From 246e679fbdfff832fd3f87a0655d9abcb105d7b8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Fri, 7 Nov 2025 20:28:49 +0100
Subject: [PATCH] add some typing in
 modular,modules,plot,schemes,symbolic,topology

---
 src/sage/modular/abvar/finite_subgroup.py     |  9 +++---
 .../modular/arithgroup/arithgroup_generic.py  |  4 +--
 src/sage/modular/arithgroup/farey_symbol.pyx  |  6 ++--
 src/sage/modules/fg_pid/fgp_module.py         | 20 ++++++-------
 .../modules/with_basis/indexed_element.pyx    |  6 ++--
 src/sage/plot/colors.py                       | 28 +++++++++----------
 .../schemes/elliptic_curves/ell_generic.py    |  8 +++---
 src/sage/schemes/elliptic_curves/height.py    | 12 ++++----
 .../schemes/elliptic_curves/isogeny_class.py  | 17 +++++------
 .../elliptic_curves/period_lattice_region.pyx |  6 ++--
 src/sage/topology/simplicial_complex.py       | 24 ++++++++--------
 src/sage/topology/simplicial_set.py           | 28 +++++++++----------
 12 files changed, 85 insertions(+), 83 deletions(-)

diff --git a/src/sage/modular/abvar/finite_subgroup.py b/src/sage/modular/abvar/finite_subgroup.py
index dda6f39e397..70e4247b0bf 100644
--- a/src/sage/modular/abvar/finite_subgroup.py
+++ b/src/sage/modular/abvar/finite_subgroup.py
@@ -143,7 +143,7 @@ class FiniteSubgroup(Module):
 
     Element = TorsionPoint
 
-    def __init__(self, abvar, field_of_definition=QQ):
+    def __init__(self, abvar, field_of_definition=QQ) -> None:
         """
         Initialize ``self``.
 
@@ -215,7 +215,7 @@ def _relative_basis_matrix(self):
             return M
 
     # General functionality
-    def __richcmp__(self, other, op):
+    def __richcmp__(self, other, op) -> bool:
         """
         Compare ``self`` to ``other``.
 
@@ -693,7 +693,7 @@ def _element_constructor_(self, x, check=True):
         x = self.lattice()(x, check=check)
         return self.element_class(self, x, check=False)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` if ``x`` is contained in this finite subgroup.
 
@@ -837,7 +837,8 @@ def invariants(self):
 
 
 class FiniteSubgroup_lattice(FiniteSubgroup):
-    def __init__(self, abvar, lattice, field_of_definition=None, check=True):
+    def __init__(self, abvar, lattice,
+                 field_of_definition=None, check=True) -> None:
         """
         A finite subgroup of a modular abelian variety that is defined by a
         given lattice.
diff --git a/src/sage/modular/arithgroup/arithgroup_generic.py b/src/sage/modular/arithgroup/arithgroup_generic.py
index 687d668e94a..649a410b6d1 100644
--- a/src/sage/modular/arithgroup/arithgroup_generic.py
+++ b/src/sage/modular/arithgroup/arithgroup_generic.py
@@ -145,7 +145,7 @@ def _element_constructor_(self, x, check=True):
             return x
         raise TypeError("matrix %s is not an element of %s" % (x, self))
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         r"""
         Test if x is an element of this group.
 
@@ -200,7 +200,7 @@ def _contains_sl2(self, a, b, c, d):
         """
         raise NotImplementedError("Please implement _contains_sl2 for %s" % self.__class__)
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         Return a hash of ``self``.
 
diff --git a/src/sage/modular/arithgroup/farey_symbol.pyx b/src/sage/modular/arithgroup/farey_symbol.pyx
index 2866b9de6e8..0107b9b2005 100644
--- a/src/sage/modular/arithgroup/farey_symbol.pyx
+++ b/src/sage/modular/arithgroup/farey_symbol.pyx
@@ -511,7 +511,7 @@ cdef class Farey:
         else:  # output == 'gens'
             return tuple((gens[a-1], len(list(g))) if a > 0 else (gens[-a-1], -len(list(g))) for a, g in groupby(tietze))
 
-    def __contains__(self, M):
+    def __contains__(self, M) -> bool:
         r"""
         Test if element is in the arithmetic group of the Farey symbol
         via LLT algorithm.
@@ -533,7 +533,7 @@ cdef class Farey:
         sig_off()
         return result
 
-    def __richcmp__(self, other, op):
+    def __richcmp__(self, other, op) -> bool:
         r"""
         Compare ``self`` to ``other``.
 
@@ -569,7 +569,7 @@ cdef class Farey:
         """
         return Farey, (self.group, self.this_ptr.dumps())
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         r"""
         Return the string representation of ``self``.
 
diff --git a/src/sage/modules/fg_pid/fgp_module.py b/src/sage/modules/fg_pid/fgp_module.py
index 105a0808b5d..59cf2c36d97 100644
--- a/src/sage/modules/fg_pid/fgp_module.py
+++ b/src/sage/modules/fg_pid/fgp_module.py
@@ -336,7 +336,7 @@ class FGP_Module_class(Module):
     # module. Should be overridden in derived classes.
     Element = FGP_Element
 
-    def __init__(self, V, W, check=True):
+    def __init__(self, V, W, check=True) -> None:
         """
         INPUT:
 
@@ -470,7 +470,7 @@ def _mul_(self, other, switch_sides=False):
         raise ValueError("Scalar multiplication of a module is only " +
                          "defined for an element of the base ring.")
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         """
         Return string representation of this module.
 
@@ -507,9 +507,9 @@ def __truediv__(self, other):
                 raise TypeError("other must be an FGP module")
         if not other.is_submodule(self):
             raise ValueError("other must be a submodule of self")
-        return self._module_constructor(self._V, other._V+self._W)
+        return self._module_constructor(self._V, other._V + self._W)
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         """
         EXAMPLES::
 
@@ -529,7 +529,7 @@ def __eq__(self, other):
             return False
         return self._V == other._V and self._W == other._W
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         """
         Return ``True`` iff ``self`` is not equal to ``other``.
 
@@ -569,7 +569,7 @@ def __ne__(self, other):
 
     # __le__ is a synonym for `is_submodule`: see below
 
-    def __lt__(self, other):
+    def __lt__(self, other) -> bool:
         """
         Return ``True`` iff ``self`` is a proper submodule of ``other``.
 
@@ -587,7 +587,7 @@ def __lt__(self, other):
         """
         return self <= other and not self == other
 
-    def __gt__(self, other):
+    def __gt__(self, other) -> bool:
         """
         Return ``True`` iff ``other`` is a proper submodule of ``self``.
 
@@ -605,7 +605,7 @@ def __gt__(self, other):
         """
         return self >= other and not self == other
 
-    def __ge__(self, other):
+    def __ge__(self, other) -> bool:
         """
         Return ``True`` iff ``other`` is a submodule of ``self``.
 
@@ -675,7 +675,7 @@ def linear_combination_of_smith_form_gens(self, x):
             raise TypeError(msg)
         return self.element_class(self, self._V(x))
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return true if ``x`` is contained in ``self``.
 
@@ -1940,7 +1940,7 @@ def ngens(self):
         """
         return len(self.gens())
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         r"""
         Calculate a hash for ``self``.
 
diff --git a/src/sage/modules/with_basis/indexed_element.pyx b/src/sage/modules/with_basis/indexed_element.pyx
index ff2579c583c..88656cd1a58 100644
--- a/src/sage/modules/with_basis/indexed_element.pyx
+++ b/src/sage/modules/with_basis/indexed_element.pyx
@@ -47,7 +47,7 @@ cdef class IndexedFreeModuleElement(ModuleElement):
         sage: isinstance(f, collections.abc.Collection)  # known bug - will be fixed by removing __contains__
         False
     """
-    def __init__(self, M, x):
+    def __init__(self, M, x) -> None:
         """
         Create a combinatorial module element.
 
@@ -84,7 +84,7 @@ cdef class IndexedFreeModuleElement(ModuleElement):
         """
         return iter(self._monomial_coefficients.items())
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return whether or not a combinatorial object ``x`` indexing a basis
         element is in the support of ``self``.
@@ -113,7 +113,7 @@ cdef class IndexedFreeModuleElement(ModuleElement):
         deprecation(34509, "using 'index in vector' is deprecated; use 'index in vector.support()' instead")
         return x in self.support()
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Return the hash value for ``self``.
 
diff --git a/src/sage/plot/colors.py b/src/sage/plot/colors.py
index bbb192c937b..4d7d5da146e 100644
--- a/src/sage/plot/colors.py
+++ b/src/sage/plot/colors.py
@@ -353,7 +353,7 @@ def rgbcolor(c, space='rgb'):
 
 
 class Color:
-    def __init__(self, r='#0000ff', g=None, b=None, space='rgb'):
+    def __init__(self, r='#0000ff', g=None, b=None, space='rgb') -> None:
         """
         A Red-Green-Blue (RGB) color model color object.  For most
         consumer-grade devices (e.g., CRTs, LCDs, and printers), as
@@ -400,7 +400,7 @@ def __init__(self, r='#0000ff', g=None, b=None, space='rgb'):
         else:
             self._rgb = rgbcolor((r, g, b), space=space)
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """
         Return a string representation of this color.
 
@@ -415,7 +415,7 @@ def __repr__(self):
         """
         return f"RGB color {self._rgb}"
 
-    def __lt__(self, right):
+    def __lt__(self, right) -> bool:
         """
         Check whether a :class:`Color` object is less than some other
         object. This doesn't make sense, and so we conclude that it is
@@ -438,7 +438,7 @@ def __lt__(self, right):
         """
         return False
 
-    def __le__(self, right):
+    def __le__(self, right) -> bool:
         """
         Check whether a :class:`Color` object is less than or equal to
         some other object. It wouldn't make sense for it to be less than
@@ -462,7 +462,7 @@ def __le__(self, right):
         """
         return self == right
 
-    def __eq__(self, right):
+    def __eq__(self, right) -> bool:
         """
         Compare two :class:`Color` objects to determine whether
         they refer to the same color.
@@ -489,7 +489,7 @@ def __eq__(self, right):
             return self._rgb == right._rgb
         return False
 
-    def __ne__(self, right):
+    def __ne__(self, right) -> bool:
         """
         Compare two :class:`Color` objects to determine whether
         they refer to different colors.
@@ -516,7 +516,7 @@ def __ne__(self, right):
         """
         return not (self == right)
 
-    def __gt__(self, right):
+    def __gt__(self, right) -> bool:
         """
         Check whether a :class:`Color` object is greater than some other
         object. This doesn't make sense, and so we conclude that it is
@@ -539,7 +539,7 @@ def __gt__(self, right):
         """
         return False
 
-    def __ge__(self, right):
+    def __ge__(self, right) -> bool:
         """
         Check whether a :class:`Color` object is greater than or equal
         to some other object. It wouldn't make sense for it to be
@@ -563,7 +563,7 @@ def __ge__(self, right):
         """
         return self == right
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Return the hash value of a color.
         Equal colors return equal hash values.
@@ -1004,7 +1004,7 @@ class ColorsDict(dict):
         sage: sorted(colors)
         ['aliceblue', 'antiquewhite', 'aqua', 'aquamarine', ...]
     """
-    def __init__(self):
+    def __init__(self) -> None:
         """
         Construct a dict-like collection of colors.  The keys are the
         color names (i.e., strings) and the values are RGB 3-tuples of
@@ -1364,7 +1364,7 @@ class Colormaps(MutableMapping):
         sage: sorted(colormaps)
         ['Accent', ...]
     """
-    def __init__(self):
+    def __init__(self) -> None:
         """
         Construct an empty mutable collection of color maps.
 
@@ -1418,7 +1418,7 @@ def __dir__(self):
                    '__setitem__', '__delitem__']
         return dir(super()) + methods + sorted(self)
 
-    def __len__(self):
+    def __len__(self) -> int:
         """
         Return the number of color maps.
 
@@ -1452,7 +1452,7 @@ def __iter__(self):
         self.load_maps()
         return iter(self.maps)
 
-    def __contains__(self, name):
+    def __contains__(self, name) -> bool:
         """
         Return whether a map is in the color maps collection.
 
@@ -1536,7 +1536,7 @@ def __getattr__(self, name):
         except KeyError:
             raise AttributeError("'{}' has no attribute or colormap {}".format(type(self).__name__, name))
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         """
         Return a string representation of the color map collection.
 
diff --git a/src/sage/schemes/elliptic_curves/ell_generic.py b/src/sage/schemes/elliptic_curves/ell_generic.py
index ba825196a04..c7e329c24e1 100644
--- a/src/sage/schemes/elliptic_curves/ell_generic.py
+++ b/src/sage/schemes/elliptic_curves/ell_generic.py
@@ -124,7 +124,7 @@ class EllipticCurve_generic(WithEqualityById, plane_curve.ProjectivePlaneCurve):
         sage: -5*P
         (179051/80089 : -91814227/22665187 : 1)
     """
-    def __init__(self, K, ainvs, category=None):
+    def __init__(self, K, ainvs, category=None) -> None:
         r"""
         Construct an elliptic curve from Weierstrass `a`-coefficients.
 
@@ -465,7 +465,7 @@ def _symbolic_(self, SR):
         x, y = SR.var('x, y')
         return y**2 + a[0]*x*y + a[2]*y == x**3 + a[1]*x**2 + a[3]*x + a[4]
 
-    def __contains__(self, P):
+    def __contains__(self, P) -> bool:
         """
         Return ``True`` if and only if P is a point on the elliptic curve.
 
@@ -1049,7 +1049,7 @@ def __getitem__(self, n):
         """
         raise NotImplementedError("not implemented.")
 
-    def __is_over_RationalField(self):
+    def __is_over_RationalField(self) -> bool:
         r"""
         Internal function. Return true iff the base ring of this elliptic
         curve is the field of rational numbers.
@@ -1065,7 +1065,7 @@ def __is_over_RationalField(self):
         """
         return isinstance(self.base_ring(), RationalField)
 
-    def is_on_curve(self, x, y):
+    def is_on_curve(self, x, y) -> bool:
         r"""
         Return ``True`` if `(x,y)` is an affine point on this curve.
 
diff --git a/src/sage/schemes/elliptic_curves/height.py b/src/sage/schemes/elliptic_curves/height.py
index 2cb478eb23a..22409a15386 100644
--- a/src/sage/schemes/elliptic_curves/height.py
+++ b/src/sage/schemes/elliptic_curves/height.py
@@ -76,7 +76,7 @@ class UnionOfIntervals:
         Unify :class:`UnionOfIntervals` with the class ``RealSet``
         introduced by :issue:`13125`; see :issue:`16063`.
     """
-    def __init__(self, endpoints):
+    def __init__(self, endpoints) -> None:
         r"""
         An union of intervals is initialized by giving an increasing list
         of endpoints, the first of which may be `-\infty` and the last of
@@ -419,7 +419,7 @@ def __and__(left, right):
         """
         return left.intersection([left, right])
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         r"""
         Return ``True`` if ``x`` is in the UnionOfIntervals.
 
@@ -443,7 +443,7 @@ def __contains__(self, x):
         """
         return x in self._endpoints or bisect.bisect_left(self._endpoints, x) % 2 == 1
 
-    def __str__(self):
+    def __str__(self) -> str:
         r"""
         Return the string representation of this UnionOfIntervals.
 
@@ -456,7 +456,7 @@ def __str__(self):
         """
         return repr(self)
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         r"""
         Return the string representation of this UnionOfIntervals.
 
@@ -766,7 +766,7 @@ class EllipticCurveCanonicalHeight:
          Elliptic Curve defined by y^2 = x^3 + 1 over Rational Field
     """
 
-    def __init__(self, E):
+    def __init__(self, E) -> None:
         r"""
         Initialize the class with an elliptic curve.
 
@@ -815,7 +815,7 @@ def __init__(self, E):
         else:
             raise ValueError("EllipticCurveCanonicalHeight class can only be created from an elliptic curve")
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         r"""
         Return the string representation.
 
diff --git a/src/sage/schemes/elliptic_curves/isogeny_class.py b/src/sage/schemes/elliptic_curves/isogeny_class.py
index a630af24d07..28043f56b95 100644
--- a/src/sage/schemes/elliptic_curves/isogeny_class.py
+++ b/src/sage/schemes/elliptic_curves/isogeny_class.py
@@ -49,7 +49,7 @@ class in the isogeny class. Over `\QQ` this is a unique reduced
         model chosen may change in future.
     """
 
-    def __init__(self, E, label=None, empty=False):
+    def __init__(self, E, label=None, empty=False) -> None:
         r"""
         Over `\QQ` we use curves since minimal models exist and there
         is a canonical choice of one.
@@ -71,7 +71,7 @@ def __init__(self, E, label=None, empty=False):
         if not empty:
             self._compute()
 
-    def __len__(self):
+    def __len__(self) -> int:
         """
         The number of curves in the class.
 
@@ -135,9 +135,9 @@ def index(self, C):
         for i, E in enumerate(self.curves):
             if C.is_isomorphic(E):
                 return i
-        raise ValueError("%s is not in isogeny class %s" % (C,self))
+        raise ValueError("%s is not in isogeny class %s" % (C, self))
 
-    def __richcmp__(self, other, op):
+    def __richcmp__(self, other, op) -> bool:
         """
         Compare ``self`` and ``other``.
 
@@ -160,7 +160,7 @@ def __richcmp__(self, other, op):
                            sorted(f.a_invariants() for f in other.curves), op)
         return NotImplemented
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Hash is based on the a-invariants of the sorted list of
         minimal models.
@@ -231,7 +231,7 @@ def _repr_(self):
         else:
             return "Isogeny class of %r" % (self.E)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         INPUT:
 
@@ -593,7 +593,8 @@ class IsogenyClass_EC_NumberField(IsogenyClass_EC):
     """
     Isogeny classes for elliptic curves over number fields.
     """
-    def __init__(self, E, reducible_primes=None, algorithm='Billerey', minimal_models=True):
+    def __init__(self, E, reducible_primes=None,
+                 algorithm='Billerey', minimal_models=True) -> None:
         r"""
         INPUT:
 
@@ -1003,7 +1004,7 @@ class IsogenyClass_EC_Rational(IsogenyClass_EC_NumberField):
     r"""
     Isogeny classes for elliptic curves over `\QQ`.
     """
-    def __init__(self, E, algorithm='sage', label=None, empty=False):
+    def __init__(self, E, algorithm='sage', label=None, empty=False) -> None:
         r"""
         INPUT:
 
diff --git a/src/sage/schemes/elliptic_curves/period_lattice_region.pyx b/src/sage/schemes/elliptic_curves/period_lattice_region.pyx
index 0640bf5585a..a8ceb5d5e73 100644
--- a/src/sage/schemes/elliptic_curves/period_lattice_region.pyx
+++ b/src/sage/schemes/elliptic_curves/period_lattice_region.pyx
@@ -48,7 +48,7 @@ cdef class PeriodicRegion:
     # the center).
     cdef readonly bint full
 
-    def __init__(self, w1, w2, data, full=True):
+    def __init__(self, w1, w2, data, full=True) -> None:
         """
         EXAMPLES::
 
@@ -312,7 +312,7 @@ cdef class PeriodicRegion:
         """
         return ~(~self).expand(corners)
 
-    def __contains__(self, z):
+    def __contains__(self, z) -> bool:
         """
         Return whether this region contains the given point.
 
@@ -518,7 +518,7 @@ cdef class PeriodicRegion:
             right._ensure_full()
         return PeriodicRegion(left.w1, left.w2, left.data ^ right.data, left.full)
 
-    def __richcmp__(left, right, op):
+    def __richcmp__(left, right, op) -> bool:
         """
         Compare two regions.
 
diff --git a/src/sage/topology/simplicial_complex.py b/src/sage/topology/simplicial_complex.py
index cc3253ec937..3340eea9c77 100644
--- a/src/sage/topology/simplicial_complex.py
+++ b/src/sage/topology/simplicial_complex.py
@@ -375,7 +375,7 @@ class Simplex(SageObject):
         TypeError: unhashable type: 'list'
     """
 
-    def __init__(self, X):
+    def __init__(self, X) -> None:
         """
         Define a simplex.  See :class:`Simplex` for full documentation.
 
@@ -446,7 +446,7 @@ def is_face(self, other) -> bool:
         """
         return self.__set.issubset(other.__set)
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` iff ``x`` is a vertex of this simplex.
 
@@ -693,10 +693,10 @@ def alexander_whitney(self, dim):
             sage: s.alexander_whitney(2)
             [(1, (0, 1, 3), (3, 4))]
         """
-        return [(ZZ.one(), Simplex(self.tuple()[:dim+1]),
+        return [(ZZ.one(), Simplex(self.tuple()[:dim + 1]),
                  Simplex(self.tuple()[dim:]))]
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         """
         Return ``True`` iff this simplex is the same as ``other``: that
         is, if the vertices of the two are the same, even with a
@@ -721,7 +721,7 @@ def __eq__(self, other):
             return False
         return set(self) == set(other)
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         """
         Return ``True`` iff this simplex is not equal to ``other``.
 
@@ -738,7 +738,7 @@ def __ne__(self, other):
         """
         return not self == other
 
-    def __lt__(self, other):
+    def __lt__(self, other) -> bool:
         """
         Return ``True`` iff the sorted tuple for this simplex is less than
         that for ``other``.
@@ -786,7 +786,7 @@ def __lt__(self, other):
         except TypeError:
             return sorted(map(str, self)) < sorted(map(str, other))
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Hash value for this simplex.  This computes the hash value of
         the Python frozenset of the underlying tuple, since this is
@@ -962,7 +962,7 @@ def __init__(self,
                  name_check=False,
                  is_mutable=True,
                  is_immutable=False,
-                 category=None):
+                 category=None) -> None:
         """
         Define a simplicial complex.  See ``SimplicialComplex`` for more
         documentation.
@@ -1146,7 +1146,7 @@ def __init__(self,
         # bigraded_betti_numbers(base_ring=base_ring)
         self._bbn_all_computed = set()
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         Compute the hash value of ``self``.
 
@@ -1173,7 +1173,7 @@ def __hash__(self):
             raise ValueError("this simplicial complex must be immutable; call set_immutable()")
         return hash(frozenset(self._facets))
 
-    def __eq__(self, right):
+    def __eq__(self, right) -> bool:
         """
         Two simplicial complexes are equal iff their vertex sets are
         equal and their sets of facets are equal.
@@ -1189,7 +1189,7 @@ def __eq__(self, right):
         """
         return isinstance(right, SimplicialComplex) and set(self._facets) == set(right._facets)
 
-    def __ne__(self, right):
+    def __ne__(self, right) -> bool:
         """
         Return ``True`` if ``self`` and ``right`` are not equal.
 
@@ -1256,7 +1256,7 @@ def _an_element_(self):
         except TypeError:
             return self.facets()[0]
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` if ``x`` is a simplex which is contained in this complex.
 
diff --git a/src/sage/topology/simplicial_set.py b/src/sage/topology/simplicial_set.py
index 7387dde2f94..a106ff67404 100644
--- a/src/sage/topology/simplicial_set.py
+++ b/src/sage/topology/simplicial_set.py
@@ -296,7 +296,7 @@ class AbstractSimplex_class(SageObject):
     """
 
     def __init__(self, dim, degeneracies=(), underlying=None, name=None,
-                 latex_name=None):
+                 latex_name=None) -> None:
         """
         A simplex of dimension ``dim``.
 
@@ -400,7 +400,7 @@ def __init__(self, dim, degeneracies=(), underlying=None, name=None,
             self.rename(name)
         self._latex_name = latex_name
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         If nondegenerate: return the id of this simplex.
 
@@ -424,7 +424,7 @@ def __hash__(self):
             return id(self)
         return hash(self.nondegenerate()) ^ hash(self._degens)
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         """
         Two nondegenerate simplices are equal if they are identical.
         Two degenerate simplices are equal if their underlying
@@ -453,7 +453,7 @@ def __eq__(self, other):
         return (self._degens == other._degens
                 and self.nondegenerate() is other.nondegenerate())
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         """
         This returns the negation of ``__eq__``.
 
@@ -471,7 +471,7 @@ def __ne__(self, other):
         """
         return not self == other
 
-    def __lt__(self, other):
+    def __lt__(self, other) -> bool:
         """
         We implement sorting in the hopes that sorted lists of simplices,
         for example as defining data for a simplicial set, will be
@@ -580,7 +580,7 @@ def __lt__(self, other):
             return False
         return id(self) < id(other)
 
-    def __gt__(self, other):
+    def __gt__(self, other) -> bool:
         """
         See :meth:`__lt__` for more doctests.
 
@@ -594,7 +594,7 @@ def __gt__(self, other):
         """
         return not (self < other or self == other)
 
-    def __le__(self, other):
+    def __le__(self, other) -> bool:
         """
         See :meth:`__lt__` for more doctests.
 
@@ -608,7 +608,7 @@ def __le__(self, other):
         """
         return self < other or self == other
 
-    def __ge__(self, other):
+    def __ge__(self, other) -> bool:
         """
         See :meth:`__lt__` for more doctests.
 
@@ -916,7 +916,7 @@ def _latex_(self):
 # __ge__, __le__. Inheriting from AbstractSimplex_class first seems to
 # be slightly faster.
 class NonDegenerateSimplex(AbstractSimplex_class, WithEqualityById):
-    def __init__(self, dim, name=None, latex_name=None):
+    def __init__(self, dim, name=None, latex_name=None) -> None:
         """
         A nondegenerate simplex.
 
@@ -1225,7 +1225,7 @@ def face(self, simplex, i):
             return self.faces(simplex)[i]
         return None
 
-    def __contains__(self, x):
+    def __contains__(self, x) -> bool:
         """
         Return ``True`` if ``x`` is a simplex which is contained in this complex.
 
@@ -3204,7 +3204,7 @@ class SimplicialSet_finite(SimplicialSet_arbitrary, GenericCellComplex):
     """
 
     def __init__(self, data, base_point=None, name=None, check=True,
-                 category=None, latex_name=None):
+                 category=None, latex_name=None) -> None:
         r"""
         TESTS::
 
@@ -3379,7 +3379,7 @@ def face(sigma, i):
             self.rename(name)
         self._latex_name = latex_name
 
-    def __eq__(self, other):
+    def __eq__(self, other) -> bool:
         """
         Return ``True`` if ``self`` and ``other`` are equal as simplicial sets.
 
@@ -3413,7 +3413,7 @@ def __eq__(self, other):
                     and not other.is_pointed()
                     and sorted(self._data) == sorted(other._data))
 
-    def __ne__(self, other):
+    def __ne__(self, other) -> bool:
         """
         Return ``True`` if ``self`` and ``other`` are not equal as simplicial sets.
 
@@ -3439,7 +3439,7 @@ def __ne__(self, other):
     # computes their hash. If the tuple self._data is long, this can
     # take a long time.
     @cached_method
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         The hash is formed from that of the tuple ``self._data``.