fix all pycodestyle E303 warnings in all folders c*

src/sage/calculus/calculus.py

@@ -2442,7 +2442,6 @@ def maxima_options(**kwds):
 syms_default = dict(syms_cur)
 
 
-
 def _find_var(name, interface=None):
     """
     Function to pass to Parser for constructing

src/sage/categories/affine_weyl_groups.py

@@ -14,7 +14,6 @@
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 
 
-
 class AffineWeylGroups(Category_singleton):
     """
     The category of affine Weyl groups

src/sage/categories/algebras_with_basis.py

@@ -274,7 +274,6 @@ def one(self):
             # version of module morphism, this would not take
             # advantage of the block structure
 
-
     class TensorProducts(TensorProductsCategory):
         """
         The category of algebras with basis constructed by tensor product of algebras with basis

src/sage/categories/category.py

@@ -1470,7 +1470,6 @@ def _test_category(self, **options):
 
     _cmp_key = _cmp_key
 
-
     ##########################################################################
     # Construction of the associated abstract classes for parents, elements, ...
     ##########################################################################
@@ -2817,7 +2816,6 @@ def _make_named_class(self, name, method_provider, cache=False, **options):
         self._make_named_class_cache[key] = result
         return result
 
-
     @abstract_method
     def _make_named_class_key(self, name):
         r"""

src/sage/categories/classical_crystals.py

@@ -107,7 +107,6 @@ def additional_structure(self):
         """
         return None
 
-
     class ParentMethods:
 
         def demazure_character(self, w, f=None):

src/sage/categories/coalgebras.py

@@ -79,7 +79,6 @@ def counit(self, x):
             and Hopf algebras using the counit.
             """
 
-
         @abstract_method
         def coproduct(self, x):
             """

src/sage/categories/complex_reflection_or_generalized_coxeter_groups.py

@@ -842,7 +842,6 @@ def is_reducible(self):
             """
             return not self.is_irreducible()
 
-
     class ElementMethods:
         def apply_simple_reflection_left(self, i):
             r"""

src/sage/categories/crystals.py

@@ -388,7 +388,6 @@ def __iter__(self, index_set=None, max_depth=float('inf')):
             R = RecursivelyEnumeratedSet(self.module_generators, succ, structure=None)
             return R.breadth_first_search_iterator(max_depth)
 
-
         def subcrystal(self, index_set=None, generators=None, max_depth=float("inf"),
                        direction="both", contained=None,
                        virtualization=None, scaling_factors=None,

src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py

@@ -44,7 +44,6 @@ def __init__(self, base_ring):
         CombinatorialFreeModule.__init__(self, base_ring, NonNegativeIntegers(),
                                          category=GradedHopfAlgebrasWithBasis(base_ring).Connected())
 
-
     @cached_method
     def one_basis(self):
         """

src/sage/categories/examples/sets_cat.py

@@ -149,9 +149,6 @@ def _element_constructor_(self, e):
     element_class = Integer
 
 
-
-
-
 from sage.misc.abstract_method import abstract_method
 class PrimeNumbers_Abstract(UniqueRepresentation, Parent):
     """
@@ -556,9 +553,6 @@ def _integer_(self, IntRing):
             return IntRing(self.value)
 
 
-
-
-
 #*************************************************************************#
 class PrimeNumbers_Facade(PrimeNumbers_Abstract):
     r"""

src/sage/categories/examples/with_realizations.py

@@ -303,7 +303,6 @@ def super_categories(self):
             return [A.Realizations(),
                     category.Realizations().WithBasis()]
 
-
         class ParentMethods:
 
             def from_set(self, *args):

src/sage/categories/filtered_hopf_algebras_with_basis.py

@@ -65,7 +65,6 @@ def super_categories(self):
             R = self.base_category().base_ring()
             return [HopfAlgebras(R).Filtered()]
 
-
     class Connected(CategoryWithAxiom_over_base_ring):
         class ParentMethods:
             @cached_method

src/sage/categories/finite_dimensional_algebras_with_basis.py

@@ -313,7 +313,6 @@ def semisimple_quotient(self):
             result.rename("Semisimple quotient of {}".format(self))
             return result
 
-
         @cached_method
         def center_basis(self):
             r"""
@@ -819,7 +818,6 @@ def peirce_summand(self, ei, ej):
             return self.submodule([self.from_vector(v) for v in ideal.basis()],
                                   already_echelonized=True)
 
-
         def peirce_decomposition(self, idempotents=None, check=True):
             r"""
             Return a Peirce decomposition of ``self``.

src/sage/categories/finite_dimensional_semisimple_algebras_with_basis.py

@@ -105,7 +105,6 @@ def central_orthogonal_idempotents(self):
             return tuple([x.lift()
                           for x in self.center().central_orthogonal_idempotents()])
 
-
     class Commutative(CategoryWithAxiom_over_base_ring):
 
         class ParentMethods:

src/sage/categories/generalized_coxeter_groups.py

@@ -68,7 +68,6 @@ def additional_structure(self):
         """
         return None
 
-
     class Finite(CategoryWithAxiom):
         """
         The category of finite generalized Coxeter groups.

src/sage/categories/graded_modules_with_basis.py

@@ -67,7 +67,6 @@ def degree_negation(self, element):
                                       for key, value in
                                       element.monomial_coefficients(copy=False).items()])
 
-
         def submodule(self, gens, check=True, already_echelonized=False,
                       unitriangular=False, support_order=None, category=None,
                       *args, **opts):

src/sage/categories/hecke_modules.py

@@ -84,7 +84,6 @@ def super_categories(self):
         R = self.base_ring()
         return [ModulesWithBasis(R)]
 
-
     def _repr_object_names(self):
         """
         Return the names of the objects of this category.

src/sage/categories/semigroups.py

@@ -510,7 +510,6 @@ def _pow_int(self, n):
                 raise ArithmeticError("only positive powers are supported in a semigroup")
             return generic_power(self, n)
 
-
     class SubcategoryMethods:
 
         @cached_method

src/sage/categories/sets_cat.py

@@ -2215,7 +2215,6 @@ def example(self):
             S3 = FiniteEnumeratedSets().example()
             return cartesian_product([S1, S2, S3])
 
-
         class ParentMethods:
             def __iter__(self):
                 r"""

src/sage/categories/topological_spaces.py

@@ -141,7 +141,6 @@ def extra_super_categories(self):
                 """
                 return [TopologicalSpaces().Connected()]
 
-
     class Compact(CategoryWithAxiom):
         """
         The category of compact topological spaces.

src/sage/categories/weyl_groups.py

@@ -349,7 +349,6 @@ def is_pieri_factor(self):
 
             return self in self.parent().pieri_factors()
 
-
         def left_pieri_factorizations(self, max_length=None):
             r"""
             Returns all factorizations of ``self`` as `uv`, where `u`
@@ -494,7 +493,6 @@ def stanley_symmetric_function_as_polynomial(self, max_length=None):
                            for (u,v) in self.left_pieri_factorizations(max_length)
                            if u != W.one()))
 
-
         def stanley_symmetric_function(self):
             r"""
             Return the affine Stanley symmetric function indexed by ``self``.

src/sage/coding/encoder.py

@@ -194,7 +194,6 @@ def __call__(self, m):
         """
         return self.encode(m)
 
-
     def unencode(self, c, nocheck=False):
         r"""
         Return the message corresponding to the codeword ``c``.

src/sage/coding/extended_code.py

@@ -179,14 +179,6 @@ def random_element(self):
         return vector(F, c_list)
 
 
-
-
-
-
-
-
-
-
 class ExtendedCodeExtendedMatrixEncoder(Encoder):
     r"""
     Encoder using original code's generator matrix to compute the extended code's one.
@@ -286,14 +278,6 @@ def generator_matrix(self):
         return M
 
 
-
-
-
-
-
-
-
-
 class ExtendedCodeOriginalCodeDecoder(Decoder):
     r"""
     Decoder which decodes through a decoder over the original code.

src/sage/coding/golay_code.py

@@ -396,8 +396,6 @@ def parity_check_matrix(self):
         return H
 
 
-
-
 ####################### registration ###############################
 
 GolayCode._registered_encoders["GeneratorMatrix"] = LinearCodeGeneratorMatrixEncoder

src/sage/coding/guruswami_sudan/gs_decoder.py

@@ -534,8 +534,6 @@ def gs_satisfactory(tau, s, l, C = None, n_k = None):
         n,k = n_k_params(C, n_k)
         return l > 0 and s > 0 and n * s * (s+1) < (l+1) * (2*s*(n-tau) - (k-1) * l)
 
-
-
     ####################### decoder itself ###############################
     def __init__(self, code, tau = None, parameters = None, interpolation_alg = None, root_finder = None):
         r"""
@@ -712,7 +710,6 @@ def parameters(self):
         """
         return (self._s, self._ell)
 
-
     def multiplicity(self):
         r"""
         Returns the multiplicity parameter of ``self``.

src/sage/coding/information_set_decoder.py

@@ -345,8 +345,6 @@ def _latex_(self):
         return "\\textnormal{{ISD Algorithm ({}) for }}{} \\textnormal{{decoding {} errors}}".format(self._algorithm_name, self.code()._latex_(), _format_decoding_interval(self.decoding_interval()))
 
 
-
-
 class LeeBrickellISDAlgorithm(InformationSetAlgorithm):
     r"""
     The Lee-Brickell algorithm for information-set decoding.
@@ -629,8 +627,6 @@ def _calibrate_select(self, estimates):
         self._time_estimate = estimates[search_size]
 
 
-
-
 class LinearCodeInformationSetDecoder(Decoder):
     r"""
     Information-set decoder for any linear code.

src/sage/coding/linear_code_no_metric.py

@@ -1148,7 +1148,6 @@ def __init__(self, code, systematic_positions=None):
             # Test that the systematic positions are an information set
             self.generator_matrix()
 
-
     def __eq__(self, other):
         r"""
         Tests equality between LinearCodeSystematicEncoder objects.

src/sage/coding/punctured_code.py

@@ -92,7 +92,6 @@ def _insert_punctured_positions(l, punctured_points, value = None):
     return final
 
 
-
 class PuncturedCode(AbstractLinearCode):
     r"""
     Representation of a punctured code.
@@ -425,13 +424,6 @@ def generator_matrix(self):
         return M
 
 
-
-
-
-
-
-
-
 class PuncturedCodeOriginalCodeDecoder(Decoder):
     r"""
     Decoder decoding through a decoder over the original code of its punctured code.
@@ -580,7 +572,6 @@ def _repr_(self):
         """
         return "Decoder of %s through %s" % (self.code(), self.original_decoder())
 
-
     def _latex_(self):
         r"""
         Returns a latex representation of ``self``.

src/sage/coding/self_dual_codes.py

@@ -606,7 +606,6 @@ def self_dual_binary_codes(n):
                   "6":self_dual_codes_18_6,"7":self_dual_codes_18_7,"8":self_dual_codes_18_8}
         return self_dual_codes
 
-
     if n == 20:
     # all of these of these are Type I; 2 of these codes
     # are formally equivalent but with different automorphism groups;

src/sage/combinat/designs/bibd.py

@@ -333,7 +333,6 @@ def balanced_incomplete_block_design(v, k, lambd=1, existence=False, use_LJCR=Fa
                 else:
                     return BIBD(B.ground_set(), B.blocks(), k=k, lambd=1, copy=False)
 
-
     if ( (k+lambd)*(k+lambd-1) == lambd*(v+k+lambd-1) and
          balanced_incomplete_block_design(v+k+lambd, k+lambd, lambd, existence=True) is True):
         # By removing a block and all points of that block from the
@@ -661,7 +660,6 @@ def BIBD_from_TD(v,k,existence=False):
     return BIBD
 
 
-
 def BIBD_from_difference_family(G, D, lambd=None, check=True):
     r"""
     Return the BIBD associated to the difference family ``D`` on the group ``G``.

src/sage/combinat/designs/database.py

@@ -543,7 +543,6 @@ def OA_8_69():
         for BB in OA_8_7:
             OA.append([B[i] for i in BB])
 
-
     # Adding the  missing 0..0,1..1,... rows
     done = sum(O1,[])+sum(O2,[])
     missing = [x for x in range(73) if x not in done and x not in oval]

src/sage/combinat/designs/difference_family.py

@@ -923,7 +923,6 @@ def radical_difference_family(K, k, l=1, existence=False, check=True):
         elif existence:
             return True
 
-
     if check and not is_difference_family(K, D, v, k, l):
         raise RuntimeError("radical_difference_family produced a wrong "
                            "difference family with parameters v={}, "
@@ -1805,7 +1804,6 @@ def supplementary_difference_set_from_rel_diff_set(q, existence=False, check=Tru
     psi1 = ((1 + P.monomial((q-1)//2)) * theta1).mod(P.monomial(q-1) - 1)
     psi2 = (1 + (1 + P.monomial((q-1)//2)) * theta2).mod(P.monomial(q-1) - 1)
 
-
     K1 = list(map(Integer, psi1.exponents()))
     K2 = list(map(Integer, psi2.exponents()))
     K3 = list(map(Integer, psi3.exponents()))

src/sage/combinat/designs/ext_rep.py

@@ -660,7 +660,6 @@ def __init__(self, node):
              ('block', {}, [[6, 8, 10]])]
         """
 
-
         if isinstance(node, str):
             node = (node, {}, [])
         name, attributes, children = node

src/sage/combinat/designs/incidence_structures.py

@@ -2000,7 +2000,6 @@ def is_resolvable(self, certificate=False, solver=None, verbose=0, check=True,
         else:
             return True
 
-
     def coloring(self, k=None, solver=None, verbose=0,
                  *, integrality_tolerance=1e-3):
         r"""

src/sage/combinat/designs/orthogonal_arrays_build_recursive.py

@@ -1604,7 +1604,6 @@ def brouwer_separable_design(k,t,q,x,check=False,verbose=False,explain_construct
         # The set of size x
         OA.extend([N-xx-1 for xx in B] for B in orthogonal_array(k,x))
 
-
     # iv)
     elif (x == q**2+1 and
           orthogonal_array( k  ,  x  ,existence=True) and # d0