gh-40865: some typing -> bool for is_* methods
    
just adding some simple `-> bool` annotations

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40865
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py

@@ -74,7 +74,7 @@ class RepresentationType(Enum):
         sage: chmr.RepresentationType.RegularLeft.is_regular()
         True
     """
-    def is_split(self):
+    def is_split(self) -> bool:
         r"""
         Return ``True`` if this representation type is absolutely split,
         ``False`` else-wise.
@@ -88,7 +88,7 @@ def is_split(self):
         """
         return self.value['split']
 
-    def is_regular(self):
+    def is_regular(self) -> bool:
         r"""
         Return ``True`` if this representation type is regular, ``False``
         else-wise.

src/sage/categories/crystals.py

@@ -152,7 +152,7 @@ def example(self, choice='highwt', **kwds):
 
     class MorphismMethods:
         @cached_method
-        def is_isomorphism(self):
+        def is_isomorphism(self) -> bool:
             """
             Check if ``self`` is a crystal isomorphism.
 
@@ -178,7 +178,7 @@ def is_isomorphism(self):
 
         # TODO: This could be moved to sets
         @cached_method
-        def is_embedding(self):
+        def is_embedding(self) -> bool:
             """
             Check if ``self`` is an injective crystal morphism.
 
@@ -213,7 +213,7 @@ def is_embedding(self):
             return True
 
         @cached_method
-        def is_strict(self):
+        def is_strict(self) -> bool:
             """
             Check if ``self`` is a strict crystal morphism.
 
@@ -1301,7 +1301,7 @@ def number_of_connected_components(self):
             """
             return len(self.connected_components_generators())
 
-        def is_connected(self):
+        def is_connected(self) -> bool:
             """
             Return ``True`` if ``self`` is a connected crystal.
 
@@ -1528,7 +1528,7 @@ def s(self, i):
                     b = b.e(i)
             return b
 
-        def is_highest_weight(self, index_set=None):
+        def is_highest_weight(self, index_set=None) -> bool:
             r"""
             Return ``True`` if ``self`` is a highest weight.
 
@@ -1550,9 +1550,10 @@ def is_highest_weight(self, index_set=None):
                 index_set = self.index_set()
             return all(self.e(i) is None for i in index_set)
 
-        def is_lowest_weight(self, index_set=None):
+        def is_lowest_weight(self, index_set=None) -> bool:
             r"""
             Return ``True`` if ``self`` is a lowest weight.
+
             Specifying the option ``index_set`` to be a subset `I` of the
             index set of the underlying crystal, finds all lowest
             weight vectors for arrows in `I`.

src/sage/categories/monoids.py

@@ -274,7 +274,7 @@ def _div_(left, right):
             """
             return left * ~right
 
-        def is_one(self):
+        def is_one(self) -> bool:
             r"""
             Return whether ``self`` is the one of the monoid.
 
@@ -603,7 +603,7 @@ def algebra_generators(self):
 
         class ElementMethods:
 
-            def is_central(self):
+            def is_central(self) -> bool:
                 r"""
                 Return whether the element ``self`` is central.
 

src/sage/combinat/partition_kleshchev.py

@@ -428,7 +428,7 @@ def mullineux_conjugate(self):
         KP = mu.parent()
         return KP.element_class(KP, mu.add_cell(*mu.cogood_cells( r-c-self.parent()._multicharge[0]) ))
 
-    def is_regular(self):
+    def is_regular(self) -> bool:
         r"""
         Return ``True`` if ``self`` is a `e`-regular partition tuple.
 
@@ -454,7 +454,7 @@ def is_regular(self):
         KP = self.parent()
         return super().is_regular(KP._e, KP._multicharge)
 
-    def is_restricted(self):
+    def is_restricted(self) -> bool:
         r"""
         Return ``True`` if ``self`` is an `e`-restricted partition tuple.
 
@@ -811,7 +811,7 @@ def mullineux_conjugate(self):
         KP = mu.parent()
         return KP.element_class(KP, mu.add_cell(*mu.cogood_cells( r-c-self.parent()._multicharge[k])))
 
-    def is_regular(self):
+    def is_regular(self) -> bool:
         r"""
         Return ``True`` if ``self`` is a `e`-regular partition tuple.
 
@@ -835,7 +835,7 @@ def is_regular(self):
         KP = self.parent()
         return _is_regular(self.to_list(), KP._multicharge, KP._convention)
 
-    def is_restricted(self):
+    def is_restricted(self) -> bool:
         r"""
         Return ``True`` if ``self`` is an `e`-restricted partition tuple.
 

src/sage/combinat/root_system/reflection_group_complex.py

@@ -852,7 +852,7 @@ def discriminant_in_invariant_ring(self, invariants=None):
         return sum(coeffs[i] * mons[i] for i in range(m))
 
     @cached_method
-    def is_crystallographic(self):
+    def is_crystallographic(self) -> bool:
         r"""
         Return ``True`` if ``self`` is crystallographic.
 
@@ -890,9 +890,10 @@ def is_crystallographic(self):
             sage: W.is_crystallographic()
             False
         """
-        return self.is_real() and all(t.to_matrix().base_ring() is QQ for t in self.simple_reflections())
+        return self.is_real() and all(t.to_matrix().base_ring() is QQ
+                                      for t in self.simple_reflections())
 
-    def number_of_irreducible_components(self):
+    def number_of_irreducible_components(self) -> int:
         r"""
         Return the number of irreducible components of ``self``.
 
@@ -908,7 +909,7 @@ def number_of_irreducible_components(self):
         """
         return len(self._type)
 
-    def irreducible_components(self):
+    def irreducible_components(self) -> list:
         r"""
         Return a list containing the irreducible components of ``self``
         as finite reflection groups.

src/sage/combinat/species/structure.py

@@ -182,11 +182,10 @@ def _relabel(self, i):
             [1, 2, 3]
         """
         if isinstance(i, (int, Integer)):
-            return self._labels[i-1]
-        else:
-            return i
+            return self._labels[i - 1]
+        return i
 
-    def is_isomorphic(self, x):
+    def is_isomorphic(self, x) -> bool:
         """
         EXAMPLES::
 
@@ -203,7 +202,7 @@ def is_isomorphic(self, x):
         if self.parent() != x.parent():
             return False
 
-        #We don't care about the labels for isomorphism testing
+        # We don't care about the labels for isomorphism testing
         return self.canonical_label()._list == x.canonical_label()._list
 
 

src/sage/combinat/subword_complex.py

@@ -349,7 +349,7 @@ def root_configuration(self):
         Phi = self.parent().group().roots()
         return [Phi[i] for i in self._root_configuration_indices()]
 
-    def kappa_preimage(self):
+    def kappa_preimage(self) -> list:
         r"""
         Return the fiber of ``self`` under the `\kappa` map.
 
@@ -403,7 +403,7 @@ def kappa_preimage(self):
                 if all(w.action_on_root_indices(i, side='left') < N
                        for i in root_conf)]
 
-    def is_vertex(self):
+    def is_vertex(self) -> bool:
         r"""
         Return ``True`` if ``self`` is a vertex of the brick polytope
         of ``self.parent``.
@@ -1445,7 +1445,7 @@ def greedy_facet(self, side='positive'):
 
     # topological properties
 
-    def is_sphere(self):
+    def is_sphere(self) -> bool:
         r"""
         Return ``True`` if the subword complex ``self`` is a sphere.
 
@@ -1472,7 +1472,7 @@ def is_sphere(self):
         w = W.demazure_product(self._Q)
         return w == self._pi
 
-    def is_ball(self):
+    def is_ball(self) -> bool:
         r"""
         Return ``True`` if the subword complex ``self`` is a ball.
 
@@ -1499,7 +1499,7 @@ def is_ball(self):
         """
         return not self.is_sphere()
 
-    def is_pure(self):
+    def is_pure(self) -> bool:
         r"""
         Return ``True`` since all subword complexes are pure.
 
@@ -1541,7 +1541,7 @@ def dimension(self):
     # root and weight
 
     @cached_method
-    def is_root_independent(self):
+    def is_root_independent(self) -> bool:
         r"""
         Return ``True`` if ``self`` is root-independent.
 
@@ -1569,7 +1569,7 @@ def is_root_independent(self):
         return M.rank() == max(M.ncols(), M.nrows())
 
     @cached_method
-    def is_double_root_free(self):
+    def is_double_root_free(self) -> bool:
         r"""
         Return ``True`` if ``self`` is double-root-free.
 

src/sage/dynamics/arithmetic_dynamics/wehlerK3.py

@@ -142,7 +142,7 @@ def __init__(self, polys):
         vars = R.variable_names()
         A = ProductProjectiveSpaces([2, 2],R.base_ring(),vars)
         CR = A.coordinate_ring()
-        #Check for following:
+        # Check for following:
         #    Is the user calling in 2 polynomials from a list or tuple?
         #    Is there one biquadratic and one bilinear polynomial?
         if len(polys) != 2:
@@ -411,7 +411,7 @@ def Hpoly(self, component, i, j):
             sage: X.Hpoly(0, 1, 0)
              2*y0*y1^3 + 2*y0*y1*y2^2 - y1*y2^3
         """
-        #Check Errors in Passed in Values
+        # Check Errors in Passed in Values
         if component not in [0, 1]:
             raise ValueError("component can only be 1 or 0")
 
@@ -709,7 +709,7 @@ def Ramification_poly(self, i):
              4*((self._Lcoeff(i, 2))**2)*(self._Qcoeff(i, 1, 1))*(self._Qcoeff(i, 0, 0))
 
     @cached_method
-    def is_degenerate(self):
+    def is_degenerate(self) -> bool:
         r"""
         Function will return ``True`` if there is a fiber (over the algebraic closure of the
         base ring) of dimension greater than 0 and ``False`` otherwise.
@@ -751,7 +751,7 @@ def is_degenerate(self):
         PP = self.ambient_space()
         K = FractionField(PP[0].base_ring())
         R = PP.coordinate_ring()
-        PS = PP[0] #check for x fibers
+        PS = PP[0]  # check for x fibers
         vars = list(PS.gens())
         R0 = PolynomialRing(K, 3, vars) #for dimension calculation to work,
             #must be done with Polynomial ring over a field
@@ -763,7 +763,7 @@ def is_degenerate(self):
         if I.dimension() != 0:
             return True
 
-        PS = PP[1] #check for y fibers
+        PS = PP[1]  # check for y fibers
         vars = list(PS.gens())
         R0 = PolynomialRing(K,3,vars) #for dimension calculation to work,
         #must be done with Polynomial ring over a field
@@ -840,7 +840,7 @@ def degenerate_fibers(self):
         phi = R.hom(vars + [0, 0, 0], R0)
         I = phi(I)
         xFibers = []
-        #check affine charts
+        # check affine charts
         for n in range(3):
             affvars = list(R0.gens())
             del affvars[n]
@@ -871,7 +871,7 @@ def degenerate_fibers(self):
         phi = PP.coordinate_ring().hom([0, 0, 0] + vars, R0)
         I = phi(I)
         yFibers = []
-        #check affine charts
+        # check affine charts
         for n in range(3):
             affvars = list(R0.gens())
             del affvars[n]
@@ -898,7 +898,7 @@ def degenerate_fibers(self):
     @cached_method
     def degenerate_primes(self, check=True):
         r"""
-        Determine which primes `p` ``self`` has degenerate fibers over `\GF{p}`.
+        Determine primes `p` such that ``self`` has degenerate fibers over `\GF{p}`.
 
         If ``check`` is ``False``, then may return primes that do not have degenerate fibers.
         Raises an error if the surface is degenerate.
@@ -995,7 +995,7 @@ def degenerate_primes(self, check=True):
             if power == 1:
                 bad_primes = bad_primes+GB[i].lt().coefficients()[0].support()
         bad_primes = sorted(set(bad_primes))
-        #check to return only the truly bad primes
+        # check to return only the truly bad primes
         if check:
             for p in bad_primes:
                 X = self.change_ring(GF(p))
@@ -1041,7 +1041,7 @@ def is_smooth(self) -> bool:
         R = self.ambient_space().coordinate_ring()
         I = R.ideal(M.minors(2) + [self.L,self.Q])
         T = PolynomialRing(self.ambient_space().base_ring().fraction_field(), 4, 'h')
-        #check the 9 affine charts for a singular point
+        # check the 9 affine charts for a singular point
         for l in xmrange([3, 3]):
             vars = list(T.gens())
             vars.insert(l[0], 1)
@@ -1577,7 +1577,7 @@ def phi(self, a, **kwds):
             (-1 : 0 : 1 , 0 : 1 : 0)
         """
         A = self.sigmaX(a, **kwds)
-        kwds.update({"check":False})
+        kwds.update({"check": False})
         return self.sigmaY(A, **kwds)
 
     def psi(self, a, **kwds):
@@ -1617,7 +1617,7 @@ def psi(self, a, **kwds):
             (0 : 0 : 1 , 0 : 1 : 0)
         """
         A = self.sigmaY(a, **kwds)
-        kwds.update({"check":False})
+        kwds.update({"check": False})
         return self.sigmaX(A, **kwds)
 
     def lambda_plus(self, P, v, N, m, n, prec=100):
@@ -2411,9 +2411,9 @@ def orbit_psi(self, P, N, **kwds):
             Orb.append(Q)
         return Orb
 
-    def is_isomorphic(self, right):
+    def is_isomorphic(self, right) -> bool:
         r"""
-        Check to see if two K3 surfaces have the same defining ideal.
+        Check whether two K3 surfaces have the same defining ideal.
 
         INPUT:
 
@@ -2449,10 +2449,12 @@ def is_isomorphic(self, right):
         """
         return self.defining_ideal() == right.defining_ideal()
 
-    def is_symmetric_orbit(self, orbit):
+    def is_symmetric_orbit(self, orbit) -> bool:
         r"""
-        Check to see if the orbit is symmetric (i.e. if one of the points on the
-        orbit is fixed by '\sigma_x' or '\sigma_y').
+        Check whether the orbit is symmetric.
+
+        This means that one of the points on the
+        orbit is fixed by '\sigma_x' or '\sigma_y'.
 
         INPUT: