various ruff fixes in groups (PERF, etc)

src/sage/groups/additive_abelian/additive_abelian_wrapper.py

@@ -77,6 +77,7 @@
 
 from sage.misc.superseded import deprecated_function_alias
 
+
 class UnwrappingMorphism(Morphism):
     r"""
     The embedding into the ambient group. Used by the coercion framework.
@@ -213,7 +214,7 @@ def __init__(self, universe, gens, invariants):
         self._universe = universe
         self._gen_elements = tuple(universe(x) for x in gens)
         self._gen_orders = invariants
-        cover,rels = addgp.cover_and_relations_from_invariants(invariants)
+        cover, rels = addgp.cover_and_relations_from_invariants(invariants)
         addgp.AdditiveAbelianGroup_fixed_gens.__init__(self, cover, rels, cover.gens())
         self._unset_coercions_used()
         self.register_embedding(UnwrappingMorphism(self))
@@ -488,13 +489,13 @@ def torsion_subgroup(self, n=None):
             if n <= 0:
                 raise ValueError('n must be a positive integer')
             gens, ords = [], []
-            for g,o in genords:
+            for g, o in genords:
                 if not o:
                     continue
                 d = n.gcd(o)
                 if d == 1:
                     continue
-                gens.append(o//d * g)
+                gens.append(o // d * g)
                 ords.append(d)
         return AdditiveAbelianGroupWrapper(self.universe(), gens, ords)
 
@@ -691,9 +692,9 @@ def _expand_basis_pgroup(p, alphas, vals, beta, h, rel):
     if not (isinstance(alphas, list) and isinstance(vals, list)):
         raise TypeError('alphas and vals must be lists for mutability')
     if not len(alphas) == len(vals) == k - 1:
-        raise ValueError(f'alphas and/or vals have incorrect length')
-#    assert not sum(r*a for r,a in zip(rel, alphas+[beta]))
-#    assert all(a.order() == p**v for a,v in zip(alphas,vals))
+        raise ValueError('alphas and/or vals have incorrect length')
+    #    assert not sum(r*a for r,a in zip(rel, alphas+[beta]))
+    #    assert all(a.order() == p**v for a,v in zip(alphas,vals))
 
     if rel[-1] < 0:
         raise ValueError('rel must have nonnegative entries')
@@ -726,8 +727,8 @@ def _expand_basis_pgroup(p, alphas, vals, beta, h, rel):
         return
 
     # step 3
-    j = next(j for j,r in enumerate(rel) if r == min_r)
-    alphas[j] = sum(a * (r//rel[j]) for a,r in zip(alphas+[beta], rel))
+    j = next(j for j, r in enumerate(rel) if r == min_r)
+    alphas[j] = sum(a * (r // rel[j]) for a, r in zip(alphas + [beta], rel))
 
     # step 4
     if not alphas[j]:
@@ -752,7 +753,8 @@ def _expand_basis_pgroup(p, alphas, vals, beta, h, rel):
     else:
         alphas.append(beta)
         vals.append(h)
-#    assert alphas[-1].order() == p**vals[-1]
+    #    assert alphas[-1].order() == p**vals[-1]
+
 
 def basis_from_generators(gens, ords=None):
     r"""
@@ -803,7 +805,8 @@ def basis_from_generators(gens, ords=None):
     gammas = []
     ms = []
     for p in ps:
-        pgens = [(o.prime_to_m_part(p) * g, o.p_primary_part(p)) for g, o in zip(gens, ords) if not o % p]
+        pgens = [(o.prime_to_m_part(p) * g, o.p_primary_part(p))
+                 for g, o in zip(gens, ords) if not o % p]
         assert pgens
         pgens.sort(key=lambda tup: tup[1])
 
@@ -814,7 +817,7 @@ def basis_from_generators(gens, ords=None):
         while pgens:
             beta, ord_beta = pgens.pop()
             try:
-                dlog = _discrete_log_pgroup(p, vals, alphas, beta)
+                _ = _discrete_log_pgroup(p, vals, alphas, beta)
             except ValueError:
                 pass
             else:
@@ -845,8 +848,8 @@ def basis_from_generators(gens, ords=None):
                 gammas.append(a)
                 ms.append(p ** v)
 
-##    assert len({sum(i*g for i,g in zip(vec,gammas))
-##                for vec in __import__('itertools').product(*map(range,ms))}) \
-##               == __import__('sage').misc.misc_c.prod(ms)
+#    assert len({sum(i*g for i,g in zip(vec,gammas))
+#                for vec in __import__('itertools').product(*map(range,ms))}) \
+#               == __import__('sage').misc.misc_c.prod(ms)
 
     return gammas, ms

src/sage/groups/braid.py

@@ -2590,8 +2590,8 @@ def __init__(self, names):
         rels = []
         for i in range(1, n):
             rels.append(free_group([i, i + 1, i, -i - 1, -i, -i - 1]))
-            for j in range(i + 2, n + 1):
-                rels.append(free_group([i, j, -i, -j]))
+            rels.extend(free_group([i, j, -i, -j])
+                        for j in range(i + 2, n + 1))
         cat = Groups().Infinite()
         FinitelyPresentedGroup.__init__(self, free_group, tuple(rels),
                                         category=cat)

src/sage/groups/class_function.py

@@ -605,10 +605,9 @@ def irreducible_constituents(self):
         L = self._gap_classfunction.ConstituentsOfCharacter()
         return tuple(ClassFunction(self._group, list(l)) for l in L)
 
-    def decompose(self):
+    def decompose(self) -> tuple:
         r"""
-        Returns a list of the characters that appear in the decomposition
-        of chi.
+        Return a list of the characters appearing the decomposition of ``self``.
 
         EXAMPLES::
 
@@ -618,14 +617,13 @@ def decompose(self):
             ((3, Character of Symmetric group of order 5! as a permutation group),
              (2, Character of Symmetric group of order 5! as a permutation group))
         """
-        L = []
-        for irr in self.irreducible_constituents():
-            L.append((self.scalar_product(irr), irr))
+        L = [(self.scalar_product(irr), irr)
+             for irr in self.irreducible_constituents()]
         return tuple(L)
 
     def norm(self):
         r"""
-        Returns the norm of self.
+        Return the norm of ``self``.
 
         EXAMPLES::
 
@@ -635,7 +633,7 @@ def norm(self):
         """
         return self._gap_classfunction.Norm()
 
-    def values(self):
+    def values(self) -> list:
         r"""
         Return the list of values of self on the conjugacy classes.
 
@@ -665,7 +663,7 @@ def values(self):
 
     def central_character(self):
         r"""
-        Returns the central character of self.
+        Return the central character of ``self``.
 
         EXAMPLES::
 
@@ -677,7 +675,7 @@ def central_character(self):
 
     def determinant_character(self):
         r"""
-        Returns the determinant character of self.
+        Return the determinant character of ``self``.
 
         EXAMPLES::
 
@@ -1310,10 +1308,9 @@ def irreducible_constituents(self):
         L = self._gap_classfunction.ConstituentsOfCharacter()
         return tuple(ClassFunction_libgap(self._group, l) for l in L)
 
-    def decompose(self):
+    def decompose(self) -> tuple:
         r"""
-        Return a list of the characters that appear in the decomposition
-        of ``self``.
+        Return a list of the characters appearing the decomposition of ``self``.
 
         EXAMPLES::
 
@@ -1323,9 +1320,8 @@ def decompose(self):
             ((3, Character of Symmetric group of order 5! as a permutation group),
              (2, Character of Symmetric group of order 5! as a permutation group))
         """
-        L = []
-        for irr in self.irreducible_constituents():
-            L.append((self.scalar_product(irr), irr))
+        L = [(self.scalar_product(irr), irr)
+             for irr in self.irreducible_constituents()]
         return tuple(L)
 
     def norm(self):

src/sage/groups/cubic_braid.py

@@ -128,7 +128,7 @@ def eliminate_item(tietze_list):
             return None
         first = tietze_list[0]
         second = None
-        for i in range(1,l):
+        for i in range(1, l):
             if tietze_list[i] in (first, -first):
                 if i == 1:
                     second = tietze_list[i]
@@ -502,17 +502,17 @@ def find_root(domain):
                     # --------------------------------------------------------------------
                     cbg_type = self.parent()._cbg_type
                     if cbg_type == CubicBraidGroup.type.AssionS:
-                        characteristic = 3 # making Assion type S relations vanish
+                        characteristic = 3  # making Assion type S relations vanish
                     elif cbg_type == CubicBraidGroup.type.AssionU:
-                        characteristic = 2 # making Assion type U relations vanish
+                        characteristic = 2  # making Assion type U relations vanish
                     else:
                         characteristic = 0
                 try:
                     characteristic = Integer(characteristic)
                 except ValueError:
                     raise ValueError('characteristic must be in integer')
 
-                if not characteristic.is_zero()  and not characteristic.is_prime():
+                if not characteristic.is_zero() and not characteristic.is_prime():
                     raise ValueError('characteristic must be a prime')
                 if characteristic.is_zero():
                     from sage.rings.number_field.number_field import CyclotomicField
@@ -526,7 +526,7 @@ def find_root(domain):
                 root_bur = find_root(domain)
                 domain = root_bur.parent()
 
-            else: # domain is not None
+            else:  # domain is not None
                 root_bur = find_root(domain)
 
         else:  # root_bur is not None
@@ -550,11 +550,11 @@ def conv2domain(laur_pol):
         from sage.matrix.constructor import matrix
 
         d1, d2 = burau_ori.dimensions()
-        burau_mat = matrix(d1, d2, lambda i,j: conv2domain(burau_ori[i,j]))
+        burau_mat = matrix(d1, d2, lambda i, j: conv2domain(burau_ori[i, j]))
 
         if unitary:
-            burau_mat_adj = matrix(d1, d2, lambda i,j: conv2domain(burau_ori_adj[i,j]))
-            herm_form = matrix(d1, d2, lambda i,j: conv2domain(herm_form_ori[i,j]))
+            burau_mat_adj = matrix(d1, d2, lambda i, j: conv2domain(burau_ori_adj[i, j]))
+            herm_form = matrix(d1, d2, lambda i, j: conv2domain(herm_form_ori[i, j]))
             return burau_mat, burau_mat_adj, herm_form
 
         return burau_mat
@@ -764,15 +764,14 @@ def __init__(self, names, cbg_type=None):
 
         # 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)]
+        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
+        # first the braid relations
         rels = list(self._braid_group.relations())
 
-        # than the cubic relation
-        for i in range(n):
-            rels.append(b[i]**3)
+        # than the cubic relations
+        rels.extend(b[i]**3 for i in range(n))
 
         # than Assion's relation Satz 2.2 for cbg_type=CubicBraidGroup.type.AssionS
         # and Satz 2.4 for cbg_type=CubicBraidGroup.type.AssionU
@@ -1276,7 +1275,7 @@ def create_unitary_realization(self, 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:
-                    transvections.append(xbas[pos+1]+xbas[pos+2]+xbas[pos+3]) # t_{3i+2} = x_{3i+1} + x_{3i+2} + x_{3i+3}
+                    transvections.append(xbas[pos+1]+xbas[pos+2]+xbas[pos+3])  # t_{3i+2} = x_{3i+1} + x_{3i+2} + x_{3i+3}
 
             # -----------------------------------------------------------
             # Conversion-Map from transvection vector to transvection
@@ -1299,15 +1298,14 @@ def transvec2mat(v, bas=bas, bform=bform, fact=a):
             set_classical_realization(self, base_group, proj_group, centralizing_matrix, transvec_matrices)
             return
 
-        #----------------------------------------------------------------------------------------------------------
-        #----------------------------------------------------------------------------------------------------------
+        # ----------------------------------------------------------------
         # local functions declaration section finishes here
-        #----------------------------------------------------------------------------------------------------------
-        #----------------------------------------------------------------------------------------------------------
+        # ----------------------------------------------------------------
 
-        # -------------------------------------------------------------------------------
+        # ----------------------------------------------------------------
         # initialization of constants
-        # -------------------------------------------------------------------------------
+        # ----------------------------------------------------------------
+
         n = self.strands()
 
         # -------------------------------------------------------------------------------
@@ -1317,7 +1315,7 @@ def transvec2mat(v, bas=bas, bform=bform, fact=a):
             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)
+            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:
@@ -1543,8 +1541,9 @@ def as_matrix_group(self, root_bur=None, domain=None, characteristic=None, var='
                 unitary = True
         gen_list = []
         for braid_gen in self.gens():
-            bur_mat = braid_gen.burau_matrix(root_bur=root_bur, domain=domain, characteristic=characteristic,
-                     var=var, reduced=reduced)
+            bur_mat = braid_gen.burau_matrix(root_bur=root_bur, domain=domain,
+                                             characteristic=characteristic,
+                                             var=var, reduced=reduced)
             if unitary:
                 bur_mat, bur_mat_ad, herm_form = bur_mat
 
@@ -1809,7 +1808,7 @@ def as_reflection_group(self):
         if not is_chevie_available():
             raise ImportError("the GAP3 package 'CHEVIE' is needed to obtain the corresponding reflection groups")
 
-        if self._cbg_type != CubicBraidGroup.type.Coxeter or self.strands() > 5  or self.strands() < 2:
+        if self._cbg_type != CubicBraidGroup.type.Coxeter or self.strands() > 5 or self.strands() < 2:
             raise ValueError("no reflection group defined")
 
         # -------------------------------------------------------------------------------

src/sage/groups/finitely_presented.py

@@ -1005,7 +1005,7 @@ def as_permutation_group(self, limit=4096000):
         from sage.combinat.permutation import Permutation
         from sage.groups.perm_gps.permgroup import PermutationGroup
         return PermutationGroup([
-                Permutation(coset_table[2*i]) for i in range(len(coset_table)//2)])
+            Permutation(coset_table[2*i]) for i in range(len(coset_table)//2)])
 
     def direct_product(self, H, reduced=False, new_names=True):
         r"""
@@ -1548,14 +1548,13 @@ def sorted_presentation(self):
         L1 = []
         for rel in L0:
             C = [rel]
-            for j in range(len(rel) - 1):
-                C.append(rel[j + 1:] + rel[:j + 1])
+            C.extend(rel[j + 1:] + rel[:j + 1] for j in range(len(rel) - 1))
             C1 = [tuple(-j for j in reversed(l)) for l in C]
             C += C1
             C.sort()
             L1.append(C[0])
         L1.sort()
-        return F/L1
+        return F / L1
 
     def epimorphisms(self, H):
         r"""

src/sage/groups/generic.py

@@ -901,7 +901,7 @@ def discrete_log(a, base, ord=None, bounds=None, operation='*', identity=None, i
         power = lambda x, y: multiple(x, y, operation=operation, identity=identity, inverse=inverse, op=op)
     if bounds:
         lb, ub = map(integer_ring.ZZ, bounds)
-    if (op is None or identity is None or inverse is None or ord is None) and operation not in addition_names+multiplication_names:
+    if (op is None or identity is None or inverse is None or ord is None) and operation not in addition_names + multiplication_names:
         raise ValueError("ord, op, identity, and inverse must all be specified for this operation")
     if ord is None:
         if operation in multiplication_names:
@@ -1500,7 +1500,6 @@ def has_order(P, n, operation='+'):
             return False
         n = n.factor()
 
-    G = P.parent()
     if operation in addition_names:
         isid = lambda el: not el
         mult = lambda el, n: multiple(el, n, operation='+')

src/sage/groups/kernel_subgroup.py

@@ -21,6 +21,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 
+
 class KernelSubgroup(UniqueRepresentation, Parent):
     r"""
     The kernel (normal) subgroup.