gh-40969: some pep8 cleanup in algebras/steenrod
    
only trivial changes for pycodestyle standard in algebras/steenrod

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40969
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -990,7 +990,7 @@ def maximal_order(self, take_shortcuts=True, order_basis=None):
             ....:           (-511, 608), (493, 880), (105, -709), (-213, 530),
             ....:           (97, 745)]
             sage: all(QuaternionAlgebra(a, b).maximal_order().is_maximal()
-            ....:     for (a, b) in invars)
+            ....:     for a, b in invars)
             True
         """
         if self.base_ring() != QQ:
@@ -1071,7 +1071,7 @@ def maximal_order(self, take_shortcuts=True, order_basis=None):
 
                 e_n = []
                 x_rows = A.solve_left(matrix([V(vec.coefficient_tuple())
-                                              for (vec, val) in f]),
+                                              for vec, val in f]),
                                       check=False).rows()
                 denoms = [x.denominator() for x in x_rows]
                 for i in range(4):
@@ -1199,7 +1199,7 @@ def order_with_level(self, level):
         fact = M1.factor()
         B = O.basis()
 
-        for (p, r) in fact:
+        for p, r in fact:
             a = int(-p) // 2
             for v in GF(p)**4:
                 x = sum([int(v[i] + a) * B[i] for i in range(4)])
@@ -4584,10 +4584,9 @@ def normalize_basis_at_p(e, p, B=QuaternionAlgebraElement_abstract.pair):
         sage: e = [A(1), k, j, 1/2 + 1/2*i + 1/2*j + 1/2*k]
         sage: e_norm = normalize_basis_at_p(e, 2)
         sage: V = QQ**4
-        sage: V.span([V(x.coefficient_tuple()) for (x,_) in e_norm]).dimension()
+        sage: V.span([V(x.coefficient_tuple()) for x, _ in e_norm]).dimension()
         4
     """
-
     N = len(e)
     if N == 0:
         return []

src/sage/algebras/steenrod/steenrod_algebra.py

@@ -648,7 +648,7 @@ def _basis_key_iterator(self):
         EXAMPLES::
 
             sage: A = SteenrodAlgebra(3,basis='adem')
-            sage: for (idx,key) in zip((1,..,10),A._basis_key_iterator()):
+            sage: for idx, key in zip((1,..,10),A._basis_key_iterator()):
             ....:     print("> %2d %-20s %s" % (idx,key,A.monomial(key)))
             >  1 ()                   1
             >  2 (1,)                 beta
@@ -767,17 +767,15 @@ def _repr_(self) -> str:
             sage: SteenrodAlgebra(p=5, profile=(lambda n: 4, lambda n: 1))
             sub-Hopf algebra of mod 5 Steenrod algebra, milnor basis, profile function ([4, 4, 4, ..., 4, 4, +Infinity, +Infinity, +Infinity, ...], [1, 1, 1, ..., 1, 1, 2, 2, ...])
         """
-        def abridge_list(l):
+        def abridge_list(li):
             """
-            String rep for list ``l`` if ``l`` is short enough;
+            String rep for list ``li`` if ``li`` is short enough;
             otherwise print the first few terms and the last few
             terms, with an ellipsis in between.
             """
-            if len(l) < 8:
-                l_str = str(l)
-            else:
-                l_str = str(l[:3]).rstrip("]") + ", ..., " + str(l[-2:]).lstrip("[")
-            return l_str
+            if len(li) < 8:
+                return str(li)
+            return str(li[:3]).rstrip("]") + ", ..., " + str(li[-2:]).lstrip("[")
 
         from sage.rings.infinity import Infinity
         profile = self._profile
@@ -1345,8 +1343,8 @@ def coprod_list(t):
                         right_q = sorted(all_q - a)
                         sign = Permutation(convert_perm(left_q + right_q)).signature()
                         tens_q[(tuple(left_q), tuple(right_q))] = sign
-                    tens = {((q[0], l), (q[1], r)): tq
-                            for l, r in zip(left_p, right_p)
+                    tens = {((q[0], lp), (q[1], rp)): tq
+                            for lp, rp in zip(left_p, right_p)
                             for q, tq in tens_q.items()}
                     return self.tensor_square()._from_dict(tens, coerce=True)
             elif basis == 'serre-cartan':
@@ -1642,14 +1640,14 @@ def _milnor_on_basis(self, t):
         elif basis == 'woody' or basis == 'woodz':
             # each entry in t is a pair (m,k), corresponding to w(m,k), defined by
             # `w(m,k) = \text{Sq}^{2^m (2^{k+1}-1)}`.
-            for (m, k) in t:
+            for m, k in t:
                 ans = ans * A.Sq(2**m * (2**(k+1) - 1))
 
         # wall[_long]
         elif basis.find('wall') >= 0:
             # each entry in t is a pair (m,k), corresponding to Q^m_k, defined by
             # `Q^m_k = Sq(2^k) Sq(2^{k+1}) ... Sq(2^m)`.
-            for (m, k) in t:
+            for m, k in t:
                 exponent = 2**k
                 ans = ans * A.Sq(exponent)
                 for i in range(m-k):
@@ -1660,22 +1658,22 @@ def _milnor_on_basis(self, t):
         elif basis.find('pst') >= 0:
             if not self._generic:
                 # each entry in t is a pair (i,j), corresponding to P^i_j
-                for (i, j) in t:
+                for i, j in t:
                     ans = ans * A.pst(i, j)
             else:
                 # t = (Q, P) where Q is the tuple of Q_i's, and P is a
                 # tuple with entries of the form ((i,j), n),
                 # corresponding to (P^i_j)^n
                 if t[0]:
                     ans = ans * A.Q(*t[0])
-                for ((i, j), n) in t[1]:
+                for (i, j), n in t[1]:
                     ans = ans * (A.pst(i, j))**n
 
         # arnona[_long]
         elif basis.find('arnona') >= 0:
             # each entry in t is a pair (m,k), corresponding to X^m_k, defined by
             # `X^m_k = Sq(2^m) ... Sq(2^{k+1}) Sq(2^k)`
-            for (m, k) in t:
+            for m, k in t:
                 exponent = 2**k
                 X = A.Sq(exponent)
                 for i in range(m-k):
@@ -1689,7 +1687,7 @@ def _milnor_on_basis(self, t):
                 # each entry in t is a pair (i,j), corresponding to
                 # c_{i,j}, the iterated commutator defined by c_{i,1}
                 # = Sq(2^i) and c_{i,j} = [c_{i,j-1}, Sq(2^{i+j-1})].
-                for (i, j) in t:
+                for i, j in t:
                     comm = A.Sq(2**i)
                     for k in range(2, j+1):
                         y = A.Sq(2**(i+k-1))
@@ -1703,7 +1701,7 @@ def _milnor_on_basis(self, t):
                 # c_{i,j} = [P(p^{i+j-1}), c_{i,j-1}].
                 if t[0]:
                     ans = ans * A.Q(*t[0])
-                for ((i, j), n) in t[1]:
+                for (i, j), n in t[1]:
                     comm = A.P(p**i)
                     for k in range(2, j+1):
                         y = A.P(p**(i+k-1))
@@ -1947,7 +1945,7 @@ def q_degree(m, prime=3):
         if basis == 'woody' or basis == 'woodz':
             # each entry in t is a pair (m,k), corresponding to w(m,k), defined by
             # `w(m,k) = \text{Sq}^{2^m (2^{k+1}-1)}`.
-            return sum(2**m * (2**(k+1)-1) for (m, k) in t)
+            return sum(2**m * (2**(k+1)-1) for m, k in t)
 
         # wall, arnon_a
         if basis.find('wall') >= 0 or basis.find('arnona') >= 0:
@@ -1958,7 +1956,7 @@ def q_degree(m, prime=3):
             # Arnon A: each entry in t is a pair (m,k), corresponding
             # to X^m_k, defined by `X^m_k = Sq(2^m) ... Sq(2^{k+1})
             # Sq(2^k)`
-            return sum(2**k * (2**(m-k+1)-1) for (m, k) in t)
+            return sum(2**k * (2**(m-k+1)-1) for m, k in t)
 
         # pst, comm
         if basis.find('pst') >= 0 or basis.find('comm') >= 0:
@@ -1969,7 +1967,7 @@ def q_degree(m, prime=3):
                 # to c_{i,j}, the iterated commutator defined by
                 # c_{i,1} = Sq(2^i) and c_{i,j} = [c_{i,j-1},
                 # Sq(2^{i+j-1})].
-                return sum(2**m * (2**k - 1) for (m, k) in t)
+                return sum(2**m * (2**k - 1) for m, k in t)
             # p odd:
             #
             # Pst: have pair (Q, P) where Q is a tuple of Q's, as in
@@ -1982,7 +1980,7 @@ def q_degree(m, prime=3):
             # iterated commutator defined by c_{s,1} = P(p^s) and
             # c_{s,t} = [P(p^{s+t-1}), c_{s,t-1}].
             q_deg = q_degree(t[0], prime=p)
-            p_deg = sum(2 * n * p**s * (p**t - 1) for ((s, t), n) in t[1])
+            p_deg = sum(2 * n * p**s * (p**t - 1) for (s, t), n in t[1])
             return q_deg + p_deg
 
     # coercion methods:
@@ -2236,7 +2234,7 @@ def basis(self, d=None):
             Lazy family (Term map from basis key family of mod 7 Steenrod algebra, milnor basis
              to mod 7 Steenrod algebra, milnor basis(i))_{i in basis key family
              of mod 7 Steenrod algebra, milnor basis}
-            sage: for (idx,a) in zip((1,..,9),A7.basis()):
+            sage: for idx, a in zip((1,..,9),A7.basis()):
             ....:      print("{} {}".format(idx, a))
             1 1
             2 Q_0
@@ -3435,7 +3433,7 @@ def coproduct(self, algorithm='milnor'):
                 1
                 sage: Sq(*supp[0][1])
                 Sq(2)
-                sage: [(Sq(*x), Sq(*y)) for (x,y) in supp]
+                sage: [(Sq(*x), Sq(*y)) for x, y in supp]
                 [(1, Sq(2)), (Sq(1), Sq(1)), (Sq(2), 1)]
 
             The ``support`` of an element does not include the
@@ -3453,7 +3451,7 @@ def coproduct(self, algorithm='milnor'):
                  (((), (1,)), ((), (1,))): 2,
                  (((), (2,)), ((), ())): 2}
                 sage: mc = b.monomial_coefficients()
-                sage: sorted([(A3.monomial(x), A3.monomial(y), mc[x,y]) for (x,y) in mc])
+                sage: sorted([(A3.monomial(x), A3.monomial(y), mc[x,y]) for x, y in mc])
                 [(1, P(2), 2), (P(1), P(1), 2), (P(2), 1, 2)]
             """
             A = self.parent()
@@ -3627,7 +3625,7 @@ def may_weight(self):
                 return wt
             else:  # p odd
                 wt = Infinity
-                for (mono1, mono2) in self.milnor().support():
+                for mono1, mono2 in self.milnor().support():
                     P_wt = 0
                     index = 1
                     for n in mono2:

src/sage/algebras/steenrod/steenrod_algebra_bases.py

@@ -361,13 +361,13 @@ def steenrod_algebra_basis(n, basis='milnor', p=2, **kwds):
         return serre_cartan_basis(n, p, **kwds)
     # Atomic bases, p odd:
     elif generic and (basis_name.find('pst') >= 0
-                    or basis_name.find('comm') >= 0):
+                      or basis_name.find('comm') >= 0):
         return atomic_basis_odd(n, basis_name, p, **kwds)
     # Atomic bases, p=2
     elif not generic and (basis_name == 'woody' or basis_name == 'woodz'
-                     or basis_name == 'wall' or basis_name == 'arnona'
-                     or basis_name.find('pst') >= 0
-                     or basis_name.find('comm') >= 0):
+                          or basis_name == 'wall' or basis_name == 'arnona'
+                          or basis_name.find('pst') >= 0
+                          or basis_name.find('comm') >= 0):
         return atomic_basis(n, basis_name, **kwds)
     # Arnon 'C' basis
     elif not generic and basis == 'arnonc':
@@ -726,7 +726,7 @@ def serre_cartan_basis(n, p=2, bound=1, **kwds):
                 for vec in serre_cartan_basis(n - last, bound=2 * last):
                     new = vec + (last,)
                     result.append(new)
-        else: # p odd
+        else:  # p odd
             if n % (2 * (p-1)) == 0 and n//(2 * (p-1)) >= bound:
                 result = [(0, int(n//(2 * (p-1))), 0)]
             elif n == 1:
@@ -739,7 +739,7 @@ def serre_cartan_basis(n, p=2, bound=1, **kwds):
                 if n - 2*(p-1)*last > 0:
                     for vec in serre_cartan_basis(n - 2*(p-1)*last,
                                                   p, p*last, generic=generic):
-                        result.append(vec + (last,0))
+                        result.append(vec + (last, 0))
             # case 2: append P^{last} beta
             if bound == 1:
                 bound = 0
@@ -849,7 +849,7 @@ def degree_dictionary(n, basis):
             m = 0
             deg = 2**m * (2**(k+1) - 1)
             while deg <= n:
-                dict[deg] = (m,k)
+                dict[deg] = (m, k)
                 if m > 0:
                     m = m - 1
                     k = k + 1
@@ -862,7 +862,7 @@ def degree_dictionary(n, basis):
             m = 0
             deg = 2**k * (2**(m-k+1) - 1)
             while deg <= n:
-                dict[deg] = (m,k)
+                dict[deg] = (m, k)
                 if k == 0:
                     m = m + 1
                     k = m
@@ -875,9 +875,9 @@ def degree_dictionary(n, basis):
             deg = 2**s * (2**t - 1)
             while deg <= n:
                 if basis.find('pst') >= 0:
-                    dict[deg] = (s,t)
+                    dict[deg] = (s, t)
                 else:  # comm
-                    dict[deg] = (s,t)
+                    dict[deg] = (s, t)
                 if s == 0:
                     s = t
                     t = 1
@@ -889,18 +889,18 @@ def degree_dictionary(n, basis):
 
     def sorting_pair(s, t, basis):   # pair used for sorting the basis
         if basis.find('wood') >= 0 and basis.find('z') >= 0:
-            return (-s-t,-s)
+            return (-s-t, -s)
         elif basis.find('wood') >= 0 or basis.find('wall') >= 0 or \
                 basis.find('arnon') >= 0:
-            return (-s,-t)
+            return (-s, -t)
         elif basis.find('rlex') >= 0:
-            return (t,s)
+            return (t, s)
         elif basis.find('llex') >= 0:
-            return (s,t)
+            return (s, t)
         elif basis.find('deg') >= 0:
-            return (s+t,t)
+            return (s+t, t)
         elif basis.find('revz') >= 0:
-            return (s+t,s)
+            return (s+t, s)
 
     from sage.rings.infinity import Infinity
     profile = kwds.get("profile", None)
@@ -926,7 +926,7 @@ def sorting_pair(s, t, basis):   # pair used for sorting the basis
             okay = True
             if basis.find('pst') >= 0:
                 if profile is not None and len(profile) > 0:
-                    for (s,t) in big_list:
+                    for s, t in big_list:
                         if ((len(profile) > t-1 and profile[t-1] <= s)
                             or (len(profile) <= t-1 and trunc < Infinity)):
                             okay = False
@@ -1087,7 +1087,7 @@ def sorting_pair(s, t, basis):   # pair used for sorting the basis
                                 okay = False
                                 break
 
-                        for ((s, t), _) in p_mono:
+                        for (s, t), _ in p_mono:
                             if ((len(profile[0]) > t-1 and profile[0][t-1] <= s)
                                 or (len(profile[0]) <= t-1 and trunc < Infinity)):
                                 okay = False
@@ -1135,7 +1135,7 @@ def steenrod_basis_error_check(dim, p, **kwds):
     generic = kwds.get('generic', p != 2)
 
     if not generic:
-        bases = ('adem','woody', 'woodz', 'wall', 'arnona', 'arnonc',
+        bases = ('adem', 'woody', 'woodz', 'wall', 'arnona', 'arnonc',
                  'pst_rlex', 'pst_llex', 'pst_deg', 'pst_revz',
                  'comm_rlex', 'comm_llex', 'comm_deg', 'comm_revz')
     else:
@@ -1146,29 +1146,35 @@ def steenrod_basis_error_check(dim, p, **kwds):
     for i in range(dim):
         if i % 5 == 0:
             verbose("up to dimension %s" % i)
-        milnor_dim = len(steenrod_algebra_basis.f(i,'milnor',p=p,generic=generic))
+        milnor_dim = len(steenrod_algebra_basis.f(i, 'milnor', p=p,
+                                                  generic=generic))
         for B in bases:
-            if milnor_dim != len(steenrod_algebra_basis.f(i,B,p,generic=generic)):
+            if milnor_dim != len(steenrod_algebra_basis.f(i, B, p,
+                                                          generic=generic)):
                 print("problem with milnor/{} in dimension {}".format(B, i))
-            mat = convert_to_milnor_matrix.f(i,B,p,generic=generic)
+            mat = convert_to_milnor_matrix.f(i, B, p, generic=generic)
             if mat.nrows() != 0 and not mat.is_invertible():
                 print("%s invertibility problem in dim %s at p=%s" % (B, i, p))
 
     verbose("done checking, no profiles")
 
     bases = ('pst_rlex', 'pst_llex', 'pst_deg', 'pst_revz')
     if not generic:
-        profiles = [(4,3,2,1), (2,2,3,1,1), (0,0,0,2)]
+        profiles = [(4, 3, 2, 1), (2, 2, 3, 1, 1), (0, 0, 0, 2)]
     else:
-        profiles = [((3,2,1), ()), ((), (2,1,2)), ((3,2,1), (2,2,2,2))]
+        profiles = [((3, 2, 1), ()), ((), (2, 1, 2)), ((3, 2, 1), (2, 2, 2, 2))]
 
     for i in range(dim):
         if i % 5 == 0:
             verbose("up to dimension %s" % i)
         for pro in profiles:
-            milnor_dim = len(steenrod_algebra_basis.f(i,'milnor',p=p,profile=pro,generic=generic))
+            milnor_dim = len(steenrod_algebra_basis.f(i, 'milnor', p=p,
+                                                      profile=pro,
+                                                      generic=generic))
             for B in bases:
-                if milnor_dim != len(steenrod_algebra_basis.f(i,B,p,profile=pro,generic=generic)):
+                if milnor_dim != len(steenrod_algebra_basis.f(i, B, p,
+                                                              profile=pro,
+                                                              generic=generic)):
                     print("problem with milnor/%s in dimension %s with profile %s" % (B, i, pro))
 
     verbose("done checking with profiles")