From 7ab8ccff185f779571cd6d4b78f0f9e7e365b0d6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Fri, 14 Nov 2025 20:01:56 +0100
Subject: [PATCH] typing "__contains__" in categories,geometry,groups,monoids

---
 src/sage/categories/algebras.py                    |  2 +-
 src/sage/categories/category.py                    |  2 +-
 src/sage/categories/category_types.py              |  4 ++--
 src/sage/categories/commutative_algebras.py        |  2 +-
 .../categories/examples/finite_coxeter_groups.py   |  4 ++--
 .../categories/examples/finite_enumerated_sets.py  |  6 +++---
 .../examples/infinite_enumerated_sets.py           |  4 ++--
 src/sage/categories/examples/sets_cat.py           | 14 +++++++-------
 src/sage/categories/facade_sets.py                 |  2 +-
 src/sage/categories/fields.py                      |  2 +-
 src/sage/categories/finite_fields.py               |  2 +-
 src/sage/categories/homset.py                      |  6 +++---
 src/sage/categories/integral_domains.py            |  2 +-
 src/sage/categories/number_fields.py               |  2 +-
 src/sage/categories/objects.py                     |  2 +-
 src/sage/categories/sets_cat.py                    |  4 ++--
 .../categories/unique_factorization_domains.py     |  2 +-
 src/sage/geometry/cone.py                          |  6 +++---
 src/sage/geometry/fan.py                           |  2 +-
 .../hyperplane_arrangement/affine_subspace.py      |  2 +-
 .../geometry/hyperplane_arrangement/hyperplane.py  |  2 +-
 src/sage/geometry/relative_interior.py             |  4 ++--
 src/sage/geometry/toric_lattice.py                 |  2 +-
 src/sage/groups/abelian_gps/abelian_group.py       |  2 +-
 src/sage/groups/abelian_gps/dual_abelian_group.py  |  2 +-
 src/sage/groups/conjugacy_classes.py               |  4 ++--
 src/sage/groups/libgap_mixin.py                    |  2 +-
 src/sage/groups/perm_gps/permgroup_named.py        | 10 +++++-----
 src/sage/monoids/free_abelian_monoid.py            |  2 +-
 src/sage/monoids/free_monoid.py                    |  2 +-
 src/sage/monoids/string_monoid.py                  |  4 ++--
 31 files changed, 54 insertions(+), 54 deletions(-)

diff --git a/src/sage/categories/algebras.py b/src/sage/categories/algebras.py
index db42b0ea6d1..9fe03c5c309 100644
--- a/src/sage/categories/algebras.py
+++ b/src/sage/categories/algebras.py
@@ -59,7 +59,7 @@ class Algebras(CategoryWithAxiom_over_base_ring):
     _base_category_class_and_axiom = (AssociativeAlgebras, 'Unital')
 
     # For backward compatibility?
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Membership testing.
 
diff --git a/src/sage/categories/category.py b/src/sage/categories/category.py
index 360127f0a78..7643bb08abe 100644
--- a/src/sage/categories/category.py
+++ b/src/sage/categories/category.py
@@ -684,7 +684,7 @@ def _subcategory_hook_(self, category):
         """
         return issubclass(category.parent_class, self.parent_class)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Membership testing.
 
diff --git a/src/sage/categories/category_types.py b/src/sage/categories/category_types.py
index c29a4e385c0..2b976b54083 100644
--- a/src/sage/categories/category_types.py
+++ b/src/sage/categories/category_types.py
@@ -491,7 +491,7 @@ def _subcategory_hook_(self, C):
             return C.base() in base_ring
         return False
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return whether ``x`` is an object of this category.
 
@@ -605,7 +605,7 @@ def ring(self):
         """
         return self.ambient()
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/commutative_algebras.py b/src/sage/categories/commutative_algebras.py
index aa3107fc509..506004a2dbb 100644
--- a/src/sage/categories/commutative_algebras.py
+++ b/src/sage/categories/commutative_algebras.py
@@ -46,7 +46,7 @@ class CommutativeAlgebras(CategoryWithAxiom_over_base_ring):
      - coproduct ( = tensor product over base ring)
     """
 
-    def __contains__(self, A):
+    def __contains__(self, A) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/examples/finite_coxeter_groups.py b/src/sage/categories/examples/finite_coxeter_groups.py
index 9764e5b3587..032f93cbb25 100644
--- a/src/sage/categories/examples/finite_coxeter_groups.py
+++ b/src/sage/categories/examples/finite_coxeter_groups.py
@@ -103,7 +103,7 @@ def __init__(self, n=5):
         Parent.__init__(self, category=FiniteCoxeterGroups())
         self.n = n
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         EXAMPLES::
 
@@ -114,7 +114,7 @@ def _repr_(self):
         """
         return "The %s-th dihedral group of order %s" % (self.n, 2 * self.n)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         r"""
         Check if the element ``x`` is in the mathematical parent ``self``.
 
diff --git a/src/sage/categories/examples/finite_enumerated_sets.py b/src/sage/categories/examples/finite_enumerated_sets.py
index 04b7d2f0dad..e14386904e4 100644
--- a/src/sage/categories/examples/finite_enumerated_sets.py
+++ b/src/sage/categories/examples/finite_enumerated_sets.py
@@ -81,7 +81,7 @@ def __init__(self):
         Parent.__init__(self, facade=IntegerRing(),
                         category=FiniteEnumeratedSets())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         TESTS::
 
@@ -90,7 +90,7 @@ def _repr_(self):
         """
         return "An example of a finite enumerated set: {1,2,3}"
 
-    def __contains__(self, o):
+    def __contains__(self, o) -> bool:
         """
         EXAMPLES::
 
@@ -182,7 +182,7 @@ def retract(self, x):
         """
         return x ** 2
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Membership testing by checking whether the preimage by the
         bijection is in the ambient space.
diff --git a/src/sage/categories/examples/infinite_enumerated_sets.py b/src/sage/categories/examples/infinite_enumerated_sets.py
index 49935ff6d02..4d1dc54dc31 100644
--- a/src/sage/categories/examples/infinite_enumerated_sets.py
+++ b/src/sage/categories/examples/infinite_enumerated_sets.py
@@ -91,7 +91,7 @@ def __init__(self):
         """
         Parent.__init__(self, category=InfiniteEnumeratedSets())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         TESTS::
 
@@ -100,7 +100,7 @@ def _repr_(self):
         """
         return "An example of an infinite enumerated set: the nonnegative integers"
 
-    def __contains__(self, elt):
+    def __contains__(self, elt) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/examples/sets_cat.py b/src/sage/categories/examples/sets_cat.py
index c28f483df03..57a7656dd8c 100644
--- a/src/sage/categories/examples/sets_cat.py
+++ b/src/sage/categories/examples/sets_cat.py
@@ -115,9 +115,9 @@ def an_element(self):
             sage: x.parent()
             Integer Ring
         """
-        return self(47) # if speed is needed, call: self.element_class(47)
+        return self(47)  # if speed is needed, call: self.element_class(47)
 
-    def __contains__(self, p):
+    def __contains__(self, p) -> bool:
         """
         TESTS::
 
@@ -393,7 +393,7 @@ def __init__(self):
         super().__init__()
         self._populate_coercion_lists_(embedding=IntegerRing())
 
-    def __contains__(self, p):
+    def __contains__(self, p) -> bool:
         """
         TESTS::
 
@@ -502,7 +502,7 @@ def __init__(self):
         self.mor = Hom(self, IntegerRing())(lambda z: z.value)
         self._populate_coercion_lists_(embedding=self.mor)
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         TESTS::
 
@@ -511,7 +511,7 @@ def _repr_(self):
         """
         return "Set of prime numbers (wrapper implementation)"
 
-    def __contains__(self, p):
+    def __contains__(self, p) -> bool:
         """
         TESTS::
 
@@ -665,7 +665,7 @@ def __init__(self):
         """
         Parent.__init__(self, facade=IntegerRing(), category=Sets())
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         TESTS::
 
@@ -674,7 +674,7 @@ def _repr_(self):
         """
         return "Set of prime numbers (facade implementation)"
 
-    def __contains__(self, p):
+    def __contains__(self, p) -> bool:
         """
         TESTS::
 
diff --git a/src/sage/categories/facade_sets.py b/src/sage/categories/facade_sets.py
index 0bdd7c6df2b..e9ce33c9bf2 100644
--- a/src/sage/categories/facade_sets.py
+++ b/src/sage/categories/facade_sets.py
@@ -180,7 +180,7 @@ def is_parent_of(self, element):
             from sage.structure.element import parent
             return parent(element) in parents
 
-        def __contains__(self, element):
+        def __contains__(self, element) -> bool:
             """
             Membership testing.
 
diff --git a/src/sage/categories/fields.py b/src/sage/categories/fields.py
index 0c07b4d85e2..62288165df0 100644
--- a/src/sage/categories/fields.py
+++ b/src/sage/categories/fields.py
@@ -61,7 +61,7 @@ def extra_super_categories(self):
         """
         return [EuclideanDomains(), NoetherianRings()]
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/finite_fields.py b/src/sage/categories/finite_fields.py
index 7c418ec596d..55a69ab48b6 100644
--- a/src/sage/categories/finite_fields.py
+++ b/src/sage/categories/finite_fields.py
@@ -66,7 +66,7 @@ def extra_super_categories(self):
         """
         return [EnumeratedSets().Finite()]
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
index 94a65904c90..1e627d87516 100644
--- a/src/sage/categories/homset.py
+++ b/src/sage/categories/homset.py
@@ -1074,7 +1074,7 @@ def element_class_set_morphism(self):
         """
         return self.__make_element_class__(morphism.SetMorphism)
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         """
         For two homsets, it is tested whether the domain, the codomain and
         the category coincide.
@@ -1094,7 +1094,7 @@ def __eq__(self, other):
                 and self._codomain == other._codomain
                 and self.__category == other.__category)
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         """
         Check for not-equality of ``self`` and ``other``.
 
@@ -1113,7 +1113,7 @@ def __ne__(self, other):
         """
         return not (self == other)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Test whether the parent of the argument is ``self``.
 
diff --git a/src/sage/categories/integral_domains.py b/src/sage/categories/integral_domains.py
index d426366243e..65653640002 100644
--- a/src/sage/categories/integral_domains.py
+++ b/src/sage/categories/integral_domains.py
@@ -62,7 +62,7 @@ class IntegralDomains(CategoryWithAxiom):
     """
     _base_category_class_and_axiom = (Domains, "Commutative")
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/categories/number_fields.py b/src/sage/categories/number_fields.py
index c6edc341bb1..73dfb39c105 100644
--- a/src/sage/categories/number_fields.py
+++ b/src/sage/categories/number_fields.py
@@ -68,7 +68,7 @@ def super_categories(self):
         """
         return [Fields().Infinite()]
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         r"""
         Return ``True`` if ``x`` is a number field.
 
diff --git a/src/sage/categories/objects.py b/src/sage/categories/objects.py
index 169adf5af77..4dd1c61e2c7 100644
--- a/src/sage/categories/objects.py
+++ b/src/sage/categories/objects.py
@@ -62,7 +62,7 @@ def super_categories(self):
         """
         return []
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Anything is in the category of objects.
 
diff --git a/src/sage/categories/sets_cat.py b/src/sage/categories/sets_cat.py
index a44e7ae97d5..4d8dee22b9f 100644
--- a/src/sage/categories/sets_cat.py
+++ b/src/sage/categories/sets_cat.py
@@ -1037,7 +1037,7 @@ def is_parent_of(self, element):
             return parent(element) == self
 
         @abstract_method
-        def __contains__(self, x):
+        def __contains__(self, x) -> bool:
             """
             Test whether the set ``self`` contains the object ``x``.
 
@@ -3116,7 +3116,7 @@ def _an_element_(self):
                 return self.a_realization().an_element()
 
             # TODO: maybe this could be taken care of by Sets.Facade()?
-            def __contains__(self, x):
+            def __contains__(self, x) -> bool:
                 r"""
                 Test whether ``x`` is in ``self``, that is if it is an
                 element of some realization of ``self``.
diff --git a/src/sage/categories/unique_factorization_domains.py b/src/sage/categories/unique_factorization_domains.py
index f01763d4a7e..a9704872d84 100644
--- a/src/sage/categories/unique_factorization_domains.py
+++ b/src/sage/categories/unique_factorization_domains.py
@@ -60,7 +60,7 @@ def additional_structure(self):
         """
         return None
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         EXAMPLES::
 
diff --git a/src/sage/geometry/cone.py b/src/sage/geometry/cone.py
index 933f3341613..2a6cdfc2e5b 100644
--- a/src/sage/geometry/cone.py
+++ b/src/sage/geometry/cone.py
@@ -1560,7 +1560,7 @@ def _PPL_cone(self):
             self._PPL_C_Polyhedron = C_Polyhedron(gs)
         return self._PPL_C_Polyhedron
 
-    def __contains__(self, point):
+    def __contains__(self, point) -> bool:
         r"""
         Check if ``point`` is contained in ``self``.
 
@@ -1599,7 +1599,7 @@ def __getstate__(self):
             False
         """
         state = copy(self.__dict__)
-        state.pop("_PPL_C_Polyhedron", None) # PPL is not picklable.
+        state.pop("_PPL_C_Polyhedron", None)  # PPL is not picklable.
 
         # TODO: do we want to keep the face lattice in the pickle?
         # Currently there is an unpickling loop if do:
@@ -1611,7 +1611,7 @@ def __getstate__(self):
         state.pop("_face_lattice", None)
         return state
 
-    def _contains(self, point, region='whole cone'):
+    def _contains(self, point, region='whole cone') -> bool:
         r"""
         Check if ``point`` is contained in ``self``.
 
diff --git a/src/sage/geometry/fan.py b/src/sage/geometry/fan.py
index b4f00a3bab4..6ade0e7c3d9 100644
--- a/src/sage/geometry/fan.py
+++ b/src/sage/geometry/fan.py
@@ -1327,7 +1327,7 @@ def __richcmp__(self, right, op):
         else:
             return NotImplemented
 
-    def __contains__(self, cone):
+    def __contains__(self, cone) -> bool:
         r"""
         Check if ``cone`` is equivalent to a cone of the fan.
 
diff --git a/src/sage/geometry/hyperplane_arrangement/affine_subspace.py b/src/sage/geometry/hyperplane_arrangement/affine_subspace.py
index 94d004f987f..034bba9cf36 100644
--- a/src/sage/geometry/hyperplane_arrangement/affine_subspace.py
+++ b/src/sage/geometry/hyperplane_arrangement/affine_subspace.py
@@ -254,7 +254,7 @@ def __lt__(self, other):
             return False
         return self <= other
 
-    def __contains__(self, q):
+    def __contains__(self, q) -> bool:
         r"""
         Test whether the point ``q`` is in the affine space.
 
diff --git a/src/sage/geometry/hyperplane_arrangement/hyperplane.py b/src/sage/geometry/hyperplane_arrangement/hyperplane.py
index 38e0761330b..f751811db12 100644
--- a/src/sage/geometry/hyperplane_arrangement/hyperplane.py
+++ b/src/sage/geometry/hyperplane_arrangement/hyperplane.py
@@ -249,7 +249,7 @@ def _normal_pivot(self):
                 max_value = values[i]
         return max_pos
 
-    def __contains__(self, q):
+    def __contains__(self, q) -> bool:
         r"""
         Test whether the point ``q`` is in the hyperplane.
 
diff --git a/src/sage/geometry/relative_interior.py b/src/sage/geometry/relative_interior.py
index 3d7aa5d1c36..8dc9f95018c 100644
--- a/src/sage/geometry/relative_interior.py
+++ b/src/sage/geometry/relative_interior.py
@@ -56,7 +56,7 @@ def __init__(self, polyhedron):
             if hasattr(polyhedron, "_add_dependent_object"):
                 polyhedron._add_dependent_object(self)
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         TESTS::
 
@@ -67,7 +67,7 @@ def __hash__(self):
         """
         return hash(self._polyhedron) ^ 1789
 
-    def __contains__(self, point):
+    def __contains__(self, point) -> bool:
         r"""
         Return whether ``self`` contains ``point``.
 
diff --git a/src/sage/geometry/toric_lattice.py b/src/sage/geometry/toric_lattice.py
index 53346206c05..b24384b3c68 100644
--- a/src/sage/geometry/toric_lattice.py
+++ b/src/sage/geometry/toric_lattice.py
@@ -483,7 +483,7 @@ def _coerce_map_from_(self, other):
             return None
         return super()._convert_map_from_(other)
 
-    def __contains__(self, point):
+    def __contains__(self, point) -> bool:
         r"""
         Check if ``point`` is an element of ``self``.
 
diff --git a/src/sage/groups/abelian_gps/abelian_group.py b/src/sage/groups/abelian_gps/abelian_group.py
index 22109fb13fa..80a117f041d 100644
--- a/src/sage/groups/abelian_gps/abelian_group.py
+++ b/src/sage/groups/abelian_gps/abelian_group.py
@@ -1741,7 +1741,7 @@ def __init__(self, ambient, gens, names='f', category=None):
             category = Groups().Commutative().Subobjects()
         AbelianGroup_class.__init__(self, invs, names, category=category)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Test whether ``x`` is an element of this subgroup.
 
diff --git a/src/sage/groups/abelian_gps/dual_abelian_group.py b/src/sage/groups/abelian_gps/dual_abelian_group.py
index 1c353a90136..9a06c276048 100644
--- a/src/sage/groups/abelian_gps/dual_abelian_group.py
+++ b/src/sage/groups/abelian_gps/dual_abelian_group.py
@@ -332,7 +332,7 @@ def invariants(self):
         # TODO: deprecate
         return self.group().gens_orders()
 
-    def __contains__(self, X):
+    def __contains__(self, X) -> bool:
         """
         Implement "in".
 
diff --git a/src/sage/groups/conjugacy_classes.py b/src/sage/groups/conjugacy_classes.py
index e51995e51d8..a367e61ac7d 100644
--- a/src/sage/groups/conjugacy_classes.py
+++ b/src/sage/groups/conjugacy_classes.py
@@ -159,7 +159,7 @@ def __ne__(self, other):
         """
         return not (self == other)
 
-    def __contains__(self, element):
+    def __contains__(self, element) -> bool:
         r"""
         Check if ``element`` belongs to the conjugacy class ``self``.
 
@@ -440,7 +440,7 @@ def cardinality(self):
         """
         return self._gap_().Size().sage()
 
-    def __contains__(self, g):
+    def __contains__(self, g) -> bool:
         r"""
         Containment test.
 
diff --git a/src/sage/groups/libgap_mixin.py b/src/sage/groups/libgap_mixin.py
index a6054fb0371..c1bf5ef7742 100644
--- a/src/sage/groups/libgap_mixin.py
+++ b/src/sage/groups/libgap_mixin.py
@@ -22,7 +22,7 @@
 
 
 class GroupMixinLibGAP:
-    def __contains__(self, elt):
+    def __contains__(self, elt) -> bool:
         r"""
         TESTS::
 
diff --git a/src/sage/groups/perm_gps/permgroup_named.py b/src/sage/groups/perm_gps/permgroup_named.py
index d0c139469e6..2975421e51d 100644
--- a/src/sage/groups/perm_gps/permgroup_named.py
+++ b/src/sage/groups/perm_gps/permgroup_named.py
@@ -2035,7 +2035,7 @@ def __init__(self):
     # We override the __call__ as the elements are not instances of Element
     __call__ = DisjointUnionEnumeratedSets._element_constructor_facade
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         TESTS::
 
@@ -2044,7 +2044,7 @@ def _repr_(self):
         """
         return "Transitive Groups"
 
-    def __contains__(self, G):
+    def __contains__(self, G) -> bool:
         r"""
         EXAMPLES::
 
@@ -2111,7 +2111,7 @@ def _repr_(self):
         """
         return "Transitive Groups of degree %s" % (self._degree,)
 
-    def __contains__(self, G):
+    def __contains__(self, G) -> bool:
         r"""
         EXAMPLES::
 
@@ -2445,7 +2445,7 @@ def _repr_(self):
         """
         return "Primitive Groups"
 
-    def __contains__(self, G):
+    def __contains__(self, G) -> bool:
         r"""
         Test whether `G` is in ``self``.
 
@@ -2518,7 +2518,7 @@ def _repr_(self):
         """
         return "Primitive Groups of degree %s" % (self._degree)
 
-    def __contains__(self, G):
+    def __contains__(self, G) -> bool:
         r"""
         Test whether `G` is in ``self``.
 
diff --git a/src/sage/monoids/free_abelian_monoid.py b/src/sage/monoids/free_abelian_monoid.py
index 26144cbe6c6..77da79e29cb 100644
--- a/src/sage/monoids/free_abelian_monoid.py
+++ b/src/sage/monoids/free_abelian_monoid.py
@@ -224,7 +224,7 @@ def __call__(self, x):
             return x
         return self.element_class(self, x)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` if `x` is an element of this abelian monoid.
 
diff --git a/src/sage/monoids/free_monoid.py b/src/sage/monoids/free_monoid.py
index 4d6afef8e9f..e5efbf477e7 100644
--- a/src/sage/monoids/free_monoid.py
+++ b/src/sage/monoids/free_monoid.py
@@ -271,7 +271,7 @@ def _element_constructor_(self, x, check=True):
 
         raise TypeError("argument x (= %s) is of the wrong type" % x)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         return isinstance(x, FreeMonoidElement) and x.parent() == self
 
     def gen(self, i=0):
diff --git a/src/sage/monoids/string_monoid.py b/src/sage/monoids/string_monoid.py
index 61814c421c5..e60bbbf0b02 100644
--- a/src/sage/monoids/string_monoid.py
+++ b/src/sage/monoids/string_monoid.py
@@ -54,10 +54,10 @@ def __init__(self, n, alphabet=()):
         FreeMonoid.__init__(self, n)
         self._alphabet = alphabet
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         return isinstance(x, StringMonoidElement) and x.parent() == self
 
-    def alphabet(self):
+    def alphabet(self) -> tuple:
         return tuple(self._alphabet)
 
     def one(self):