gh-36654: More fixes for e221

    
a few more fixes for pycodestyle E221

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36654
Reported by: Frédéric Chapoton
Reviewer(s): Kwankyu Lee

src/sage/groups/cubic_braid.py

@@ -141,7 +141,7 @@ def eliminate_item(tietze_list):
         if second is None:
             return None
         middle = tietze_list[1:i]
-        end    = tietze_list[i+1:l]
+        end = tietze_list[i+1:l]
         if first == second:
             return [-first] + middle + end
         else:
@@ -490,7 +490,7 @@ def find_root(domain):
                     if root[0] == 0:
                         continue
                     root_bur = root[0]
-                    if root[1]  == 1:
+                    if root[1] == 1:
                         break
                 return root_bur
 
@@ -747,7 +747,7 @@ def __init__(self, names, cbg_type=None):
             sage: U5 = AssionGroupU(5)       # indirect doctest
             sage: TestSuite(U5).run()        # long time
         """
-        n  = Integer(len(names))
+        n = Integer(len(names))
         if n < 1:
             raise ValueError("the number of strands must be an integer larger than one")
 
@@ -759,12 +759,12 @@ def __init__(self, names, cbg_type=None):
         free_group = FreeGroup(names)
         self._cbg_type = cbg_type
         self._nstrands = n + 1
-        self._ident  = self._cbg_type.value + self._nstrands.str()
+        self._ident = self._cbg_type.value + self._nstrands.str()
         self._braid_group = BraidGroup(names)
 
         # internal naming of elements for convenience
-        b  = [free_group([i]) for i in range(1, n+1)]
-        t  = [free_group([i,  i+1]) ** 3 for i in range(1, n)]
+        b = [free_group([i]) for i in range(1, n+1)]
+        t = [free_group([i,  i+1]) ** 3 for i in range(1, n)]
         ti = [free_group([-i, -i-1]) ** 3 for i in range(1, n)]
 
         # first the braid relation
@@ -796,12 +796,12 @@ def __init__(self, names, cbg_type=None):
         # the following global pointers to classical group realizations will be set in the private method
         # _create_classical_realization
         # ------------------------------------------------------------------------------------------------
-        self._classical_group             = None   # This is the classical Group returned by as_classical_group
-        self._classical_base_group        = None   # this only differs for special cases for Assion groups from the former
-        self._classical_invariant_form    = None   # invariant form of the classical base group
-        self._classical_embedding         = None   # if self._classical_group different from self._classical_base_group
-        self._centralizing_matrix         = None   # for Assion groups: element in classical base group commuting with self
-        self._centralizing_element        = None   # image under nat. map of the former one in the proj. classical group
+        self._classical_group = None   # This is the classical Group returned by as_classical_group
+        self._classical_base_group = None   # this only differs for special cases for Assion groups from the former
+        self._classical_invariant_form = None   # invariant form of the classical base group
+        self._classical_embedding = None   # if self._classical_group different from self._classical_base_group
+        self._centralizing_matrix = None   # for Assion groups: element in classical base group commuting with self
+        self._centralizing_element = None   # image under nat. map of the former one in the proj. classical group
         return
 
     def _repr_(self):
@@ -1095,7 +1095,7 @@ def set_classical_realization(self, base_group, proj_group, centralizing_matrix,
             # ------------------------------------------------------------------------------
             # Setting the List of Braid Images
             # ------------------------------------------------------------------------------
-            im_gens  = [base_group(m) for m in transvec_matrices]
+            im_gens = [base_group(m) for m in transvec_matrices]
 
             # ------------------------------------------------------------------------------
             # By the work of Assion no check on the group homomorphism is needed, at all.
@@ -1109,7 +1109,7 @@ def set_classical_realization(self, base_group, proj_group, centralizing_matrix,
             # ------------------------------------------------------------------------------
             # Do the projective group realization if needed
             # ------------------------------------------------------------------------------
-            embedding      = self._classical_embedding
+            embedding = self._classical_embedding
             classical_group = None
             if proj_group is None:
                 classical_group = base_group
@@ -1128,19 +1128,19 @@ def set_classical_realization(self, base_group, proj_group, centralizing_matrix,
                     nat_hom = base_group.hom(proj_group.gens(), check=check)
                     centralizing_element = nat_hom(centralizing_matrix)
                     classical_group_gens = [nat_hom(m) for m in transvec_matrices]
-                    classical_group     = proj_group.subgroup(classical_group_gens, canonicalize=False)
+                    classical_group = proj_group.subgroup(classical_group_gens, canonicalize=False)
                     hom_to_classic = self.hom(classical_group.gens(), check=check)
                     classical_group.register_conversion(hom_to_classic)
 
             # ------------------------------------------------------------------------------
             # register constructed items
             # ------------------------------------------------------------------------------
-            self._classical_group             = classical_group
-            self._classical_base_group        = base_group
-            self._classical_invariant_form    = base_group.invariant_form()
-            self._centralizing_matrix         = centralizing_matrix
-            self._centralizing_element        = centralizing_element
-            self._classical_embedding         = embedding
+            self._classical_group = classical_group
+            self._classical_base_group = base_group
+            self._classical_invariant_form = base_group.invariant_form()
+            self._centralizing_matrix = centralizing_matrix
+            self._centralizing_element = centralizing_element
+            self._classical_embedding = embedding
             return
 
         # -------------------------------------------------------------------------------
@@ -1211,7 +1211,7 @@ def transvec2mat(v, bas=bas, bform=bform, fact=1):
             # ------------------------------------------------------------------------------
             centralizing_vector = xbas[mhalf-1]
             centralizing_matrix = base_group(transvec2mat(centralizing_vector, fact=1))
-            transvec_matrices   = [transvec2mat(v) for v in transvections]
+            transvec_matrices = [transvec2mat(v) for v in transvections]
 
             set_classical_realization(self, base_group, proj_group, centralizing_matrix, transvec_matrices)
             return
@@ -1273,9 +1273,9 @@ def create_unitary_realization(self, m):
             for j in range(mthird):
                 pos = 3*(j+1)-1
                 transvections.append(xbas[pos-1])                             # t_{3i}   = x_{3i-1}
-                if pos + 1  < m:
+                if pos + 1 < m:
                     transvections.append(xbas[pos-1]+xbas[pos]+xbas[pos+1])   # t_{3i+1} = x_{3i-1} + x_{3i} + x_{3i+1}
-                if pos + 3  < m:
+                if pos + 3 < m:
                     transvections.append(xbas[pos+1]+xbas[pos+2]+xbas[pos+3]) # t_{3i+2} = x_{3i+1} + x_{3i+2} + x_{3i+3}
 
             # -----------------------------------------------------------
@@ -1294,7 +1294,7 @@ def transvec2mat(v, bas=bas, bform=bform, fact=a):
             # ------------------------------------------------------------------------------
             centralizing_vector = xbas[m-2]+xbas[m-1]
             centralizing_matrix = base_group(transvec2mat(centralizing_vector, fact=1))
-            transvec_matrices   = [transvec2mat(v) for v in transvections]
+            transvec_matrices = [transvec2mat(v) for v in transvections]
 
             set_classical_realization(self, base_group, proj_group, centralizing_matrix, transvec_matrices)
             return
@@ -1314,13 +1314,13 @@ def transvec2mat(v, bas=bas, bform=bform, fact=a):
         # Setting the Classical group
         # -------------------------------------------------------------------------------
         if self._cbg_type == CubicBraidGroup.type.AssionS:
-            dim_sympl_group   = n-1              # S(n-1) = Sp(n-1, 3)
-            if n % 2  == 0:
-                dim_sympl_group   = n            # S(n-1) = subgroup of PSp(n, 3)
+            dim_sympl_group = n-1              # S(n-1) = Sp(n-1, 3)
+            if n % 2 == 0:
+                dim_sympl_group = n            # S(n-1) = subgroup of PSp(n, 3)
             create_sympl_realization(self,  dim_sympl_group)
         elif self._cbg_type == CubicBraidGroup.type.AssionU:
             dim_unitary_group = n-1              # U(n-1) = GU(n-1, 2)
-            if n % 3  == 0:
+            if n % 3 == 0:
                 dim_unitary_group = n            # U(n-1) = subgroup PGU(n, 3)
             create_unitary_realization(self, dim_unitary_group)
         else:
@@ -1344,11 +1344,11 @@ def transvec2mat(v, bas=bas, bform=bform, fact=a):
             UCF = UniversalCyclotomicField()
             z12 = UCF.gen(12)
             classical_group = self.as_matrix_group(root_bur=~z12, domain=UCF, reduced='unitary')
-            self._classical_group            = classical_group
-            self._classical_base_group       = classical_group
-            self._classical_embedding        = classical_group
+            self._classical_group = classical_group
+            self._classical_base_group = classical_group
+            self._classical_embedding = classical_group
             if self._classical_invariant_form is None:
-                self._classical_invariant_form  = classical_group.ambient().invariant_form()
+                self._classical_invariant_form = classical_group.ambient().invariant_form()
         return
 
     def _element_constructor_(self, x, **kwds):

src/sage/misc/superseded.py

@@ -363,10 +363,10 @@ def __init__(self, issue_number, func, module, instance=None, unbound=None):
         try:
             self.__dict__.update(func.__dict__)
         except AttributeError:
-            pass # Cython classes don't have __dict__
+            pass  # Cython classes don't have __dict__
         self.func = func
-        self.issue_number  = issue_number
-        self.instance = instance # for use with methods
+        self.issue_number = issue_number
+        self.instance = instance  # for use with methods
         self.unbound = unbound
         self.__module__ = module
         if isinstance(func, type(deprecation)):

src/sage/modules/free_module.py

@@ -2459,7 +2459,7 @@ def aux(length, norm, max_):
         iters = [iter(R) for _ in range(len(G))]
         for x in iters:
             next(x)     # put at 0
-        zero  = R(0)
+        zero = R.zero()
         v = [zero for _ in range(len(G))]
         n = 0
         z = self(0)
@@ -3889,11 +3889,11 @@ def intersection(self, other):
             V2 = self
         A1 = V1.basis_matrix()
         A2 = V2.basis_matrix()
-        S  = A1.stack(A2)
-        K  = S.integer_kernel(self.base_ring()).basis_matrix()
-        n  = int(V1.dimension())
+        S = A1.stack(A2)
+        K = S.integer_kernel(self.base_ring()).basis_matrix()
+        n = int(V1.dimension())
         K = K.matrix_from_columns(range(n))
-        B = K*A1
+        B = K * A1
         return self.span(B)
 
     def __and__(self, other):
@@ -5219,10 +5219,10 @@ def __quotient_matrices(self, sub):
         # Our algorithm is to note that D is determined if we just
         # replace both A and S by the submatrix got from their pivot
         # columns.
-        P  = A.pivots()
+        P = A.pivots()
         AA = A.matrix_from_columns(P)
         SS = S.matrix_from_columns(P)
-        D  = SS * AA**(-1)
+        D = SS * AA**(-1)
 
         # Compute the image of each basis vector for ``self`` under the
         # map "write an element of ``self`` in terms of the basis A" then

src/sage/modules/with_basis/morphism.py

@@ -1055,7 +1055,7 @@ def coreduced(self, y):
         on_basis = self.on_basis()
         assert y in G
 
-        result    = G.zero()
+        result = G.zero()
         remainder = y
 
         while not remainder.is_zero():
@@ -1447,7 +1447,7 @@ def __init__(self, domain, diagonal, codomain=None, category=None):
         if codomain is None:
             raise ValueError("The codomain should be specified")
         if not (domain.basis().keys() == codomain.basis().keys() and
-                domain.base_ring()    == codomain.base_ring()):
+                domain.base_ring() == codomain.base_ring()):
             raise ValueError("The domain and codomain should have the same base ring "
                              "and the same basis indexing")
         from collections.abc import Callable

src/sage/plot/plot3d/platonic.py

@@ -152,6 +152,7 @@ def prep(G, center, size, kwds):
         G = G.translate(center)
     return G
 
+
 @rename_keyword(alpha='opacity')
 def tetrahedron(center=(0, 0, 0), size=1, **kwds):
     """
@@ -255,15 +256,16 @@ def tetrahedron(center=(0, 0, 0), size=1, **kwds):
     one = RR.one()
     sqrt2 = RR(2).sqrt()
     sqrt6 = RR(6).sqrt()
-    point_list = [(0,0,1),
-                  (2*sqrt2/3,        0, -one/3),
-                  ( -sqrt2/3,  sqrt6/3, -one/3),
-                  ( -sqrt2/3, -sqrt6/3, -one/3)]
+    point_list = [(0, 0, 1),
+                  (2*sqrt2/3, 0, -one/3),
+                  (-sqrt2/3, sqrt6/3, -one/3),
+                  (-sqrt2/3, -sqrt6/3, -one/3)]
     face_list = [[0,1,2],[1,3,2],[0,2,3],[0,3,1]]
     if 'aspect_ratio' not in kwds:
         kwds['aspect_ratio'] = [1, 1, 1]
     return index_face_set(face_list, point_list, enclosed=True, center=center, size=size, **kwds)
 
+
 @rename_keyword(alpha='opacity')
 def cube(center=(0, 0, 0), size=1, color=None, frame_thickness=0,
          frame_color=None, **kwds):
@@ -405,6 +407,7 @@ def cube(center=(0, 0, 0), size=1, color=None, frame_thickness=0,
             B += frame3d((-0.5,-0.5,-0.5),(0.5,0.5,0.5), thickness=frame_thickness, color=frame_color)
     return prep(B, center, size, kwds)
 
+
 @rename_keyword(alpha='opacity')
 def octahedron(center=(0, 0, 0), size=1, **kwds):
     r"""
@@ -440,7 +443,8 @@ def octahedron(center=(0, 0, 0), size=1, **kwds):
     kwds['enclosed'] = True
     if 'aspect_ratio' not in kwds:
         kwds['aspect_ratio'] = [1, 1, 1]
-    return prep(Box(1,1,1).dual(**kwds), center, size, kwds)
+    return prep(Box(1, 1, 1).dual(**kwds), center, size, kwds)
+
 
 @rename_keyword(alpha='opacity')
 def dodecahedron(center=(0, 0, 0), size=1, **kwds):
@@ -514,21 +518,21 @@ def dodecahedron(center=(0, 0, 0), size=1, **kwds):
     - Robert Bradshaw, William Stein
     """
     RR = RDF
-    one = RR(1)
+    one = RR.one()
     sqrt3 = RR(3).sqrt()
     sqrt5 = RR(5).sqrt()
     R3 = RR**3
-    rot = matrix(RR, [[  -one/2,-sqrt3/2, 0],
-                      [ sqrt3/2,  -one/2, 0],
-                      [       0,       0, 1]])
-    rot2 = rot*rot
+    rot = matrix(RR, [[-one / 2, -sqrt3 / 2, 0],
+                      [sqrt3 / 2, -one / 2, 0],
+                      [0, 0, 1]])
+    rot2 = rot * rot
 
     # The top
-    Q = R3([0,0,1])
+    Q = R3([0, 0, 1])
     # The first ring
     P1 = R3([2*one/3, 0, sqrt5/3])
     # The second ring
-    R1 = R3([sqrt5/3,  1/sqrt3, one/3])
+    R1 = R3([sqrt5/3, 1/sqrt3, one/3])
     R2 = R3([sqrt5/3, -1/sqrt3, one/3])
 
     top = [Q, P1, rot*P1, rot2*P1, R1, rot*R2, rot*R1, rot2*R2, rot2*R1, R2]
@@ -555,6 +559,7 @@ def dodecahedron(center=(0, 0, 0), size=1, **kwds):
 #        vertex_spheres += [faces.stickers(['red','yellow','blue','purple','black','orange'], .1, .1)] # [faces]
 #        return Graphics3dGroup(vertex_spheres)
 
+
 @rename_keyword(alpha='opacity')
 def icosahedron(center=(0, 0, 0), size=1, **kwds):
     r"""