gh-39994: typing annotation for is_something in modules/
    
This is adding the annotation `-> bool` in appropriate places in
`modules/` folder

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #39994
Reported by: Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/modules/fg_pid/fgp_module.py

@@ -795,7 +795,7 @@ def has_canonical_map_to(self, A):
             return True
         return self.V().is_submodule(A.V()) and self.W().is_submodule(A.W())
 
-    def is_submodule(self, A):
+    def is_submodule(self, A) -> bool:
         """
         Return ``True`` if ``self`` is a submodule of ``A``.
 
@@ -1864,7 +1864,7 @@ def construction(self):
         from sage.modules.module_functors import QuotientModuleFunctor
         return (QuotientModuleFunctor(self._W), self._V)
 
-    def is_finite(self):
+    def is_finite(self) -> bool:
         """
         Return ``True`` if ``self`` is finite and ``False`` otherwise.
 

src/sage/modules/filtered_vector_space.py

@@ -517,7 +517,7 @@ def ambient_vector_space(self):
         return VectorSpace(self.base_ring(), self.dimension())
 
     @cached_method
-    def is_constant(self):
+    def is_constant(self) -> bool:
         """
         Return whether the filtration is constant.
 
@@ -544,7 +544,7 @@ def is_constant(self):
         f = self._filt
         return (len(f) == 1) or (len(f) == 2 and f[1][0] == infinity)
 
-    def is_exhaustive(self):
+    def is_exhaustive(self) -> bool:
         r"""
         Return whether the filtration is exhaustive.
 
@@ -567,7 +567,7 @@ def is_exhaustive(self):
         return self.get_degree(minus_infinity).dimension() == \
             self.ambient_vector_space().dimension()
 
-    def is_separating(self):
+    def is_separating(self) -> bool:
         r"""
         Return whether the filtration is separating.
 

src/sage/modules/fp_graded/free_module.py

@@ -501,7 +501,7 @@ def generator_degrees(self):
         """
         return self._generator_degrees
 
-    def is_trivial(self):
+    def is_trivial(self) -> bool:
         r"""
         Return ``True`` if this module is trivial and ``False`` otherwise.
 

src/sage/modules/fp_graded/module.py

@@ -564,7 +564,7 @@ def connectivity(self):
 
         return infinity
 
-    def is_trivial(self):
+    def is_trivial(self) -> bool:
         r"""
         Return ``True`` if ``self`` is isomorphic to the trivial module
         and ``False`` otherwise.
@@ -599,7 +599,7 @@ def is_trivial(self):
         """
         return self.connectivity() == infinity
 
-    def has_relations(self):
+    def has_relations(self) -> bool:
         r"""
         Return ``True`` if no relations are defined, and ``False``
         otherwise.

src/sage/modules/fp_graded/morphism.py

@@ -611,7 +611,7 @@ def __mul__(self, g):
         return homset([self(g(x)) for x in g.domain().generators()])
 
     @cached_method
-    def is_zero(self):
+    def is_zero(self) -> bool:
         r"""
         Decide if ``self`` is the zero homomorphism.
 
@@ -647,7 +647,7 @@ def is_zero(self):
     __bool__ = is_zero
 
     @cached_method
-    def is_identity(self):
+    def is_identity(self) -> bool:
         r"""
         Decide if ``self`` is the identity endomorphism.
 
@@ -1583,7 +1583,7 @@ def image(self, top_dim=None, verbose=False):
         # its image equals im(self)
         return Hom(I, j0.codomain())(j0._values)
 
-    def is_injective(self, top_dim=None, verbose=False):
+    def is_injective(self, top_dim=None, verbose=False) -> bool:
         r"""
         Return ``True`` if and only if ``self`` has a trivial kernel.
 
@@ -1614,7 +1614,7 @@ def is_injective(self, top_dim=None, verbose=False):
         j0 = self._resolve_kernel(top_dim, verbose)
         return j0.domain().is_trivial()
 
-    def is_surjective(self):
+    def is_surjective(self) -> bool:
         r"""
         Return ``True`` if and only if ``self`` has a trivial cokernel.
 

src/sage/modules/fp_graded/steenrod/morphism.py

@@ -90,7 +90,7 @@ def _flatten(f):
         return enveloping_profile_elements(elements,
                                            char=self.base_ring().characteristic())
 
-    def is_injective(self, top_dim=None, verbose=False):
+    def is_injective(self, top_dim=None, verbose=False) -> bool:
         r"""
         Return ``True`` if ``self`` is injective.
 

src/sage/modules/free_module.py

@@ -984,7 +984,7 @@ def degree(self):
         """
         return self.__degree
 
-    def is_sparse(self):
+    def is_sparse(self) -> bool:
         """
         Return ``True`` if the underlying representation of this module uses
         sparse vectors, and ``False`` otherwise.
@@ -998,7 +998,7 @@ def is_sparse(self):
         """
         return self.__is_sparse
 
-    def is_exact(self):
+    def is_exact(self) -> bool:
         """
         Test whether elements of this module are represented exactly.
 
@@ -1517,7 +1517,7 @@ def _eq(self, other):
         # in the same ambient space
         return self.is_submodule(other) and other.is_submodule(self)
 
-    def is_submodule(self, other):
+    def is_submodule(self, other) -> bool:
         r"""
         Return ``True`` if ``self`` is a submodule of ``other``.
 
@@ -2303,7 +2303,7 @@ def _eq(self, other):
             return self.echelonized_basis_matrix() == other.echelonized_basis_matrix()
         return self.is_submodule(other) and other.is_submodule(self)
 
-    def is_submodule(self, other):
+    def is_submodule(self, other) -> bool:
         r"""
         Return ``True`` if ``self`` is a submodule of ``other``.
 
@@ -3285,7 +3285,7 @@ def _inner_product_is_dot_product(self):
         """
         return True
 
-    def is_ambient(self):
+    def is_ambient(self) -> bool:
         """
         Return ``False`` since this is not an ambient free module.
 
@@ -3310,7 +3310,7 @@ def is_ambient(self):
         """
         return False
 
-    def is_dense(self):
+    def is_dense(self) -> bool:
         """
         Return ``True`` if the underlying representation of
         this module uses dense vectors, and ``False`` otherwise.
@@ -3324,7 +3324,7 @@ def is_dense(self):
         """
         return not self.is_sparse()
 
-    def is_full(self):
+    def is_full(self) -> bool:
         """
         Return ``True`` if the rank of this module equals its
         degree.
@@ -3339,7 +3339,7 @@ def is_full(self):
         """
         return self.rank() == self.degree()
 
-    def is_finite(self):
+    def is_finite(self) -> bool:
         """
         Return ``True`` if the underlying set of this free module is finite.
 
@@ -4754,7 +4754,7 @@ def intersection(self, other):
         B = [A1.linear_combination_of_rows(v.list()[:n]) for v in K.basis()]
         return self.ambient_vector_space().submodule(B, check=False)
 
-    def is_subspace(self, other):
+    def is_subspace(self, other) -> bool:
         """
         ``True`` if this vector space is a subspace of ``other``.
 
@@ -5800,7 +5800,7 @@ def _latex_(self):
             t = "(%s)" % t
         return "%s^{%s}" % (t, self.rank())
 
-    def is_ambient(self):
+    def is_ambient(self) -> bool:
         """
         Return ``True`` since this module is an ambient
         module.
@@ -8011,7 +8011,7 @@ def _echelonized_basis(self, ambient, basis):
         # Return the first rank rows (i.e., the nonzero rows).
         return E.rows()[:E.rank()]
 
-    def is_ambient(self):
+    def is_ambient(self) -> bool:
         """
         Return ``False`` since this is not an ambient module.
 

src/sage/modules/free_module_element.pyx

@@ -3619,9 +3619,9 @@ cdef class FreeModuleElement(Vector):   # abstract base class
             ...
             ArithmeticError: degrees (1 and 2) must be the same
         """
-        return (self.conjugate()).dot_product(right)
+        return self.conjugate().dot_product(right)
 
-    def is_dense(self):
+    def is_dense(self) -> bool:
         """
         Return ``True`` if this is a dense vector, which is just a
         statement about the data structure, not the number of nonzero
@@ -3639,7 +3639,7 @@ cdef class FreeModuleElement(Vector):   # abstract base class
     cdef bint is_dense_c(self) noexcept:
         return self.parent().is_dense()
 
-    def is_sparse(self):
+    def is_sparse(self) -> bool:
         """
         Return ``True`` if this is a sparse vector, which is just a
         statement about the data structure, not the number of nonzero
@@ -3657,7 +3657,7 @@ cdef class FreeModuleElement(Vector):   # abstract base class
     cdef bint is_sparse_c(self) noexcept:
         return self.parent().is_sparse()
 
-    def is_vector(self):
+    def is_vector(self) -> bool:
         """
         Return ``True``, since this is a vector.
 

src/sage/modules/free_module_integer.py

@@ -509,7 +509,7 @@ def discriminant(self):
         return abs(self.gram_matrix().determinant())
 
     @cached_method
-    def is_unimodular(self):
+    def is_unimodular(self) -> bool:
         """
         Return ``True`` if this lattice is unimodular.
 

src/sage/modules/free_module_morphism.py

@@ -658,7 +658,7 @@ class BaseIsomorphism1D(Morphism):
                 Multivariate Polynomial Ring in x, y over Rational Field
           To:   Multivariate Polynomial Ring in x, y over Rational Field
     """
-    def _repr_type(self):
+    def _repr_type(self) -> str:
         r"""
         EXAMPLES::
 
@@ -669,7 +669,7 @@ def _repr_type(self):
         """
         return "Isomorphism"
 
-    def is_injective(self):
+    def is_injective(self) -> bool:
         r"""
         EXAMPLES::
 
@@ -680,7 +680,7 @@ def is_injective(self):
         """
         return True
 
-    def is_surjective(self):
+    def is_surjective(self) -> bool:
         r"""
         EXAMPLES::