gh-40829: a few fixes for pycodestyle
    
some in recently introduced code

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40829
Reported by: Frédéric Chapoton
Reviewer(s): Martin Rubey

Author: Release Manager

src/sage/graphs/connectivity.pyx

@@ -777,6 +777,7 @@ def blocks_and_cuts_tree(G):
                 g.add_edge(('B', bloc), ('C', c))
     return g
 
+
 def biconnected_components_subgraphs(G):
     r"""
     Return a list of biconnected components as graph objects.
@@ -816,6 +817,7 @@ def biconnected_components_subgraphs(G):
 
     return [G.subgraph(c) for c in blocks_and_cut_vertices(G)[0]]
 
+
 def is_edge_cut(G, edges):
     """
     Check whether ``edges`` form an edge cut.

src/sage/interfaces/khoca.py

@@ -182,8 +182,8 @@ def prepare_data(data):
         for i in data:
             # i[0]: degree, i[1]: height, i[2]: torsion i[3]: rank
             d, h, t, r = i
-            # make d compatibil with Sage
-            d = int(t/2) - d
+            # make d compatible with Sage
+            d = int(t / 2) - d
             if (h, d, t) in data_as_dict:
                 data_as_dict[(h, d, t)] += r
             else:
@@ -207,9 +207,9 @@ def prepare_data(data):
     raw_data = khoca_raw_data(link, ring, red_typ=False, **kwds)
     if 'reduced' in kwds:
         red = kwds['reduced']
-        if type(red) == bool:
+        if isinstance(red, bool):
             if red:
                 return raw_data['red']
-            else:
-                raise TypeError('reduced must be a boolean')
+        else:
+            raise TypeError('reduced must be a boolean')
     return raw_data['unred']

src/sage/interfaces/regina.py

@@ -338,7 +338,7 @@ def set(self, var, value):
         """
         self._lazy_init()
         globs = self._regina_globals
-        if type(value) != str:
+        if not isinstance(value, str):
             globs[var] = value
             return
         try:
@@ -428,7 +428,7 @@ def _convert_args_kwds(self, *args, **kwds):
         def convert_arg(arg):
             if isinstance(arg, InterfaceElement) and arg.parent() is self:
                 return arg._inst
-            elif type(arg) in (list, tuple):
+            elif isinstance(arg, (list, tuple)):
                 return type(arg)([convert_arg(i) for i in arg])
             elif hasattr(arg, '_regina_'):
                 reg = arg._regina_(self)
@@ -832,9 +832,9 @@ def is_native(inst):
         if operation in ('+', '*'):
             if is_native(sinst) and is_native(oinst):
                 if operation == '*':
-                    return P(sinst*oinst)
+                    return P(sinst * oinst)
                 else:
-                    return P(sinst+oinst)
+                    return P(sinst + oinst)
             if type(sinst) == type(oinst):
                 if hasattr(self, 'addTermsLast'):
                     new = self.__deepcopy__()
@@ -860,7 +860,7 @@ def is_native(inst):
                 return (~self)**(-exp)
         if operation == '1/':
             if is_native(sinst):
-                return P(1/sinst)
+                return P(1 / sinst)
             if hasattr(self, 'inverse'):
                 return self.inverse()
         return super()._operation(operation, other=other)
@@ -919,7 +919,6 @@ def from_detail_str(lc):
             """
             if locals:
                 lc.update(locals)
-            from sage.repl.preparse import implicit_mul
             from sage.misc.sage_eval import sage_eval
             s = self.detail().split('\n')[0]
             s = s.replace(' ', '')

src/sage/libs/gap/element.pyx

@@ -1006,7 +1006,6 @@ cdef class GapElement(RingElement):
             GAP_Leave()
             gap_sig_off()
 
-
     cdef bint _compare_less(self, Element other) except -2:
         """
         Compare ``self`` with ``other``.
@@ -1030,7 +1029,6 @@ cdef class GapElement(RingElement):
             GAP_Leave()
             gap_sig_off()
 
-
     cpdef _add_(self, right):
         r"""
         Add two GapElement objects.

src/sage/matrix/matrix2.pyx

@@ -19588,7 +19588,7 @@ cdef class Matrix(Matrix1):
             k = row_profile_exhausted + row_profile_self + row_extension
 
             # calculate sorting permutation, sort k by (shifts[c]+d, c)
-            k_rows = [x[2] for x in  self._krylov_row_coordinates(shifts, degrees, k)]
+            k_rows = [x[2] for x in self._krylov_row_coordinates(shifts, degrees, k)]
             k_perm = Permutation([x + 1 for x in k_rows])
 
             # fast calculation of rows formed by indices in k
@@ -19633,7 +19633,7 @@ cdef class Matrix(Matrix1):
             k = row_profile_exhausted + row_profile_self
             R = exhausted.stack(R)
 
-            k_rows = [x[2] for x in  self._krylov_row_coordinates(shifts, degrees, k)]
+            k_rows = [x[2] for x in self._krylov_row_coordinates(shifts, degrees, k)]
             k_perm = Permutation([x + 1 for x in k_rows])
 
             R.permute_rows(k_perm)

src/sage/rings/finite_rings/integer_mod_ring.py

@@ -1972,33 +1972,32 @@ def _roots_univariate_polynomial(self, f, ring=None, multiplicities=True, algori
         if deg < 0:
             # All residue classes are roots of the zero polynomial
             return [*map(self, range(self.cardinality()))]
-        elif deg == 0:
+        if deg == 0:
             return []
-        elif deg == 1:
+        if deg == 1:
             # assume form a*x + b
             b, a = f.list()
             if a.is_unit():
                 return [-b * (~a)]
-            else:
-                al, bl = a.lift(), b.lift()
 
-                N = self.order()
-                g = N.gcd(al)
+            al, bl = a.lift(), b.lift()
+
+            N = self.order()
+            g = N.gcd(al)
 
-                if bl % g != 0:
-                    return [] # No solution
-                else:
-                    # whole eqn divided by g
-                    N_by_g = N.divide_knowing_divisible_by(g)
-                    a_by_g = al.divide_knowing_divisible_by(g)
-                    _R = Zmod(N_by_g)
-                    assert _R(a_by_g).is_unit()
+            if bl % g != 0:
+                return []  # No solution
 
-                    # single root
-                    _root = self(f.roots(_R, multiplicities=False)[0])
-                    inc = self(N_by_g)
-                    return [_root + k*inc for k in range(g)]
+            # whole eqn divided by g
+            N_by_g = N.divide_knowing_divisible_by(g)
+            a_by_g = al.divide_knowing_divisible_by(g)
+            _R = Zmod(N_by_g)
+            assert _R(a_by_g).is_unit()
 
+            # single root
+            _root = self(f.roots(_R, multiplicities=False)[0])
+            inc = self(N_by_g)
+            return [_root + k * inc for k in range(g)]
 
         # Finite fields are a base case
         if self.is_field():

src/sage/rings/function_field/element.pyi

@@ -1,7 +1,6 @@
 from typing import Any, List
 from sage.structure.element import FieldElement
 
-
 class FunctionFieldElement(FieldElement):
     _x: Any
     _matrix: Any

src/sage/rings/function_field/element_polymod.pyi

@@ -3,7 +3,6 @@ from sage.structure.richcmp import richcmp
 from sage.structure.element import FieldElement
 from sage.rings.function_field.element import FunctionFieldElement
 
-
 class FunctionFieldElement_polymod(FunctionFieldElement):
     def __init__(self, parent: Any, x: Any, reduce: bool = True) -> None:
         ...

src/sage/rings/function_field/element_rational.pyi

@@ -3,7 +3,6 @@ from sage.structure.richcmp import richcmp, richcmp_not_equal
 from sage.structure.element import FieldElement
 from sage.rings.function_field.element import FunctionFieldElement
 
-
 class FunctionFieldElement_rational(FunctionFieldElement):
     def __init__(self, parent: Any, x: Any, reduce: bool = True) -> None:
         ...

src/sage/structure/element.pyx

@@ -3215,7 +3215,7 @@ cdef class CommutativeRingElement(RingElement):
         return I.reduce(self)
 
 
-    ##############################################
+##############################################
 
 cdef class Expression(CommutativeRingElement):