gh-38858: autopep8 fixes for E302 in matrix,rings,groups,dynamics

    
as the next step towards activiting the check for E302 in our linter

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: #38858
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

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):
 

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`.

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``.

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.

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):
 

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.

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).

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

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.

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

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::

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.

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.