gh-36856: various details in modules folder (ruff, cython-lint, roles)
    
This is fixing various little details in the `modules` folders,
including some suggestions from `ruff` and `cython-lint`.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36856
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/modules/fg_pid/fgp_module.py

@@ -1806,7 +1806,7 @@ def list(self):
             sage: list(V/W)
             [(0), (1)]
         """
-        return [e for e in self]
+        return list(self)
 
     def __iter__(self):
         """

src/sage/modules/filtered_vector_space.py

@@ -465,7 +465,7 @@ def make_subspace(indices):
         indices = set(filtration.pop(infinity, []))
         V = make_subspace(indices)
         filtered_subspaces = [(infinity, V)]
-        for deg in reversed(sorted(filtration.keys())):
+        for deg in sorted(filtration.keys(), reverse=True):
             next_V = V
             indices.update(filtration[deg])
             V = make_subspace(indices)
@@ -775,13 +775,13 @@ def presentation(self):
 
     def _repr_field_name(self):
         """
-        Return an abbreviated field name as string
+        Return an abbreviated field name as string.
 
         .. NOTE: This should rather be a method of fields and rings.
 
         RAISES:
 
-        ``NotImplementedError``: The field does not have an
+        :class:`NotImplementedError`: The field does not have an
         abbreviated name defined.
 
         EXAMPLES::

src/sage/modules/finite_submodule_iter.pyx

@@ -283,7 +283,7 @@ cdef class FiniteFieldsubspace_iterator(FiniteZZsubmodule_iterator):
             sage: all(Y[i]-X[i] == v for i in range(len(X)))
             True
         """
-        cdef Py_ssize_t d, i, p
+        cdef Py_ssize_t i, p
         cdef list pows, order
 
         F = basis[0].base_ring()
@@ -366,7 +366,6 @@ cdef class FiniteFieldsubspace_projPoint_iterator:
             85
         """
         from sage.matrix.constructor import matrix
-        cdef i
         self._basis = list(basis)
         self._basis_length = len(self._basis)
         self._immutable = immutable

src/sage/modules/free_module.py

@@ -563,7 +563,7 @@ def VectorSpace(K, dimension_or_basis_keys=None, sparse=False, inner_product_mat
         (0, 0, 1)
         ]
 
-    The base must be a field or a ``TypeError`` is raised.
+    The base must be a field or a :class:`TypeError` is raised.
 
     ::
 
@@ -1720,8 +1720,8 @@ def submodule(self, gens, check=True, already_echelonized=False):
             Echelon basis matrix:
             [3 3 0]
 
-        We try to create a submodule that isn't really a submodule,
-        which results in an ``ArithmeticError`` exception::
+        We try to create a submodule that is not really a submodule,
+        which results in an :class:`ArithmeticError` exception::
 
             sage: W.submodule([B[0] - B[1]])
             Traceback (most recent call last):
@@ -2722,7 +2722,7 @@ def coordinates(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -4637,7 +4637,7 @@ def span_of_basis(self, basis, base_ring=None, check=True, already_echelonized=F
             [3 3 0]
 
         The basis vectors must be linearly independent or a
-        ``ValueError`` exception is raised::
+        :class:`ValueError` exception is raised::
 
             sage: W.span_of_basis([[2,2,2], [3,3,3]])
             Traceback (most recent call last):
@@ -4696,7 +4696,7 @@ def subspace(self, gens, check=True, already_echelonized=False):
             [1 1 0]
 
         With ``check=True`` (the default) the mistake is correctly
-        detected and reported with an ``ArithmeticError`` exception::
+        detected and reported with an :class:`ArithmeticError` exception::
 
             sage: W.subspace([[1,1,0]], check=True)
             Traceback (most recent call last):
@@ -5799,7 +5799,7 @@ def coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -6150,7 +6150,7 @@ def coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -7001,7 +7001,7 @@ def echelon_coordinates(self, v, check=True):
 
             \sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -7441,7 +7441,7 @@ def coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -7498,7 +7498,7 @@ def echelon_coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -7652,7 +7652,7 @@ def coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in self, raise an ``ArithmeticError`` exception.
+        If `v` is not in self, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -8054,7 +8054,7 @@ def echelon_coordinates(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in ``self``, raise an ``ArithmeticError`` exception.
+        If `v` is not in ``self``, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 
@@ -8117,7 +8117,7 @@ def coordinate_vector(self, v, check=True):
 
             \\sum c_i B_i = v.
 
-        If `v` is not in ``self``, raise an ``ArithmeticError`` exception.
+        If `v` is not in ``self``, raise an :class:`ArithmeticError` exception.
 
         EXAMPLES::
 

src/sage/modules/free_module_element.pyx

@@ -4788,11 +4788,10 @@ cdef class FreeModuleElement_generic_sparse(FreeModuleElement):
             sage: v.nonzero_positions()
             [0, 1, 3, 4]
         """
-        #WARNING: In creation, we do not check that the indices i satisfy
+        # WARNING: In creation, we do not check that the indices i satisfy
         #     0 <= i < degree
         # or even that the indices are integers.
         FreeModuleElement.__init__(self, parent)
-        R = self.base_ring()
         cdef Py_ssize_t i
         cdef dict entries_dict, e
         if not entries:

src/sage/modules/free_module_integer.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 """
 Discrete subgroups of `\\ZZ^n`
 

src/sage/modules/free_quadratic_module.py

@@ -207,7 +207,7 @@ def QuadraticSpace(K, dimension, inner_product_matrix, sparse=False):
         (0, 0, 1)
         ]
 
-    The base must be a field or a ``TypeError`` is raised::
+    The base must be a field or a :class:`TypeError` is raised::
 
         sage: QuadraticSpace(ZZ,5,identity_matrix(ZZ,2))
         Traceback (most recent call last):
@@ -791,7 +791,7 @@ def span_of_basis(self, basis, check=True, already_echelonized=False):
             [3 3 0]
 
         The basis vectors must be linearly independent or a
-        ``ValueError`` exception is raised::
+        :class:`ValueError` exception is raised::
 
             sage: W.span_of_basis([[2,2,2], [3,3,3]])
             Traceback (most recent call last):
@@ -1341,7 +1341,7 @@ def change_ring(self, R):
         element of ``self`` into a vector over the fraction field of `R`,
         then taking the resulting `R`-module.
 
-        This raises a ``TypeError`` if coercion is not possible.
+        This raises a :class:`TypeError` if coercion is not possible.
 
         INPUT:
 

src/sage/modules/matrix_morphism.py

@@ -321,7 +321,7 @@ def inverse(self):
         r"""
         Return the inverse of this matrix morphism, if the inverse exists.
 
-        Raises a ``ZeroDivisionError`` if the inverse does not exist.
+        This raises a :class:`ZeroDivisionError` if the inverse does not exist.
 
         EXAMPLES:
 

src/sage/modules/module.pyx

@@ -205,7 +205,7 @@ cdef class Module(Parent):
         Return the base extension of ``self`` to `R`.
 
         This is the same as ``self.change_ring(R)`` except that a
-        ``TypeError`` is raised if there is no canonical coerce map
+        :class:`TypeError` is raised if there is no canonical coerce map
         from the base ring of ``self`` to `R`.
 
         INPUT:

src/sage/modules/tensor_operations.py

@@ -282,7 +282,7 @@ def __init__(self, vector_collections, operation='product'):
         assert all(V.base_ring() is base_ring for V in vector_collections)
         self._V = tuple(vector_collections)
         self._vectors = []
-        self._index_map = dict()
+        self._index_map = {}
         if operation == 'product':
             self._init_product()
         elif operation == 'symmetric':