gh-40848: type annotation for is_simple and is_smooth
    
and a few other `-> bool` on the way

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40848
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/algebras/lie_algebras/verma_module.py

@@ -552,7 +552,7 @@ def _dominant_data(self):
         wt, w = (self._weight + P.rho()).to_dominant_chamber(reduced_word=True)
         return (wt - P.rho(), w)
 
-    def is_singular(self):
+    def is_singular(self) -> bool:
         r"""
         Return if ``self`` is a singular Verma module.
 
@@ -582,7 +582,7 @@ def is_singular(self):
         """
         return not self._dominant_data[0].is_dominant()
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Return if ``self`` is a simple module.
 
@@ -1083,7 +1083,7 @@ def _composition_(self, right, homset):
             return homset.element_class(homset, right._scalar * self._scalar)
         return super()._composition_(right, homset)
 
-    def is_injective(self):
+    def is_injective(self) -> bool:
         r"""
         Return if ``self`` is injective or not.
 
@@ -1112,7 +1112,7 @@ def is_injective(self):
             return False
         return bool(self._scalar)
 
-    def is_surjective(self):
+    def is_surjective(self) -> bool:
         r"""
         Return if ``self`` is surjective or not.
 

src/sage/dynamics/arithmetic_dynamics/wehlerK3.py

@@ -1003,7 +1003,7 @@ def degenerate_primes(self, check=True):
                     bad_primes.remove(p)
         return bad_primes
 
-    def is_smooth(self):
+    def is_smooth(self) -> bool:
         r"""
         Function will return the status of the smoothness of the surface.
 

src/sage/geometry/cone.py

@@ -3240,7 +3240,7 @@ def is_isomorphic(self, other):
         raise NotImplementedError("isomorphism check for not strictly convex "
                                   "cones is not implemented")
 
-    def is_simplicial(self):
+    def is_simplicial(self) -> bool:
         r"""
         Check if ``self`` is simplicial.
 
@@ -3262,7 +3262,7 @@ def is_simplicial(self):
         return self.nrays() == self.dim()
 
     @cached_method
-    def is_smooth(self):
+    def is_smooth(self) -> bool:
         r"""
         Check if ``self`` is smooth.
 
@@ -3310,7 +3310,7 @@ def is_empty(self):
         """
         return False
 
-    def is_trivial(self):
+    def is_trivial(self) -> bool:
         """
         Check if the cone has no rays.
 
@@ -3328,7 +3328,7 @@ def is_trivial(self):
 
     is_compact = is_trivial
 
-    def is_strictly_convex(self):
+    def is_strictly_convex(self) -> bool:
         r"""
         Check if ``self`` is strictly convex.
 

src/sage/geometry/hyperplane_arrangement/arrangement.py

@@ -1612,7 +1612,7 @@ def center(self):
         return self.is_central(certificate=True)[1]
 
     @cached_method
-    def is_simplicial(self):
+    def is_simplicial(self) -> bool:
         r"""
         Test whether the arrangement is simplicial.
 

src/sage/geometry/polyhedron/base3.py

@@ -1100,7 +1100,7 @@ def a_maximal_chain(self):
                 for face in comb_chain] + \
                [universe]
 
-    def is_simplex(self):
+    def is_simplex(self) -> bool:
         r"""
         Return whether the polyhedron is a simplex.
 
@@ -1152,7 +1152,7 @@ def simplicity(self):
             raise NotImplementedError("this function is implemented for polytopes only")
         return self.combinatorial_polyhedron().simplicity()
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         """
         Test for simplicity of a polytope.
 
@@ -1203,7 +1203,7 @@ def simpliciality(self):
             raise NotImplementedError("this function is implemented for polytopes only")
         return self.combinatorial_polyhedron().simpliciality()
 
-    def is_simplicial(self):
+    def is_simplicial(self) -> bool:
         """
         Test if the polytope is simplicial.
 

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -2128,7 +2128,7 @@ cdef class CombinatorialPolyhedron(SageObject):
         return smallInteger(simpliciality)
 
     @cached_method
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Test whether the polytope is simple.
 
@@ -2239,7 +2239,7 @@ cdef class CombinatorialPolyhedron(SageObject):
         return smallInteger(simplicity)
 
     @cached_method
-    def is_lawrence_polytope(self):
+    def is_lawrence_polytope(self) -> bool:
         r"""
         Return ``True`` if ``self`` is a Lawrence polytope.
 
@@ -2338,7 +2338,7 @@ cdef class CombinatorialPolyhedron(SageObject):
         return not any(vertices)
 
     @cached_method
-    def is_pyramid(self, certificate=False):
+    def is_pyramid(self, certificate=False) -> bool:
         r"""
         Test whether the polytope is a pyramid over one of its facets.
 

src/sage/groups/libgap_mixin.py

@@ -53,7 +53,7 @@ def __contains__(self, elt):
                 return False
             return elt == elt2
 
-    def is_abelian(self):
+    def is_abelian(self) -> bool:
         r"""
         Return whether the group is Abelian.
 
@@ -75,7 +75,7 @@ def is_abelian(self):
         """
         return self.gap().IsAbelian().sage()
 
-    def is_nilpotent(self):
+    def is_nilpotent(self) -> bool:
         r"""
         Return whether this group is nilpotent.
 
@@ -89,7 +89,7 @@ def is_nilpotent(self):
         """
         return self.gap().IsNilpotentGroup().sage()
 
-    def is_solvable(self):
+    def is_solvable(self) -> bool:
         r"""
         Return whether this group is solvable.
 
@@ -103,7 +103,7 @@ def is_solvable(self):
         """
         return self.gap().IsSolvableGroup().sage()
 
-    def is_supersolvable(self):
+    def is_supersolvable(self) -> bool:
         r"""
         Return whether this group is supersolvable.
 
@@ -117,7 +117,7 @@ def is_supersolvable(self):
         """
         return self.gap().IsSupersolvableGroup().sage()
 
-    def is_polycyclic(self):
+    def is_polycyclic(self) -> bool:
         r"""
         Return whether this group is polycyclic.
 
@@ -131,7 +131,7 @@ def is_polycyclic(self):
         """
         return self.gap().IsPolycyclicGroup().sage()
 
-    def is_perfect(self):
+    def is_perfect(self) -> bool:
         r"""
         Return whether this group is perfect.
 
@@ -148,7 +148,7 @@ def is_perfect(self):
         """
         return self.gap().IsPerfectGroup().sage()
 
-    def is_p_group(self):
+    def is_p_group(self) -> bool:
         r"""
         Return whether this group is a p-group.
 
@@ -162,7 +162,7 @@ def is_p_group(self):
         """
         return self.gap().IsPGroup().sage()
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Return whether this group is simple.
 
@@ -179,7 +179,7 @@ def is_simple(self):
         """
         return self.gap().IsSimpleGroup().sage()
 
-    def is_finite(self):
+    def is_finite(self) -> bool:
         """
         Test whether the matrix group is finite.
 

src/sage/groups/perm_gps/permgroup.py

@@ -1349,7 +1349,7 @@ def ngens(self):
         """
         return len(self.gens())
 
-    def is_trivial(self):
+    def is_trivial(self) -> bool:
         r"""
         Return ``True`` if this group is the trivial group.
 
@@ -4215,7 +4215,7 @@ def maximal_normal_subgroups(self):
 
     # #####################  Boolean tests #####################
 
-    def is_abelian(self):
+    def is_abelian(self) -> bool:
         """
         Return ``True`` if this group is abelian.
 
@@ -4230,7 +4230,7 @@ def is_abelian(self):
         """
         return bool(self._libgap_().IsAbelian())
 
-    def is_commutative(self):
+    def is_commutative(self) -> bool:
         """
         Return ``True`` if this group is commutative.
 
@@ -4245,7 +4245,7 @@ def is_commutative(self):
         """
         return self.is_abelian()
 
-    def is_cyclic(self):
+    def is_cyclic(self) -> bool:
         """
         Return ``True`` if this group is cyclic.
 
@@ -4357,7 +4357,7 @@ def is_isomorphic(self, right):
         iso = self._libgap_().IsomorphismGroups(right)
         return str(iso) != 'fail'
 
-    def is_monomial(self):
+    def is_monomial(self) -> bool:
         """
         Return ``True`` if the group is monomial. A finite group is monomial
         if every irreducible complex character is induced from a linear
@@ -4371,7 +4371,7 @@ def is_monomial(self):
         """
         return bool(self._libgap_().IsMonomialGroup())
 
-    def is_nilpotent(self):
+    def is_nilpotent(self) -> bool:
         """
         Return ``True`` if this group is nilpotent.
 
@@ -4386,7 +4386,7 @@ def is_nilpotent(self):
         """
         return bool(self._libgap_().IsNilpotent())
 
-    def is_normal(self, other):
+    def is_normal(self, other) -> bool:
         """
         Return ``True`` if this group is a normal subgroup of ``other``.
 
@@ -4403,7 +4403,7 @@ def is_normal(self, other):
             raise TypeError("%s must be a subgroup of %s" % (self, other))
         return bool(other._libgap_().IsNormal(self))
 
-    def is_perfect(self):
+    def is_perfect(self) -> bool:
         """
         Return ``True`` if this group is perfect. A group is perfect if it
         equals its derived subgroup.
@@ -4419,7 +4419,7 @@ def is_perfect(self):
         """
         return bool(self._libgap_().IsPerfectGroup())
 
-    def is_pgroup(self):
+    def is_pgroup(self) -> bools:
         r"""
         Return ``True`` if this group is a `p`-group.
 
@@ -4434,7 +4434,7 @@ def is_pgroup(self):
         """
         return bool(self._libgap_().IsPGroup())
 
-    def is_polycyclic(self):
+    def is_polycyclic(self) -> bool:
         r"""
         Return ``True`` if this group is polycyclic. A group is polycyclic if
         it has a subnormal series with cyclic factors. (For finite groups,
@@ -4452,7 +4452,7 @@ def is_polycyclic(self):
         """
         return bool(self._libgap_().IsPolycyclicGroup())
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         """
         Return ``True`` if the group is simple.
 

src/sage/rings/qqbar.py

@@ -3592,7 +3592,7 @@ class ANDescr(SageObject):
     ``ANDescr`` and all of its subclasses are for internal use, and should not
     be used directly.
     """
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Check whether this descriptor represents a value with the same
         algebraic degree as the number field associated with the descriptor.
@@ -4269,7 +4269,7 @@ def __bool__(self):
         self.exactify()
         return bool(self)
 
-    def is_square(self):
+    def is_square(self) -> bool:
         """
         Return whether or not this number is square.
 
@@ -6735,7 +6735,7 @@ def exactify(self):
         """
         return self
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         """
         Check whether this descriptor represents a value with the same
         algebraic degree as the number field associated with the descriptor.
@@ -7997,7 +7997,7 @@ def is_complex(self):
         """
         return not self._exactly_real
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Check whether this descriptor represents a value with the same
         algebraic degree as the number field associated with the descriptor.

src/sage/rings/semirings/tropical_variety.py

@@ -1354,7 +1354,7 @@ def weight_vectors(self):
             result[vertex] = vectors
         return result
 
-    def is_smooth(self):
+    def is_smooth(self) -> bool:
         r"""
         Return ``True`` if ``self`` is smooth and ``False`` otherwise.
 
@@ -1377,7 +1377,7 @@ def is_smooth(self):
         """
         return len(self.vertices()) == self._poly.degree() ** 2
 
-    def is_simple(self):
+    def is_simple(self) -> bool:
         r"""
         Return ``True`` if ``self`` is simple and ``False`` otherwise.