gh-35151: fix all pycodestyle E303 warnings in all folders c*

    
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### 📚 Description

This fixes the pycodestyle warning

E303 too many blank lines (2)

inside all subfolders of sage whose name starts with c

Entirely done using autopep8.

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URL: #35151
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

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