
 # Nullspace over GF
 
+
 def nullspace_GF(n=300, p=16411, system='sage'):
     """
     Given a n+1 x n  matrix over GF(p) with random
@@ -679,6 +686,7 @@ def charpoly_GF(n=100, p=16411, system='sage'):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def matrix_add_GF(n=1000, p=16411, system='sage',times=100):
     """
     Given two n x n matrix over GF(p) with random entries, add them.
@@ -805,6 +813,7 @@ def rank_GF(n=500, p=16411, system='sage'):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def rank2_GF(n=500, p=16411, system='sage'):
     """
     Rank over GF(p): Given a (n + 10) x n matrix over GF(p) with
@@ -842,6 +851,7 @@ def rank2_GF(n=500, p=16411, system='sage'):
     else:
         raise ValueError('unknown system "%s"' % system)
 
+
 def det_GF(n=400, p=16411 , system='sage'):
     """
     Dense determinant over GF(p).
@@ -905,6 +915,7 @@ def hilbert_matrix(n):
 
 # Reduced row echelon form over QQ
 
+
 def echelon_QQ(n=100, min=0, max=9, system='sage'):
     """
     Given a n x (2*n) matrix over QQ with random integer entries
@@ -945,6 +956,7 @@ def echelon_QQ(n=100, min=0, max=9, system='sage'):
 
 # Invert a matrix over QQ.
 
+
 def inverse_QQ(n=100, min=0, max=9, system='sage'):
     """
     Given a n x n matrix over QQ with random integer entries
@@ -1067,6 +1079,8 @@ def det_hilbert_QQ(n=80, system='sage'):
         return float(magma.eval('s'))
 
 # inverse of Hilbert matrix
+
+
 def invert_hilbert_QQ(n=40, system='sage'):
     """
     Run the benchmark for calculating the inverse of the hilbert
@@ -1101,6 +1115,7 @@ def invert_hilbert_QQ(n=40, system='sage'):
         magma.eval(code)
         return float(magma.eval('s'))
 
+
 def MatrixVector_QQ(n=1000,h=100,system='sage',times=1):
     """
     Compute product of square ``n`` matrix by random vector with num and
diff --git a/src/sage/matrix/matrix_integer_dense_saturation.py b/src/sage/matrix/matrix_integer_dense_saturation.py
index b537b041e08..fdd812597f5 100644
--- a/src/sage/matrix/matrix_integer_dense_saturation.py
+++ b/src/sage/matrix/matrix_integer_dense_saturation.py
@@ -68,6 +68,7 @@ def p_saturation(A, p, proof=True):
         H = H.stack(C).hermite_form(include_zero_rows=False, proof=proof)
     verbose("done saturating", tm)
 
+
 def random_sublist_of_size(k, n):
     """
     INPUT:
@@ -181,6 +182,7 @@ def solve_system_with_difficult_last_row(B, A):
     verbose("Done getting linear combinations.", tm)
     return X
 
+
 def saturation(A, proof=True, p=0, max_dets=5):
     r"""
     Compute a saturation matrix of `A`.
@@ -283,6 +285,7 @@ def saturation(A, proof=True, p=0, max_dets=5):
     C = solve_system_with_difficult_last_row(B, A)
     return C.change_ring(ZZ)._insert_zero_columns(zero_cols)
 
+
 def index_in_saturation(A, proof=True):
     r"""
     The index of A in its saturation.
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index 267a818c433..2ba59292d54 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -2664,6 +2664,7 @@ def _from_dict(self, d, coerce=True, remove_zeros=True):
         """
         return self.element_class(self, d, coerce=coerce)
 
+
 def dict_to_list(entries, nrows, ncols):
     r"""
     Given a dictionary of coordinate tuples, return the list given by
diff --git a/src/sage/rings/asymptotic/growth_group.py b/src/sage/rings/asymptotic/growth_group.py
index cf9cf74ca70..ca2afc2b92c 100644
--- a/src/sage/rings/asymptotic/growth_group.py
+++ b/src/sage/rings/asymptotic/growth_group.py
@@ -3671,6 +3671,7 @@ def non_growth_group(self):
         J = ImaginaryGroup(self.base())
         return self._non_growth_group_class_(J, self._var_)
 
+
 class MonomialGrowthGroupFunctor(AbstractGrowthGroupFunctor):
     r"""
     A :class:`construction functor <sage.categories.pushout.ConstructionFunctor>`
diff --git a/src/sage/rings/asymptotic/growth_group_cartesian.py b/src/sage/rings/asymptotic/growth_group_cartesian.py
index 0bdb3d4a1eb..19bb7d975a6 100644
--- a/src/sage/rings/asymptotic/growth_group_cartesian.py
+++ b/src/sage/rings/asymptotic/growth_group_cartesian.py
@@ -253,6 +253,8 @@ def create_object(self, version, args, **kwds):
 
 from sage.combinat.posets.cartesian_product import CartesianProductPoset
 from .growth_group import GenericGrowthGroup
+
+
 class GenericProduct(CartesianProductPoset, GenericGrowthGroup):
     r"""
     A Cartesian product of growth groups.
diff --git a/src/sage/rings/complex_interval_field.py b/src/sage/rings/complex_interval_field.py
index 0b6981cf07b..c090d6cdae2 100644
--- a/src/sage/rings/complex_interval_field.py
+++ b/src/sage/rings/complex_interval_field.py
@@ -49,6 +49,8 @@
 from sage.structure.parent import Parent
 
 cache = {}
+
+
 def ComplexIntervalField(prec=53, names=None):
     """
     Return the complex interval field with real and imaginary parts having
diff --git a/src/sage/rings/finite_rings/conway_polynomials.py b/src/sage/rings/finite_rings/conway_polynomials.py
index ff5873ee14b..70a851990ad 100644
--- a/src/sage/rings/finite_rings/conway_polynomials.py
+++ b/src/sage/rings/finite_rings/conway_polynomials.py
@@ -64,6 +64,7 @@ def conway_polynomial(p, n):
     except KeyError:
         raise RuntimeError("requested Conway polynomial not in database.")
 
+
 def exists_conway_polynomial(p, n):
     """
     Check whether the Conway polynomial of degree `n` over ``GF(p)``
@@ -99,6 +100,7 @@ def exists_conway_polynomial(p, n):
     except ImportError:
         return False
 
+
 class PseudoConwayLattice(WithEqualityById, SageObject):
     r"""
     A pseudo-Conway lattice over a given finite prime field.
@@ -328,6 +330,7 @@ def _find_pow_of_frobenius(p, n, x, y):
         raise RuntimeError("No appropriate power of Frobenius found")
     return mod(i, n)
 
+
 def _crt_non_coprime(running, a):
     """
     Extension of the ``crt`` method of ``IntegerMod`` to the case of
@@ -361,6 +364,7 @@ def _crt_non_coprime(running, a):
                 a_modulus = a_val_unit[1]
         return (running % running_modulus).crt(a % a_modulus)
 
+
 def _frobenius_shift(K, generators, check_only=False):
     """
     Given a field `K` of degree `n` over ``GF(p)`` and a dictionary
diff --git a/src/sage/rings/finite_rings/finite_field_pari_ffelt.py b/src/sage/rings/finite_rings/finite_field_pari_ffelt.py
index 9549dbc94b4..6bc637c94b3 100644
--- a/src/sage/rings/finite_rings/finite_field_pari_ffelt.py
+++ b/src/sage/rings/finite_rings/finite_field_pari_ffelt.py
@@ -21,6 +21,7 @@
 from .finite_field_base import FiniteField
 from .finite_field_constructor import GF
 
+
 class FiniteField_pari_ffelt(FiniteField):
     """
     Finite fields whose cardinality is a prime power (not a prime),
diff --git a/src/sage/rings/finite_rings/galois_group.py b/src/sage/rings/finite_rings/galois_group.py
index 32e23a40c44..1cdd70fcbb2 100644
--- a/src/sage/rings/finite_rings/galois_group.py
+++ b/src/sage/rings/finite_rings/galois_group.py
@@ -8,6 +8,7 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.finite_rings.hom_finite_field import FiniteFieldHomomorphism_generic, FrobeniusEndomorphism_finite_field
 
+
 class GaloisGroup_GFElement(AbelianGroupElement):
     def as_hom(self):
         r"""
@@ -52,6 +53,7 @@ def fixed_field(self):
         """
         return self.as_hom().fixed_field()
 
+
 class GaloisGroup_GF(GaloisGroup_cyc):
     r"""
     The Galois group of a finite field.
diff --git a/src/sage/rings/finite_rings/homset.py b/src/sage/rings/finite_rings/homset.py
index 6c15d725f43..617f9da0086 100644
--- a/src/sage/rings/finite_rings/homset.py
+++ b/src/sage/rings/finite_rings/homset.py
@@ -43,6 +43,7 @@
 from sage.rings.morphism import RingHomomorphism_im_gens
 from sage.structure.sequence import Sequence
 
+
 class FiniteFieldHomset(RingHomset_generic):
     """
     Set of homomorphisms with domain a given finite field.
diff --git a/src/sage/rings/finite_rings/maps_finite_field.py b/src/sage/rings/finite_rings/maps_finite_field.py
index e68bd5c7b94..dff8679dd1e 100644
--- a/src/sage/rings/finite_rings/maps_finite_field.py
+++ b/src/sage/rings/finite_rings/maps_finite_field.py
@@ -21,6 +21,7 @@
 
 from sage.categories.morphism import Morphism
 
+
 class FiniteFieldVectorSpaceIsomorphism(Morphism):
     """
     Base class of the vector space isomorphism between a finite field
@@ -70,6 +71,7 @@ def is_surjective(self):
         """
         return True
 
+
 class MorphismVectorSpaceToFiniteField(FiniteFieldVectorSpaceIsomorphism):
     """
     Isomorphisms from vector spaces to finite fields.
@@ -130,6 +132,7 @@ def _call_(self, v):
                 w[i*n:(i+1)*n] = v[i]._vector_()
             return E(w * self._C)
 
+
 class MorphismFiniteFieldToVectorSpace(FiniteFieldVectorSpaceIsomorphism):
     """
     Isomorphisms from finite fields to vector spaces
diff --git a/src/sage/rings/function_field/constructor.py b/src/sage/rings/function_field/constructor.py
index a316c384bd1..098da7b59da 100644
--- a/src/sage/rings/function_field/constructor.py
+++ b/src/sage/rings/function_field/constructor.py
@@ -39,6 +39,7 @@
 
 from sage.structure.factory import UniqueFactory
 
+
 class FunctionFieldFactory(UniqueFactory):
     """
     Return the function field in one variable with constant field ``F``. The
diff --git a/src/sage/rings/function_field/divisor.py b/src/sage/rings/function_field/divisor.py
index 13247abe3b0..8c72b4cdb98 100644
--- a/src/sage/rings/function_field/divisor.py
+++ b/src/sage/rings/function_field/divisor.py
@@ -74,6 +74,7 @@
 
 from .place import PlaceSet
 
+
 def divisor(field, data):
     """
     Construct a divisor from the data.
@@ -98,6 +99,7 @@ def divisor(field, data):
     divisor_group = field.divisor_group()
     return divisor_group.element_class(divisor_group, data)
 
+
 def prime_divisor(field, place, m=1):
     """
     Construct a prime divisor from the place.
diff --git a/src/sage/rings/function_field/drinfeld_modules/charzero_drinfeld_module.py b/src/sage/rings/function_field/drinfeld_modules/charzero_drinfeld_module.py
index d183848f296..06a0afdaa41 100644
--- a/src/sage/rings/function_field/drinfeld_modules/charzero_drinfeld_module.py
+++ b/src/sage/rings/function_field/drinfeld_modules/charzero_drinfeld_module.py
@@ -31,6 +31,7 @@
 
 lazy_import('sage.rings.lazy_series_ring', 'LazyPowerSeriesRing')
 
+
 class DrinfeldModule_charzero(DrinfeldModule):
     r"""
     This class implements Drinfeld `\mathbb{F}_q[T]`-modules defined
diff --git a/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py b/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
index d225820ab18..c4ad9f1376d 100644
--- a/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
+++ b/src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
@@ -46,6 +46,7 @@
 
 lazy_import('sage.rings.ring_extension', 'RingExtension_generic')
 
+
 class DrinfeldModule(Parent, UniqueRepresentation):
     r"""
     This class implements Drinfeld `\mathbb{F}_q[T]`-modules.
diff --git a/src/sage/rings/function_field/valuation.py b/src/sage/rings/function_field/valuation.py
index a192a76beb6..e92600e55b6 100644
--- a/src/sage/rings/function_field/valuation.py
+++ b/src/sage/rings/function_field/valuation.py
@@ -157,6 +157,7 @@
 from sage.rings.valuation.trivial_valuation import TrivialValuation
 from sage.rings.valuation.mapped_valuation import FiniteExtensionFromLimitValuation, MappedValuation_base
 
+
 class FunctionFieldValuationFactory(UniqueFactory):
     r"""
     Create a valuation on ``domain`` corresponding to ``prime``.
diff --git a/src/sage/rings/function_field/valuation_ring.py b/src/sage/rings/function_field/valuation_ring.py
index e1fe9751b0b..9269d21ea2d 100644
--- a/src/sage/rings/function_field/valuation_ring.py
+++ b/src/sage/rings/function_field/valuation_ring.py
@@ -72,6 +72,7 @@
 from sage.categories.homset import Hom
 from sage.categories.rings import Rings
 
+
 class FunctionFieldValuationRing(UniqueRepresentation, Parent):
     """
     Base class for valuation rings of function fields.
diff --git a/src/sage/rings/ideal.py b/src/sage/rings/ideal.py
index 4208c63c55c..dc785891828 100644
--- a/src/sage/rings/ideal.py
+++ b/src/sage/rings/ideal.py
@@ -1457,6 +1457,7 @@ def divides(self, other):
             return self.gen().divides(other.gen())
         raise NotImplementedError
 
+
 class Ideal_pid(Ideal_principal):
     """
     An ideal of a principal ideal domain.
@@ -1694,6 +1695,7 @@ def residue_field(self):
             return ZZ.residue_field(self, check=False)
         raise NotImplementedError("residue_field() is only implemented for ZZ and rings of integers of number fields.")
 
+
 class Ideal_fractional(Ideal_generic):
     """
     Fractional ideal of a ring.
@@ -1717,6 +1719,7 @@ def _repr_(self):
 # constructors for standard (benchmark) ideals, written uppercase as
 # these are constructors
 
+
 def Cyclic(R, n=None, homog=False, singular=None):
     """
     Ideal of cyclic ``n``-roots from 1-st ``n`` variables of ``R`` if ``R`` is
@@ -1782,6 +1785,7 @@ def Cyclic(R, n=None, homog=False, singular=None):
         I = singular.cyclic(n).homog(R2.gen(n-1))
     return R2.ideal(I).change_ring(R)
 
+
 def Katsura(R, n=None, homog=False, singular=None):
     r"""
     `n`-th katsura ideal of `R` if `R` is coercible to
@@ -1832,6 +1836,7 @@ def Katsura(R, n=None, homog=False, singular=None):
         I = singular.katsura(n).homog(R2.gen(n-1))
     return R2.ideal(I).change_ring(R)
 
+
 def FieldIdeal(R):
     r"""
     Let ``q = R.base_ring().order()`` and `(x_0,...,x_n)` ``= R.gens()`` then
diff --git a/src/sage/rings/lazy_series.py b/src/sage/rings/lazy_series.py
index 8520ad33f68..b48e0e6bc38 100644
--- a/src/sage/rings/lazy_series.py
+++ b/src/sage/rings/lazy_series.py
@@ -4866,6 +4866,7 @@ def _format_series(self, formatter, format_strings=False):
             return strformat("O({})".format(formatter(z**m)))
         return formatter(poly) + strformat(" + O({})".format(formatter(z**m)))
 
+
 class LazyPowerSeries(LazyCauchyProductSeries):
     r"""
     A Taylor series where the coefficients are computed lazily.
@@ -6149,6 +6150,7 @@ def _floordiv_(self, other):
                 left._approximate_order += 1
         return super()._floordiv_(other)
 
+
 class LazyPowerSeries_gcd_mixin:
     """
     A lazy power series that also implements the GCD algorithm.
@@ -6266,6 +6268,7 @@ def xgcd(self, f):
         unit = ~unit
         return (x**val, unit, unit)
 
+
 class LazyCompletionGradedAlgebraElement(LazyCauchyProductSeries):
     """
     An element of a completion of a graded algebra that is computed lazily.
diff --git a/src/sage/rings/lazy_series_ring.py b/src/sage/rings/lazy_series_ring.py
index ee3e463e988..7c61f8861b3 100644
--- a/src/sage/rings/lazy_series_ring.py
+++ b/src/sage/rings/lazy_series_ring.py
@@ -93,6 +93,7 @@
 
 from types import GeneratorType
 
+
 class LazySeriesRing(UniqueRepresentation, Parent):
     """
     Abstract base class for lazy series.
@@ -1233,6 +1234,7 @@ def _test_revert(self, **options):
         # we want to test at least 2 elements
         tester.assertGreater(count, 1, msg="only %s elements in %s.some_elements() have a compositional inverse" % (count, self))
 
+
 class LazyLaurentSeriesRing(LazySeriesRing):
     r"""
     The ring of lazy Laurent series.
@@ -3040,6 +3042,7 @@ def some_elements(self):
 
 ######################################################################
 
+
 class LazySymmetricFunctions(LazyCompletionGradedAlgebra):
     """
     The ring of lazy symmetric functions.
@@ -3417,6 +3420,7 @@ def _monomial(self, c, n):
         except (ValueError, TypeError):
             return '({})/{}^{}'.format(self.base_ring()(c), n, self.variable_name())
 
+
 def _skip_leading_zeros(iterator):
     """
     Return an iterator which discards all leading zeros.
diff --git a/src/sage/rings/monomials.py b/src/sage/rings/monomials.py
index ed154ab8c06..b10d599b6b3 100644
--- a/src/sage/rings/monomials.py
+++ b/src/sage/rings/monomials.py
@@ -1,5 +1,6 @@
 "Monomials"
 
+
 def _monomials(gens, R, n, i):
     """
     Given two lists ``gens`` and ``n`` of exactly the same length,
diff --git a/src/sage/rings/polynomial/complex_roots.py b/src/sage/rings/polynomial/complex_roots.py
index 0c94bac6035..42cf47cad86 100644
--- a/src/sage/rings/polynomial/complex_roots.py
+++ b/src/sage/rings/polynomial/complex_roots.py
@@ -90,6 +90,7 @@ def interval_roots(p, rts, prec):
 
     return irts
 
+
 def intervals_disjoint(intvs):
     """
     Given a list of complex intervals, check whether they are pairwise
diff --git a/src/sage/rings/polynomial/ideal.py b/src/sage/rings/polynomial/ideal.py
index 9eba00860b5..bf575cb0339 100644
--- a/src/sage/rings/polynomial/ideal.py
+++ b/src/sage/rings/polynomial/ideal.py
@@ -19,6 +19,7 @@
 
 from sage.rings.ideal import Ideal_pid
 
+
 class Ideal_1poly_field(Ideal_pid):
     """
     An ideal in a univariate polynomial ring over a field.
diff --git a/src/sage/rings/polynomial/laurent_polynomial_ideal.py b/src/sage/rings/polynomial/laurent_polynomial_ideal.py
index ae21901fee1..0403526ae15 100644
--- a/src/sage/rings/polynomial/laurent_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/laurent_polynomial_ideal.py
@@ -26,6 +26,7 @@
 from sage.structure.richcmp import op_EQ, op_NE, op_LT, op_LE, op_GT, op_GE
 from sage.arith.misc import GCD
 
+
 class LaurentPolynomialIdeal( Ideal_generic ):
     def __init__(self, ring, gens, coerce=True, hint=None):
         r"""
diff --git a/src/sage/rings/polynomial/laurent_polynomial_ring.py b/src/sage/rings/polynomial/laurent_polynomial_ring.py
index 40b09bbfb6e..2e4cf5ce6ea 100644
--- a/src/sage/rings/polynomial/laurent_polynomial_ring.py
+++ b/src/sage/rings/polynomial/laurent_polynomial_ring.py
@@ -77,6 +77,8 @@ def is_LaurentPolynomialRing(R):
 
 
 _cache = {}
+
+
 def LaurentPolynomialRing(base_ring, *args, **kwds):
     r"""
     Return the globally unique univariate or multivariate Laurent polynomial
@@ -251,6 +253,7 @@ def LaurentPolynomialRing(base_ring, *args, **kwds):
     _cache[R] = P
     return P
 
+
 def _split_dict_(D, indices, group_by=None):
     r"""
     Split the dictionary ``D`` by ``indices`` and ``group_by``.
@@ -331,6 +334,7 @@ def extract(T, indices):
     else:
         return result
 
+
 def _split_laurent_polynomial_dict_(P, M, d):
     r"""
     Helper function for splitting a multivariate Laurent polynomial
@@ -391,6 +395,7 @@ def value(d, R):
     return sum(P({k: 1}) * value(v, P)
                for k, v in D.items()).monomial_coefficients()
 
+
 def from_fraction_field(L, x):
     r"""
     Helper function to construct a Laurent polynomial from an element of its
diff --git a/src/sage/rings/polynomial/laurent_polynomial_ring_base.py b/src/sage/rings/polynomial/laurent_polynomial_ring_base.py
index b4f4f13289e..d9984a656b1 100644
--- a/src/sage/rings/polynomial/laurent_polynomial_ring_base.py
+++ b/src/sage/rings/polynomial/laurent_polynomial_ring_base.py
@@ -30,6 +30,7 @@
 from sage.structure.parent import Parent
 from sage.combinat.integer_vector import IntegerVectors
 
+
 class LaurentPolynomialRing_generic(CommutativeRing, Parent):
     """
     Laurent polynomial ring (base class).
diff --git a/src/sage/rings/polynomial/msolve.py b/src/sage/rings/polynomial/msolve.py
index fb22236fba9..d261bfd70b9 100644
--- a/src/sage/rings/polynomial/msolve.py
+++ b/src/sage/rings/polynomial/msolve.py
@@ -33,6 +33,7 @@
 from sage.rings.real_mpfi import RealIntervalField_class, RealIntervalField
 from sage.structure.sequence import Sequence
 
+
 def _run_msolve(ideal, options):
     r"""
     Internal utility function
@@ -63,6 +64,7 @@ def _run_msolve(ideal, options):
 
     return msolve_out.stdout
 
+
 def groebner_basis_degrevlex(ideal, proof=True):
     r"""
     Compute a degrevlex Gröbner basis using msolve
@@ -111,6 +113,7 @@ def groebner_basis_degrevlex(ideal, proof=True):
     gbasis = sage_eval(msolve_out[:-2], locals=drlpolring.gens_dict())
     return Sequence(gbasis)
 
+
 def variety(ideal, ring, *, proof=True):
     r"""
     Compute the variety of a zero-dimensional ideal using msolve.
diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
index 222da435df2..8e358652be3 100644
--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
@@ -450,6 +450,7 @@ def _groebner_basis_magma(self, deg_bound=None, prot=False, magma=magma_default)
         B = PolynomialSequence([R(e) for e in mgb], R, immutable=True)
         return B
 
+
 class MPolynomialIdeal_singular_base_repr:
     @require_field
     def syzygy_module(self):
@@ -3493,6 +3494,7 @@ def _reduce_using_macaulay2(self, f):
         R = self.ring()
         return R(k)
 
+
 class NCPolynomialIdeal(MPolynomialIdeal_singular_repr, Ideal_nc):
     def __init__(self, ring, gens, coerce=True, side='left'):
         r"""
diff --git a/src/sage/rings/polynomial/multi_polynomial_sequence.py b/src/sage/rings/polynomial/multi_polynomial_sequence.py
index 37381c084ac..ff1ec275633 100644
--- a/src/sage/rings/polynomial/multi_polynomial_sequence.py
+++ b/src/sage/rings/polynomial/multi_polynomial_sequence.py
@@ -377,6 +377,7 @@ def PolynomialSequence(arg1, arg2=None, immutable=False, cr=False, cr_str=None):
     elif K.degree() > 1:
         return PolynomialSequence_gf2e(parts, ring, immutable=immutable, cr=cr, cr_str=cr_str)
 
+
 class PolynomialSequence_generic(Sequence_generic):
     def __init__(self, parts, ring, immutable=False, cr=False, cr_str=None):
         """
@@ -1257,6 +1258,7 @@ def is_groebner(self, singular=singular):
         """
         return self.ideal().basis_is_groebner()
 
+
 class PolynomialSequence_gf2(PolynomialSequence_generic):
     r"""
     Polynomial Sequences over `\GF{2}`.
diff --git a/src/sage/rings/polynomial/ore_function_element.py b/src/sage/rings/polynomial/ore_function_element.py
index fd871fa3b76..d858838f53c 100644
--- a/src/sage/rings/polynomial/ore_function_element.py
+++ b/src/sage/rings/polynomial/ore_function_element.py
@@ -715,6 +715,7 @@ def _call_(self, x):
             return numerator.leading_coefficient() / denominator.leading_coefficient()
         raise TypeError(f"{x} is not a constant function")
 
+
 class OreFunctionBaseringInjection(Morphism):
     r"""
     Representation of the canonical homomorphism from a field `k` into a Ore
diff --git a/src/sage/rings/polynomial/polynomial_element_generic.py b/src/sage/rings/polynomial/polynomial_element_generic.py
index c3df26200e2..7bbd4e611a9 100644
--- a/src/sage/rings/polynomial/polynomial_element_generic.py
+++ b/src/sage/rings/polynomial/polynomial_element_generic.py
@@ -1049,6 +1049,7 @@ def number_of_terms(self):
         """
         return len(self.__coeffs)
 
+
 class Polynomial_generic_domain(Polynomial, IntegralDomainElement):
     def __init__(self, parent, is_gen=False, construct=False):
         Polynomial.__init__(self, parent, is_gen=is_gen)
@@ -1082,6 +1083,7 @@ def is_unit(self):
             return False
         return self[0].is_unit()
 
+
 class Polynomial_generic_field(Polynomial_singular_repr,
                                Polynomial_generic_domain,
                                EuclideanDomainElement):
@@ -1588,6 +1590,7 @@ def _roots(self, secure, minval, hint):
 class Polynomial_generic_dense_cdv(Polynomial_generic_dense_inexact, Polynomial_generic_cdv):
     pass
 
+
 class Polynomial_generic_sparse_cdv(Polynomial_generic_sparse, Polynomial_generic_cdv):
     pass
 
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
index e12977e8464..027a8997067 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
@@ -262,6 +262,7 @@ def create_object(self, version, key):
 
 PolynomialQuotientRing = PolynomialQuotientRingFactory("PolynomialQuotientRing")
 
+
 def is_PolynomialQuotientRing(x):
     from sage.misc.superseded import deprecation
     deprecation(38266,
diff --git a/src/sage/rings/polynomial/term_order.py b/src/sage/rings/polynomial/term_order.py
index 1bed10ba867..cd5cad00f8f 100644
--- a/src/sage/rings/polynomial/term_order.py
+++ b/src/sage/rings/polynomial/term_order.py
@@ -539,6 +539,7 @@
     'block'         : block_description,
 }
 
+
 class TermOrder(SageObject):
     """
     A term order.
diff --git a/src/sage/rings/qqbar_decorators.py b/src/sage/rings/qqbar_decorators.py
index 7343a0b9b08..9abca887218 100644
--- a/src/sage/rings/qqbar_decorators.py
+++ b/src/sage/rings/qqbar_decorators.py
@@ -14,6 +14,7 @@
 
 from sage.misc.decorators import decorator_keywords, sage_wraps
 
+
 @decorator_keywords
 def handle_AA_and_QQbar(func):
     r"""
diff --git a/src/sage/rings/quotient_ring.py b/src/sage/rings/quotient_ring.py
index 4cf3979265f..f98322c2183 100644
--- a/src/sage/rings/quotient_ring.py
+++ b/src/sage/rings/quotient_ring.py
@@ -1545,6 +1545,7 @@ def _contains_(self, other):
         J = R.cover_ring().ideal(Igens)
         return other.lift() in J
 
+
 class QuotientRingIdeal_principal(ideal.Ideal_principal, QuotientRingIdeal_generic):
     r"""
     Specialized class for principal quotient-ring ideals.
diff --git a/src/sage/rings/ring_extension_homset.py b/src/sage/rings/ring_extension_homset.py
index d2c13a11f0e..1ba55906d9c 100644
--- a/src/sage/rings/ring_extension_homset.py
+++ b/src/sage/rings/ring_extension_homset.py
@@ -20,6 +20,7 @@
 from sage.rings.homset import RingHomset_generic
 from sage.rings.ring_extension_morphism import RingExtensionHomomorphism
 
+
 class RingExtensionHomset(RingHomset_generic):
     r"""
     A generic class for homsets between ring extensions.