gh-39987: add some typing annotations in modular folder
    
This is adding the `-> bool` annotation to many functions and methods in
the modular folder.

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #39987
Reported by: Frédéric Chapoton
Reviewer(s): Vincent Macri

Author: Release Manager

src/sage/modular/abvar/abvar.py

@@ -1609,7 +1609,7 @@ def project_to_factor(self, n):
 
         return H(Morphism(H, mat))
 
-    def is_subvariety_of_ambient_jacobian(self):
+    def is_subvariety_of_ambient_jacobian(self) -> bool:
         """
         Return ``True`` if ``self`` is (presented as) a subvariety of the ambient
         product Jacobian.
@@ -3230,10 +3230,11 @@ def isogeny_number(self, none_if_not_known=False):
             else:
                 raise ValueError("self must be simple")
 
-    def is_simple(self, none_if_not_known=False):
+    def is_simple(self, none_if_not_known=False) -> bool:
         """
-        Return whether or not this modular abelian variety is simple, i.e.,
-        has no proper nonzero abelian subvarieties.
+        Return whether or not this modular abelian variety is simple.
+
+        This means that it has no proper nonzero abelian subvarieties.
 
         INPUT:
 
@@ -4241,7 +4242,7 @@ def group(self):
         """
         return self.modular_symbols().group()
 
-    def is_subvariety(self, other):
+    def is_subvariety(self, other) -> bool:
         """
         Return ``True`` if ``self`` is a subvariety of ``other``.
 
@@ -4294,7 +4295,7 @@ def is_subvariety(self, other):
             return ModularAbelianVariety_abstract.is_subvariety(self, other)
         return self.modular_symbols().is_submodule(other.modular_symbols())
 
-    def is_ambient(self):
+    def is_ambient(self) -> bool:
         """
         Return ``True`` if this abelian variety attached to a modular symbols
         space is attached to the cuspidal subspace of the ambient

src/sage/modular/abvar/cuspidal_subgroup.py

@@ -337,7 +337,7 @@ def lattice(self):
             return lattice
 
 
-def is_rational_cusp_gamma0(c, N, data):
+def is_rational_cusp_gamma0(c, N, data) -> bool:
     """
     Return ``True`` if the rational number c is a rational cusp of level N.
 

src/sage/modular/abvar/finite_subgroup.py

@@ -263,10 +263,10 @@ def __richcmp__(self, other, op):
         # order gets reversed in passing to lattices.
         return lx._echelon_matrix_richcmp(rx, op)
 
-    def is_subgroup(self, other):
+    def is_subgroup(self, other) -> bool:
         """
-        Return ``True`` exactly if ``self`` is a subgroup of ``other``, and both are
-        defined as subgroups of the same ambient abelian variety.
+        Return ``True`` exactly if ``self`` is a subgroup of ``other``,
+        and both are defined as subgroups of the same ambient abelian variety.
 
         EXAMPLES::
 

src/sage/modular/abvar/morphism.py

@@ -117,7 +117,7 @@ def complementary_isogeny(self):
             iM, denom = iM._clear_denom()
         return Morphism(self.parent().reversed(), iM)
 
-    def is_isogeny(self):
+    def is_isogeny(self) -> bool:
         """
         Return ``True`` if this morphism is an isogeny of abelian varieties.
 

src/sage/modular/arithgroup/arithgroup_perm.py

@@ -1116,7 +1116,7 @@ def permutation_action(self, x):
     # Group stuff
     #
 
-    def is_normal(self):
+    def is_normal(self) -> bool:
         r"""
         Test whether the group is normal.
 
@@ -1134,9 +1134,9 @@ def is_normal(self):
         G = self.relabel(inplace=False)
         s2 = G._S2
         s3 = G._S3
-        ss2 = [None]*N
-        ss3 = [None]*N
-        for j in [s2[0],s3[0]]:
+        ss2 = [None] * N
+        ss3 = [None] * N
+        for j in [s2[0], s3[0]]:
             m = G._canonical_rooted_labels(j)
             for i in range(N):
                 ss2[m[i]] = m[s2[i]]
@@ -1332,7 +1332,7 @@ def congruence_closure(self):
         from .congroup_generic import CongruenceSubgroup_constructor as CS
         return CS(N, [x.matrix() for x in self.gens()])
 
-    def is_congruence(self):
+    def is_congruence(self) -> bool:
         r"""
         Return ``True`` if this is a congruence subgroup, and ``False``
         otherwise.
@@ -1433,14 +1433,14 @@ def is_congruence(self):
             True
         """
         from sage.misc.verbose import verbose
-        if self.index() == 1: # the group is SL2Z (trivial case)
+        if self.index() == 1:  # the group is SL2Z (trivial case)
             return True
 
-        L = self.L() # action of L
-        R = self.R() # action of R
+        L = self.L()  # action of L
+        R = self.R()  # action of R
 
         if self.is_even():
-            N = L.order() # generalised level of the group
+            N = L.order()  # generalised level of the group
         else:
             N = 2 * L.order()
 
@@ -1451,13 +1451,13 @@ def is_congruence(self):
         if e == 1:
             # N is odd
             # this only gets called if self is even
-            onehalf = ZZ(2).inverse_mod(N) # i.e. 2^(-1) mod N
+            onehalf = ZZ(2).inverse_mod(N)  # i.e. 2^(-1) mod N
             rel = (R*R*L**(-onehalf))**3
             return rel.is_one()
 
         elif m == 1:
             # N is a power of 2
-            onefifth = ZZ(5).inverse_mod(N) # i.e. 5^(-1) mod N
+            onefifth = ZZ(5).inverse_mod(N)  # i.e. 5^(-1) mod N
             S = L**20*R**onefifth*L**(-4)*~R
 
             # congruence if the three below permutations are trivial
@@ -1630,7 +1630,7 @@ def __reduce__(self):
         return (OddArithmeticSubgroup_Permutation,
                 (self._S2,self._S3,self._L,self._R,canonical_labels))
 
-    def is_odd(self):
+    def is_odd(self) -> bool:
         r"""
         Test whether the group is odd.
 
@@ -1642,7 +1642,7 @@ def is_odd(self):
         """
         return True
 
-    def is_even(self):
+    def is_even(self) -> bool:
         r"""
         Test whether the group is even.
 
@@ -1947,7 +1947,7 @@ def __reduce__(self):
         return (EvenArithmeticSubgroup_Permutation,
                 (self._S2, self._S3, self._L, self._R, canonical_labels))
 
-    def is_odd(self):
+    def is_odd(self) -> bool:
         r"""
         Return ``True`` if this subgroup does not contain the matrix `-Id`.
 
@@ -1959,7 +1959,7 @@ def is_odd(self):
         """
         return False
 
-    def is_even(self):
+    def is_even(self) -> bool:
         r"""
         Return ``True`` if this subgroup contains the matrix `-Id`.
 

src/sage/modular/arithgroup/congroup_gamma0.py

@@ -244,7 +244,7 @@ def divisor_subgroups(self):
         """
         return [Gamma0_constructor(M) for M in self.level().divisors()]
 
-    def is_even(self):
+    def is_even(self) -> bool:
         r"""
         Return ``True`` precisely if this subgroup contains the matrix -1.
 
@@ -260,7 +260,7 @@ def is_even(self):
         """
         return True
 
-    def is_subgroup(self, right):
+    def is_subgroup(self, right) -> bool:
         """
         Return ``True`` if ``self`` is a subgroup of ``right``.
 

src/sage/modular/arithgroup/congroup_gamma1.py

@@ -136,7 +136,7 @@ def __reduce__(self):
         """
         return Gamma1_constructor, (self.level(),)
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         Return the \LaTeX representation of ``self``.
 
@@ -149,7 +149,7 @@ def _latex_(self):
         """
         return "\\Gamma_1(%s)" % self.level()
 
-    def is_even(self):
+    def is_even(self) -> bool:
         """
         Return ``True`` precisely if this subgroup contains the matrix -1.
 
@@ -162,9 +162,9 @@ def is_even(self):
             sage: Gamma1(15).is_even()
             False
         """
-        return self.level() in [1,2]
+        return self.level() in [1, 2]
 
-    def is_subgroup(self, right):
+    def is_subgroup(self, right) -> bool:
         """
         Return ``True`` if ``self`` is a subgroup of ``right``.
 

src/sage/modular/arithgroup/congroup_gammaH.py

@@ -434,7 +434,7 @@ def _list_of_elements_in_H(self):
         """
         return self.__Hlist
 
-    def is_even(self):
+    def is_even(self) -> bool:
         """
         Return ``True`` precisely if this subgroup contains the matrix -1.
 
@@ -1001,7 +1001,7 @@ def coset_reps(self):
             for t in reps2:
                 yield SL2Z(t) * r
 
-    def is_subgroup(self, other):
+    def is_subgroup(self, other) -> bool:
         r"""
         Return ``True`` if ``self`` is a subgroup of ``right``, and ``False``
         otherwise.

src/sage/modular/arithgroup/congroup_generic.py

@@ -180,7 +180,7 @@ def _an_element_(self):
         N = self.level()
         return self([1-N, -N, N, 1+N])
 
-    def is_congruence(self):
+    def is_congruence(self) -> bool:
         r"""
         Return ``True``, since this is a congruence subgroup.
 
@@ -189,7 +189,6 @@ def is_congruence(self):
             sage: Gamma0(7).is_congruence()
             True
         """
-
         return True
 
     def level(self):

src/sage/modular/arithgroup/congroup_sl2z.py

@@ -14,7 +14,7 @@
 #
 #  The full text of the GPL is available at:
 #
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #
 ################################################################################
 
@@ -140,7 +140,7 @@ def _repr_(self):
         """
         return "Modular Group SL(2,Z)"
 
-    def _latex_(self):
+    def _latex_(self) -> str:
         r"""
         Return the \LaTeX representation of ``self``.
 
@@ -153,7 +153,7 @@ def _latex_(self):
         """
         return "\\mbox{\\rm SL}_2(%s)" % (ZZ._latex_())
 
-    def is_subgroup(self, right):
+    def is_subgroup(self, right) -> bool:
         """
         Return ``True`` if ``self`` is a subgroup of ``right``.