gh-35355: partial fix for E221 (to be continued)

    
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### 📚 Description

Partial fix for pycodestyle E221, done using autopep8.

E221 multiple spaces before operator

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### ⌛ Dependencies

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URL: #35355
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

src/sage/algebras/rational_cherednik_algebra.py

@@ -237,7 +237,7 @@ def algebra_generators(self):
             sage: list(R.algebra_generators())
             [a1, a2, s1, s2, ac1, ac2]
         """
-        keys  = ['a'+str(i) for i in self._cartan_type.index_set()]
+        keys = ['a'+str(i) for i in self._cartan_type.index_set()]
         keys += ['s'+str(i) for i in self._cartan_type.index_set()]
         keys += ['ac'+str(i) for i in self._cartan_type.index_set()]
 

src/sage/algebras/splitting_algebra.py

@@ -217,7 +217,7 @@ def __init__(self, monic_polynomial, names='X', iterate=True, warning=True):
         deg = monic_polynomial.degree()
 
         from sage.structure.category_object import normalize_names
-        self._root_names  = normalize_names(deg-1, names)
+        self._root_names = normalize_names(deg-1, names)
         root_names = list(self._root_names)
         verbose("Create splitting algebra to base ring %s and polynomial %s (%s %s)"
                 % (base_ring, monic_polynomial, iterate, warning))
@@ -238,8 +238,8 @@ def __init__(self, monic_polynomial, names='X', iterate=True, warning=True):
         if deg < 1:
             raise ValueError("the degree of the polynomial must positive")
 
-        self._splitting_roots     = []
-        self._coefficients_list   = []
+        self._splitting_roots = []
+        self._coefficients_list = []
         self._invertible_elements = {}
 
         if isinstance(base_ring, SplittingAlgebra):
@@ -289,12 +289,12 @@ def __init__(self, monic_polynomial, names='X', iterate=True, warning=True):
 
             SplittingAlgebra.__init__(self, q, root_names_reduces, warning=False)
 
-            splitting_roots   = base_ring_step._splitting_roots   + self._splitting_roots
+            splitting_roots = base_ring_step._splitting_roots + self._splitting_roots
             coefficients_list = base_ring_step._coefficients_list + self._coefficients_list
 
             verbose("Adding roots: %s" % (splitting_roots))
 
-            self._splitting_roots   = splitting_roots
+            self._splitting_roots = splitting_roots
             self._coefficients_list = coefficients_list
         else:
             PolynomialQuotientRing_domain.__init__(self, P, p, root_name)
@@ -343,7 +343,7 @@ def __init__(self, monic_polynomial, names='X', iterate=True, warning=True):
         # ------------------------------------------------------------------
         if cf0_inv is not None:
             deg_cf = len(cf)-1
-            pf  =  P(cf)
+            pf =  P(cf)
             for root in self._splitting_roots:
                 check = self(pf)
                 if not check.is_zero():

src/sage/categories/algebra_functor.py

@@ -631,7 +631,7 @@ def _apply_functor_to_morphism(self, f):
             2*() + 2*(2,3) + (1,2,3) + 4*(1,3,2)
         """
         from sage.categories.rings import Rings
-        domain   = self(f.domain())
+        domain = self(f.domain())
         codomain = self(f.codomain())
         # we would want to use something like:
         # domain.module_morphism(on_coefficients=h, codomain=codomain, category=Rings())

src/sage/categories/cartesian_product.py

@@ -16,7 +16,7 @@
 from sage.categories.covariant_functorial_construction import CovariantFunctorialConstruction, CovariantConstructionCategory
 from sage.categories.pushout import MultivariateConstructionFunctor
 
-native_python_containers   = set([tuple, list, set, frozenset, range])
+native_python_containers = set([tuple, list, set, frozenset, range])
 
 class CartesianProductFunctor(CovariantFunctorialConstruction, MultivariateConstructionFunctor):
     """

src/sage/categories/category_with_axiom.py

@@ -2609,11 +2609,11 @@ def super_categories(self):
 
     class SubcategoryMethods:
         FiniteDimensional = axiom("FiniteDimensional")
-        Commutative       = axiom("Commutative")
-        Unital            = axiom("Unital")
-        Connected         = axiom("Connected")
-        Flying            = axiom("Flying")
-        Blue              = axiom("Blue")
+        Commutative = axiom("Commutative")
+        Unital = axiom("Unital")
+        Connected = axiom("Connected")
+        Flying = axiom("Flying")
+        Blue = axiom("Blue")
 
     class FiniteDimensional(CategoryWithAxiom):
         pass

src/sage/categories/covariant_functorial_construction.py

@@ -286,7 +286,7 @@ def _base_category_class(cls):
         """
         module_name = cls.__module__.replace(cls._functor_category.lower() + "_","")
         import sys
-        name   = cls.__name__.replace(cls._functor_category, "")
+        name = cls.__name__.replace(cls._functor_category, "")
         __import__(module_name)
         module = sys.modules[module_name]
         return (module.__dict__[name],)

src/sage/categories/distributive_magmas_and_additive_magmas.py

@@ -43,7 +43,7 @@ class AdditiveCommutative(CategoryWithAxiom):
             class AdditiveUnital(CategoryWithAxiom):
                 class Associative(CategoryWithAxiom):
                     AdditiveInverse = LazyImport('sage.categories.rngs', 'Rngs', at_startup=True)
-                    Unital          = LazyImport('sage.categories.semirings', 'Semirings', at_startup=True)
+                    Unital = LazyImport('sage.categories.semirings', 'Semirings', at_startup=True)
 
     class ParentMethods:
 

src/sage/categories/enumerated_sets.py

@@ -230,7 +230,7 @@ def __iter__(self):
             """
             # Check if .first() and .next(x) are overridden in the subclass
             if ( self.first != self._first_from_iterator and
-                 self.next  != self._next_from_iterator ):
+                 self.next != self._next_from_iterator ):
                 return self._iterator_from_next()
             #Check to see if .unrank() is overridden in the subclass
             elif self.unrank != self._unrank_from_iterator:
@@ -592,7 +592,7 @@ def list(self):
                 [1, 2, 3]
             """
             return list(self.tuple())
-        _list_default  = list # needed by the check system.
+        _list_default = list # needed by the check system.
 
         def _list_from_iterator(self):
             r"""
@@ -1108,7 +1108,7 @@ def rank(self):
             """
             return self.parent().rank(self)
 
-    Finite   = LazyImport('sage.categories.finite_enumerated_sets', 'FiniteEnumeratedSets', at_startup=True)
+    Finite = LazyImport('sage.categories.finite_enumerated_sets', 'FiniteEnumeratedSets', at_startup=True)
     Infinite = LazyImport('sage.categories.infinite_enumerated_sets', 'InfiniteEnumeratedSets', at_startup=True)
 
     class CartesianProducts(CartesianProductsCategory):

src/sage/categories/infinite_enumerated_sets.py

@@ -88,7 +88,7 @@ def list(self):
                 NotImplementedError: cannot list an infinite set
             """
             raise NotImplementedError("cannot list an infinite set")
-        _list_default  = list # needed by the check system.
+        _list_default = list # needed by the check system.
 
         def _test_enumerated_set_iter_cardinality(self, **options):
             """

src/sage/categories/quotient_fields.py

@@ -315,7 +315,7 @@ def xgcd(self, other):
                 return (P(g)/P(lcmD), P(s*selfD)/P(lcmD),P(t*otherD)/P(lcmD))
             except (AttributeError, NotImplementedError, TypeError, ValueError):
                 zero = self.parent().zero()
-                one  = self.parent().one()
+                one = self.parent().one()
                 if self != zero:
                     return (one, ~self, zero)
                 elif other != zero:
@@ -681,11 +681,11 @@ def _derivative(self, var=None):
                 try:
                     numder = num._derivative(var)
                     dender = den._derivative(var)
-                    d      = den.gcd(dender)
-                    den    = den // d
+                    d = den.gcd(dender)
+                    den = den // d
                     dender = dender // d
-                    tnum   = numder * den - num * dender
-                    tden   = self.denominator() * den
+                    tnum = numder * den - num * dender
+                    tden = self.denominator() * den
                     if not tden.is_one() and tden.is_unit():
                         try:
                             tnum = tnum * tden.inverse_of_unit()

src/sage/categories/semigroups.py

@@ -327,7 +327,7 @@ def cayley_graph(self, side="right", simple=False, elements=None,
                     generators = self.semigroup_generators()
             if isinstance(generators, (list, tuple)):
                 generators = dict((self(g), self(g)) for g in generators)
-            left  = (side == "left"  or side == "twosided")
+            left = (side == "left"  or side == "twosided")
             right = (side == "right" or side == "twosided")
 
             def add_edge(source, target, label, side_label):

src/sage/coding/channel.py

@@ -603,7 +603,7 @@ def transmit_unsafe(self, message):
         zero = V.base_ring().zero()
 
         errors = sample(range(n), number_errors + number_erasures)
-        error_positions   = errors[:number_errors]
+        error_positions = errors[:number_errors]
         erasure_positions = errors[number_errors:]
 
         error_vector = random_error_vector(n, V.base_ring(), error_positions)

src/sage/coding/code_bounds.py

@@ -656,7 +656,7 @@ def entropy_inverse(x, q=2):
     if q < 2:   # Here we check that q is actually at least 2
         raise ValueError("The value q must be an integer greater than 1")
 
-    eps  = 4.5e-16 # find_root has about this as the default xtol
+    eps = 4.5e-16 # find_root has about this as the default xtol
     ymax = 1 - 1/q
     if x <= eps:
         return 0

src/sage/coding/grs_code.py

@@ -1009,7 +1009,7 @@ def encode(self, p):
         C = self.code()
         if p.degree() >= C.dimension():
             raise ValueError("The polynomial to encode must have degree at most %s" % (C.dimension() - 1))
-        alphas    = C.evaluation_points()
+        alphas = C.evaluation_points()
         col_mults = C.column_multipliers()
         c = vector(C.base_ring(), [col_mults[i]*p(alphas[i]) for i in range(C.length())])
         return c
@@ -1057,7 +1057,7 @@ def unencode_nocheck(self, c):
 
         """
         C = self.code()
-        alphas    = C.evaluation_points()
+        alphas = C.evaluation_points()
         col_mults = C.column_multipliers()
 
         c = [c[i]/col_mults[i] for i in range(C.length())]
@@ -1229,14 +1229,14 @@ def _decode_to_code_and_message(self, r):
         r_list = copy(r)
         r_list = [r[i]/col_mults[i] for i in range(0, C.length())]
 
-        t  = (C.minimum_distance()-1) // 2
+        t = (C.minimum_distance()-1) // 2
         l0 = n-1-t
         l1 = n-1-t-(k-1)
-        S  = matrix(C.base_field(), n, l0+l1+2,
+        S = matrix(C.base_field(), n, l0+l1+2,
                     lambda i, j: (C.evaluation_points()[i])**j if j<(l0+1)
                     else r_list[i]*(C.evaluation_points()[i])**(j-(l0+1)))
-        S  = S.right_kernel()
-        S  = S.basis_matrix().row(0)
+        S = S.right_kernel()
+        S = S.basis_matrix().row(0)
         R = C.base_field()['x']
 
         Q0 = R(S.list_from_positions(range(l0 + 1)))

src/sage/combinat/cluster_algebra_quiver/mutation_type.py

@@ -763,7 +763,7 @@ def _connected_mutation_type(dg):
     elif len( exc_labels ) == 1:
         label = exc_labels[0]
         v_out = label[0]
-        v_in  = label[1]
+        v_in = label[1]
         label = label[2]
         if label == (1,-2):
             if dict_in_out[ v_in ][0] == 1 and dict_in_out[ v_in ][1] == 0:

src/sage/combinat/crystals/generalized_young_walls.py

@@ -452,7 +452,7 @@ def e(self, i):
         """
         signature = self.generate_signature(i)
         raw_signature = signature[0]
-        lastminus  = signature[1].rfind('-')
+        lastminus = signature[1].rfind('-')
         newdata = []
         if lastminus > -1:
             deletionrow = raw_signature[lastminus][1]
@@ -725,7 +725,7 @@ def in_highest_weight_crystal(self,La):
                 else:
                     p_not_found = True
                     for p in index_set:
-                        if (j+k) % (n+1)  == (p+1) % (n+1) and self.a(j,k) - self.a( (j-1) % (n+1) ,k) <= La.scalar(ac[p]):
+                        if (j+k) % (n+1) == (p+1) % (n+1) and self.a(j,k) - self.a( (j-1) % (n+1) ,k) <= La.scalar(ac[p]):
                             p_not_found = False
                             continue
                         else:

src/sage/combinat/designs/bibd.py

@@ -1372,15 +1372,15 @@ def BIBD_from_arc_in_desarguesian_projective_plane(n,k,existence=False):
     from sage.libs.gap.libgap import libgap
     from sage.matrix.constructor import Matrix
 
-    K   = GF(q,'a')
+    K = GF(q,'a')
     one = K.one()
 
     # An irreducible quadratic form over K[X,Y]
     GO = libgap.GeneralOrthogonalGroup(-1,2,q)
-    M  = libgap.InvariantQuadraticForm(GO)['matrix']
-    M  = Matrix(M)
-    M  = M.change_ring(K)
-    Q  = lambda xx,yy : M[0,0]*xx**2+(M[0,1]+M[1,0])*xx*yy+M[1,1]*yy**2
+    M = libgap.InvariantQuadraticForm(GO)['matrix']
+    M = Matrix(M)
+    M = M.change_ring(K)
+    Q = lambda xx,yy : M[0,0]*xx**2+(M[0,1]+M[1,0])*xx*yy+M[1,1]*yy**2
 
     # Here, the additive subgroup H (of order n) of K mentioned in
     # [Denniston69] is the set of all elements of K of degree < log_n

src/sage/combinat/designs/block_design.py

@@ -343,11 +343,11 @@ def DesarguesianProjectivePlaneDesign(n, point_coordinates=True, check=True):
     # we relabel the points with the integers from 0 to n^2 + n as follows:
     # - the affine plane is the set of points [x:y:1] (i.e. the third coordinate
     #   is non-zero) and gets relabeled from 0 to n^2-1
-    affine_plane   = lambda x,y: relabel[x] + n * relabel[y]
+    affine_plane = lambda x,y: relabel[x] + n * relabel[y]
 
     # - the affine line is the set of points [x:1:0] (i.e. the third coordinate is
     #   zero but not the second one) and gets relabeled from n^2 to n^2 + n - 1
-    line_infinity  = lambda x: n2 + relabel[x]
+    line_infinity = lambda x: n2 + relabel[x]
 
     # - the point is [1:0:0] and gets relabeled n^2 + n
     point_infinity = n2 + n
@@ -380,7 +380,7 @@ def DesarguesianProjectivePlaneDesign(n, point_coordinates=True, check=True):
 
     if point_coordinates:
         zero = K.zero()
-        one  = K.one()
+        one = K.one()
         d = {affine_plane(x,y): (x,y,one)
              for x in Kiter
              for y in Kiter}

src/sage/combinat/designs/database.py

@@ -514,7 +514,7 @@ def OA_8_69():
     PBD = [[x for x in B if x not in oval] for B in BIBD]
 
     sets_of_size_seven = [R for R in PBD if len(R) == 7]
-    others             = [R for R in PBD if len(R) != 7]
+    others = [R for R in PBD if len(R) != 7]
 
     # 68, 27, and 52 are the only elements appearing twice in the rows of
     # sets_of_size_seven, and each row contains exactly one of them.
@@ -628,7 +628,7 @@ def OA_8_76():
     PBD.remove([])
 
     sets_of_size_seven = [R for R in PBD if len(R) == 7]
-    others             = [R for R in PBD if len(R) != 7]
+    others = [R for R in PBD if len(R) != 7]
 
     # critical_points are the 10 elements appearing twice in the rows of the 10
     # sets_of_size_seven, and each row contains exactly two of them
@@ -1477,11 +1477,11 @@ def OA_17_560():
     """
     from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
     alpha = 5
-    beta  = 4
-    p     = 2
-    k     = 17
-    m     = 16
-    n     = p**alpha
+    beta = 4
+    p = 2
+    k = 17
+    m = 16
+    n = p**alpha
 
     G = GF((p, alpha), prefix='x')
     G_set = sorted(G) # sorted by lexicographic order, G[1] = 1
@@ -3694,7 +3694,7 @@ def DM_52_6_1():
         sage: _ = designs.difference_matrix(52,6)
     """
     from sage.rings.finite_rings.finite_field_constructor import FiniteField
-    F4  = FiniteField(4,'z')
+    F4 = FiniteField(4,'z')
     G13 = FiniteField(13)
     G = F4.cartesian_product(G13)
     z = F4('z')
@@ -3805,9 +3805,9 @@ def DM_56_8_1():
         sage: _ = designs.difference_matrix(56,8)
     """
     from sage.rings.finite_rings.finite_field_constructor import FiniteField
-    F8  = FiniteField(8,'z')
-    F7  = FiniteField(7)
-    G   = F8.cartesian_product(F7)
+    F8 = FiniteField(8,'z')
+    F7 = FiniteField(7)
+    G = F8.cartesian_product(F7)
 
     w = F8.primitive_element()
     assert w**3 == w+1
@@ -3936,7 +3936,7 @@ def DM_75_8_1():
 
     F3 = FiniteField(3)
     F5 = FiniteField(5)
-    G  = cartesian_product((F3,F5,F5))
+    G = cartesian_product((F3,F5,F5))
 
     M = [
         [(2,0,0), (0,0,0), (0,0,0), (1,0,0), (0,0,0), (1,0,0), (1,0,0), (0,0,0)],
@@ -4121,7 +4121,7 @@ def RBIBD_120_8_1():
     BIBD = new_BIBD
 
     r = {v:i for i,v in enumerate(x for x in range(n) if x not in hyperoval)}
-    BIBD  = [[r[x] for x in B] for B in BIBD ]
+    BIBD = [[r[x] for x in B] for B in BIBD ]
     equiv = [[r[x] for x in B] for B in equiv]
 
     BIBD = IncidenceStructure(range(255),BIBD)
@@ -5008,13 +5008,13 @@ def BIBD_56_11_2():
                         for k in sorted(EDS))
 
 __doc__ = __doc__.format(
-    LIST_OF_OA_CONSTRUCTIONS   = LIST_OF_OA_CONSTRUCTIONS,
+    LIST_OF_OA_CONSTRUCTIONS = LIST_OF_OA_CONSTRUCTIONS,
     LIST_OF_MOLS_CONSTRUCTIONS = LIST_OF_MOLS_CONSTRUCTIONS,
-    LIST_OF_VMT_VECTORS        = LIST_OF_VMT_VECTORS,
-    LIST_OF_BIBD               = LIST_OF_BIBD,
-    LIST_OF_DF                 = LIST_OF_DF,
-    LIST_OF_DM                 = LIST_OF_DM,
-    LIST_OF_QDM                = LIST_OF_QDM,
-    LIST_OF_EDS                = LIST_OF_EDS)
+    LIST_OF_VMT_VECTORS = LIST_OF_VMT_VECTORS,
+    LIST_OF_BIBD = LIST_OF_BIBD,
+    LIST_OF_DF = LIST_OF_DF,
+    LIST_OF_DM = LIST_OF_DM,
+    LIST_OF_QDM = LIST_OF_QDM,
+    LIST_OF_EDS = LIST_OF_EDS)
 del LIST_OF_OA_CONSTRUCTIONS, LIST_OF_MOLS_CONSTRUCTIONS, LIST_OF_VMT_VECTORS,LIST_OF_DF, LIST_OF_DM, LIST_OF_QDM, LIST_OF_EDS, LIST_OF_BIBD
 del PolynomialRing, ZZ, a,