some type annotations in categories/examples

src/sage/categories/examples/algebras_with_basis.py

@@ -2,12 +2,12 @@
 r"""
 Examples of algebras with basis
 """
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ***************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
@@ -73,7 +73,7 @@ def product_on_basis(self, w1, w2):
             sage: Words = A.basis().keys()
             sage: A.product_on_basis(Words("acb"), Words("cba"))
             B[word: acbcba]
-            sage: (a,b,c) = A.algebra_generators()
+            sage: a, b, c = A.algebra_generators()
             sage: a * (1-b)^2 * c
             B[word: abbc] - 2*B[word: abc] + B[word: ac]
         """

src/sage/categories/examples/commutative_additive_monoids.py

@@ -1,12 +1,12 @@
 """
 Examples of commutative additive monoids
 """
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
@@ -35,7 +35,7 @@ class FreeCommutativeAdditiveMonoid(FreeCommutativeAdditiveSemigroup):
 
     with product rule given by `a \times b = a` for all `a, b`::
 
-        sage: (a,b,c,d) = S.additive_semigroup_generators()
+        sage: a, b, c, d = S.additive_semigroup_generators()
 
     We conclude by running systematic tests on this commutative monoid::
 
@@ -66,7 +66,7 @@ class FreeCommutativeAdditiveMonoid(FreeCommutativeAdditiveSemigroup):
         running ._test_zero() . . . pass
     """
 
-    def __init__(self, alphabet=('a','b','c','d')):
+    def __init__(self, alphabet=('a', 'b', 'c', 'd')) -> None:
         r"""
         The free commutative monoid.
 
@@ -86,7 +86,7 @@ def __init__(self, alphabet=('a','b','c','d')):
         self.alphabet = alphabet
         Parent.__init__(self, category=CommutativeAdditiveMonoids())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         TESTS::
 

src/sage/categories/examples/commutative_additive_semigroups.py

@@ -1,12 +1,12 @@
 """
 Examples of commutative additive semigroups
 """
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.structure.parent import Parent
@@ -37,7 +37,7 @@ class FreeCommutativeAdditiveSemigroup(UniqueRepresentation, Parent):
 
     with product rule given by `a \times b = a` for all `a, b`::
 
-        sage: (a,b,c,d) = S.additive_semigroup_generators()
+        sage: a, b, c, d = S.additive_semigroup_generators()
 
     We conclude by running systematic tests on this commutative monoid::
 
@@ -66,7 +66,7 @@ class FreeCommutativeAdditiveSemigroup(UniqueRepresentation, Parent):
         running ._test_some_elements() . . . pass
     """
 
-    def __init__(self, alphabet=('a','b','c','d')):
+    def __init__(self, alphabet=('a', 'b', 'c', 'd')) -> None:
         r"""
         The free commutative monoid.
 
@@ -86,7 +86,7 @@ def __init__(self, alphabet=('a','b','c','d')):
         self.alphabet = alphabet
         Parent.__init__(self, category=CommutativeAdditiveSemigroups())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         EXAMPLES::
 
@@ -104,7 +104,7 @@ def summation(self, x, y):
         EXAMPLES::
 
             sage: F = CommutativeAdditiveSemigroups().example()
-            sage: (a,b,c,d) = F.additive_semigroup_generators()
+            sage: a, b, c, d = F.additive_semigroup_generators()
             sage: F.summation(a,b)
             a + b
             sage: (a+b) + (a+c)
@@ -125,7 +125,7 @@ def additive_semigroup_generators(self):
             sage: F.additive_semigroup_generators()
             Family (a, b, c, d)
         """
-        return Family( [self(((a,1),)) for a in self.alphabet] )
+        return Family([self(((a, 1),)) for a in self.alphabet])
         # FIXME: use this once the keys argument of FiniteFamily will be honoured
         # for the specifying the order of the elements in the family
         # return Family(self.alphabet, lambda a: self(((a,1),)))
@@ -140,10 +140,10 @@ def an_element(self):
             sage: F.an_element()
             a + 2*b + 3*c + 4*d
         """
-        return self((a, (ord(a)-96)) for a in self.alphabet)
+        return self((a, ord(a) - 96) for a in self.alphabet)
 
     class Element(ElementWrapper):
-        def __init__(self, parent, iterable):
+        def __init__(self, parent, iterable) -> None:
             """
             EXAMPLES::
 

src/sage/categories/examples/finite_coxeter_groups.py

@@ -85,7 +85,7 @@ class DihedralGroup(UniqueRepresentation, Parent):
          ((2, 1), (2,), 1)]
     """
 
-    def __init__(self, n=5):
+    def __init__(self, n=5) -> None:
         r"""
         Construct the `n`-th DihedralGroup of order `2 n`.
 
@@ -144,7 +144,7 @@ def one(self):
         """
         return self(())
 
-    def index_set(self):
+    def index_set(self) -> tuple:
         r"""
         Implement :meth:`CoxeterGroups.ParentMethods.index_set`.
 
@@ -156,7 +156,7 @@ def index_set(self):
         """
         return (1, 2)
 
-    def degrees(self):
+    def degrees(self) -> tuple:
         """
         Return the degrees of ``self``.
 
@@ -214,10 +214,9 @@ def has_right_descent(self, i, positive=False, side='right') -> bool:
             reduced_word = self.value
             if len(reduced_word) == self.parent().n:
                 return not positive
-            elif len(reduced_word) == 0:
+            if len(reduced_word) == 0:
                 return positive
-            else:
-                return (i == reduced_word[0 if side == "left" else -1]) == (not positive)
+            return (i == reduced_word[0 if side == "left" else -1]) == (not positive)
 
         def apply_simple_reflection_right(self, i):
             r"""
@@ -237,15 +236,15 @@ def apply_simple_reflection_right(self, i):
             if len(reduced_word) == n:
                 if (i == 1 and is_odd(n)) or (i == 2 and is_even(n)):
                     return self.parent()(reduced_word[:-1])
-                else:
-                    return self.parent()(reduced_word[1:])
-            elif (len(reduced_word) == n - 1 and (not self.has_descent(i))) and (reduced_word[0] == 2):
+                return self.parent()(reduced_word[1:])
+
+            if (len(reduced_word) == n - 1 and (not self.has_descent(i))) and (reduced_word[0] == 2):
                 return self.parent()((1,) + reduced_word)
-            else:
-                if self.has_descent(i):
-                    return self.parent()(reduced_word[:-1])
-                else:
-                    return self.parent()(reduced_word + (i,))
+
+            if self.has_descent(i):
+                return self.parent()(reduced_word[:-1])
+
+            return self.parent()(reduced_word + (i,))
 
 
 Example = DihedralGroup

src/sage/categories/examples/finite_monoids.py

@@ -1,12 +1,12 @@
 """
 Examples of finite monoids
 """
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
@@ -66,7 +66,7 @@ class IntegerModMonoid(UniqueRepresentation, Parent):
         running ._test_some_elements() . . . pass
     """
 
-    def __init__(self, n=12):
+    def __init__(self, n=12) -> None:
         r"""
         EXAMPLES::
 
@@ -80,7 +80,7 @@ def __init__(self, n=12):
         self.n = n
         Parent.__init__(self, category=Monoids().Finite().FinitelyGenerated())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         TESTS::
 
@@ -92,9 +92,9 @@ def _repr_(self):
 
     def semigroup_generators(self):
         r"""
-
-        Returns a set of generators for ``self``, as per
+        Return a set of generators for ``self``, as per
         :meth:`Semigroups.ParentMethods.semigroup_generators`.
+
         Currently this returns all integers mod `n`, which is of
         course far from optimal!
 

src/sage/categories/examples/finite_semigroups.py

@@ -1,12 +1,12 @@
 """
 Examples of finite semigroups
 """
-#*****************************************************************************
+# ***************************************************************************
 #  Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.sets.family import Family
@@ -107,7 +107,7 @@ class LeftRegularBand(UniqueRepresentation, Parent):
         running ._test_some_elements() . . . pass
     """
 
-    def __init__(self, alphabet=('a','b','c','d')):
+    def __init__(self, alphabet=('a', 'b', 'c', 'd')) -> None:
         r"""
         A left regular band.
 
@@ -123,7 +123,7 @@ def __init__(self, alphabet=('a','b','c','d')):
         Parent.__init__(self,
                         category=Semigroups().Finite().FinitelyGenerated())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         TESTS::
 
@@ -181,7 +181,7 @@ def an_element(self):
             'b'
         """
 
-        return self(''.join(self.alphabet[2:]+self.alphabet[0:2]))
+        return self(''.join(self.alphabet[2:] + self.alphabet[0:2]))
 
     class Element (ElementWrapper):
         wrapped_class = str

src/sage/categories/examples/finite_weyl_groups.py

@@ -73,7 +73,7 @@ class SymmetricGroup(UniqueRepresentation, Parent):
         sage: TestSuite(S).run()
     """
 
-    def __init__(self, n=4):
+    def __init__(self, n=4) -> None:
         """
         EXAMPLES::
 
@@ -84,14 +84,14 @@ def __init__(self, n=4):
         Parent.__init__(self, category=FiniteWeylGroups().Irreducible())
         self.n = n
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         EXAMPLES::
 
             sage: FiniteWeylGroups().example()
             The symmetric group on {0, ..., 3}
         """
-        return "The symmetric group on {0, ..., %s}" % (self.n-1)
+        return "The symmetric group on {0, ..., %s}" % (self.n - 1)
 
     @cached_method
     def one(self):
@@ -105,7 +105,7 @@ def one(self):
         """
         return self(tuple(range(self.n)))
 
-    def index_set(self):
+    def index_set(self) -> list[int]:
         """
         Implement :meth:`CoxeterGroups.ParentMethods.index_set`.
 
@@ -139,8 +139,8 @@ def cartan_type(self):
             ['A', 3] relabelled by {1: 0, 2: 1, 3: 2}
         """
         from sage.combinat.root_system.cartan_type import CartanType
-        C = CartanType(['A',self.n-1])
-        C = C.relabel(lambda i:i-1)
+        C = CartanType(['A', self.n - 1])
+        C = C.relabel(lambda i: i - 1)
         return C
 
     def product(self, x, y):
@@ -157,7 +157,7 @@ def product(self, x, y):
         assert y in self
         return self(tuple(x.value[i] for i in y.value))
 
-    def degrees(self):
+    def degrees(self) -> tuple:
         """
         Return the degrees of ``self``.
 
@@ -184,7 +184,7 @@ def has_right_descent(self, i) -> bool:
                 True
                 sage: S._test_has_descent()
             """
-            return (self.value[i] > self.value[i + 1])
+            return self.value[i] > self.value[i + 1]
 
 
 Example = SymmetricGroup

src/sage/categories/examples/magmas.py

@@ -48,7 +48,7 @@ class FreeMagma(UniqueRepresentation, Parent):
 
         sage: TestSuite(M).run()
     """
-    def __init__(self, alphabet=('a', 'b', 'c', 'd')):
+    def __init__(self, alphabet=('a', 'b', 'c', 'd')) -> None:
         r"""
         The free magma.
 
@@ -77,7 +77,7 @@ def __init__(self, alphabet=('a', 'b', 'c', 'd')):
 
         Parent.__init__(self, category=Magmas().FinitelyGenerated().Infinite())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         EXAMPLES::