Clean up doc tree of modules

src/doc/en/reference/modules/index.rst

@@ -1,35 +1,33 @@
 Modules
 =======
 
+Sage provides modules of various kinds over various base rings.
+
 .. toctree::
    :maxdepth: 2
 
    sage/modules/tutorial_free_modules
 
-   sage/modules/module
-   sage/modules/free_module
-   sage/modules/free_module_integer
-   sage/modules/free_module_element
-   sage/tensor/modules/finite_rank_free_module
 
-   sage/modules/complex_double_vector
-   sage/modules/real_double_vector
-   sage/modules/vector_callable_symbolic_dense
+Free modules, submodules, and quotients
+---------------------------------------
 
-   sage/modules/vector_space_homspace
-   sage/modules/vector_space_morphism
+.. toctree::
+   :maxdepth: 2
 
-   sage/modules/free_module_homspace
-   sage/modules/free_module_morphism
+   sage/modules/module
+   sage/modules/free_module
+   sage/modules/free_module_element
+   sage/modules/submodule
+   sage/modules/quotient_module
 
-   sage/modules/matrix_morphism
+See also :mod:`sage.tensor.modules.finite_rank_free_module`.
 
-   sage/modules/fg_pid/fgp_module
-   sage/modules/fg_pid/fgp_element
-   sage/modules/fg_pid/fgp_morphism
-   sage/modules/torsion_quadratic_module
+Modules with basis
+------------------
 
-   sage/modules/diamond_cutting
+.. toctree::
+   :maxdepth: 2
 
    sage/modules/with_basis/__init__
    sage/modules/with_basis/cell_module
@@ -39,24 +37,15 @@ Modules
    sage/modules/with_basis/subquotient
    sage/modules/with_basis/representation
 
-   sage/modules/finite_submodule_iter
-   sage/modules/free_quadratic_module
-   sage/modules/free_quadratic_module_integer_symmetric
-   sage/modules/misc
-   sage/modules/quotient_module
+Finitely generated modules over a PID
+-------------------------------------
 
-   sage/modules/vector_complex_double_dense
-   sage/modules/vector_double_dense
-   sage/modules/vector_integer_dense
-   sage/modules/vector_mod2_dense
-   sage/modules/vector_modn_dense
-   sage/modules/vector_rational_dense
-   sage/modules/vector_real_double_dense
-   sage/modules/vector_symbolic_dense
+.. toctree::
+   :maxdepth: 2
 
-   sage/modules/filtered_vector_space
-   sage/modules/multi_filtered_vector_space
-   sage/modules/tensor_operations
+   sage/modules/fg_pid/fgp_module
+   sage/modules/fg_pid/fgp_element
+   sage/modules/fg_pid/fgp_morphism
 
 Finitely presented graded modules
 ---------------------------------
@@ -76,4 +65,60 @@ Finitely presented graded modules
    sage/modules/fp_graded/steenrod/module
    sage/modules/fp_graded/steenrod/morphism
 
+Special modules
+---------------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/modules/free_module_integer
+   sage/modules/free_quadratic_module
+   sage/modules/free_quadratic_module_integer_symmetric
+   sage/modules/torsion_quadratic_module
+   sage/modules/filtered_vector_space
+   sage/modules/multi_filtered_vector_space
+
+Morphisms
+---------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/modules/vector_space_homspace
+   sage/modules/vector_space_morphism
+
+   sage/modules/free_module_homspace
+   sage/modules/free_module_morphism
+
+   sage/modules/matrix_morphism
+
+Vectors
+-------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/modules/vector_integer_dense
+   sage/modules/vector_mod2_dense
+   sage/modules/vector_modn_dense
+   sage/modules/vector_rational_dense
+   sage/modules/vector_symbolic_dense
+   sage/modules/vector_callable_symbolic_dense
+   sage/modules/vector_double_dense
+   sage/modules/vector_real_double_dense
+   sage/modules/vector_complex_double_dense
+   sage/modules/complex_double_vector
+   sage/modules/real_double_vector
+
+Misc
+----
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/modules/diamond_cutting
+   sage/modules/tensor_operations
+   sage/modules/finite_submodule_iter
+   sage/modules/misc
+
 .. include:: ../footer.txt

src/sage/modules/filtered_vector_space.py

@@ -1,5 +1,5 @@
 r"""
-`\ZZ`-Filtered Vector Spaces
+`\ZZ`-filtered vector spaces
 
 This module implements filtered vector spaces, that is, a descending
 sequence of vector spaces

src/sage/modules/free_module_integer.py

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 """
-Discrete Subgroups of `\\ZZ^n`
+Discrete subgroups of `\\ZZ^n`
 
 AUTHORS:
 

src/sage/modules/multi_filtered_vector_space.py

@@ -1,5 +1,5 @@
 r"""
-Multiple `\ZZ`-Graded Filtrations of a Single Vector Space
+Multiple `\ZZ`-graded filtrations of a single vector space
 
 See :mod:`filtered_vector_space` for simply graded vector spaces. This
 module implements the analog but for a collection of filtrations of

src/sage/modules/quotient_module.py

@@ -1,5 +1,5 @@
 r"""
-Quotients of finite rank free modules
+Quotients of free modules
 
 AUTHORS:
 

src/sage/modules/submodule.py

@@ -1,9 +1,9 @@
 r"""
-Submodules of finite rank free modules
+Submodules of free modules
 
-Free modules and submodules of a finite rank free module over a principla ideal
-domain have well-defined notion of rank, and they are implemented in
-:module:`sage.modules.free_module`. Here submodules with no rank are
+Free modules and submodules of a free module (of finite rank) over a principal
+ideal domain have well-defined notion of rank, and they are implemented in
+:mod:`sage.modules.free_module`. Here submodules with no rank are
 implemented. For example, submodules of free modules over multivariate
 polynomial rings with more than one variables have no notion of rank.
 

src/sage/modules/tensor_operations.py

@@ -1,5 +1,5 @@
 r"""
-Helper Classes to implement Tensor Operations
+Helper classes to implement tensor operations
 
 .. warning::
 

src/sage/modules/torsion_quadratic_module.py

@@ -1,5 +1,5 @@
 r"""
-Finite `\ZZ`-modules with with bilinear and quadratic forms.
+Finite `\ZZ`-modules with bilinear and quadratic forms
 
 AUTHORS:
 
@@ -881,7 +881,7 @@ def orthogonal_group(self, gens=None, check=False):
             try:
                 gens = [matrix(x*g for x in self.smith_form_gens()) for g in gens]
             except TypeError:
-                pass 
+                pass
             # the ambient knows what to do with the generators
             gens = tuple(ambient(g) for g in gens)
         Oq =  FqfOrthogonalGroup(ambient, gens, self, check=check)

src/sage/modules/tutorial_free_modules.py

@@ -1,5 +1,5 @@
 r"""
-Tutorial: Using Free Modules and Vector Spaces
+Tutorial: Using free modules and vector spaces
 
 .. MODULEAUTHOR:: Jason Bandlow
 

src/sage/modules/vector_complex_double_dense.pyx

@@ -1,5 +1,5 @@
 r"""
-Dense complex double vectors using a NumPy backend.
+Dense complex double vectors using a NumPy backend
 
 EXAMPLES::
 

src/sage/modules/vector_double_dense.pyx

@@ -1,5 +1,5 @@
 r"""
-Dense vectors using a NumPy backend.
+Dense vectors using a NumPy backend
 
 This serves as a base class for dense vectors over Real Double Field and
 Complex Double Field

src/sage/modules/vector_mod2_dense.pyx

@@ -3,8 +3,8 @@
 # distutils: include_dirs = M4RI_INCDIR GDLIB_INCDIR LIBPNG_INCDIR
 # distutils: extra_compile_args = M4RI_CFLAGS
 
-"""
-Vectors with elements in GF(2)
+r"""
+Vectors with elements in `\GF{2}`
 
 AUTHOR:
 
@@ -344,7 +344,7 @@ cdef class Vector_mod2_dense(free_module_element.FreeModuleElement):
         """
         cdef int i
         cdef int res = 0
-        cdef m4ri_word *row = mzd_row(self._entries, 0) 
+        cdef m4ri_word *row = mzd_row(self._entries, 0)
         for i from 0 <= i < self._entries.width:
             res += Integer(row[i]).popcount()
         return res

src/sage/modules/vector_modn_dense.pyx

@@ -1,5 +1,5 @@
 """
-Vectors with integer mod n entries, with n small
+Vectors with integer mod `n` entries, with small `n`
 
 EXAMPLES::
 

src/sage/modules/vector_real_double_dense.pyx

@@ -1,5 +1,5 @@
 r"""
-Dense real double vectors using a NumPy backend.
+Dense real double vectors using a NumPy backend
 
 EXAMPLES::
 

src/sage/modules/vector_space_homspace.py

@@ -1,5 +1,5 @@
 r"""
-Space of Morphisms of Vector Spaces (Linear Transformations)
+Space of morphisms of vector spaces (linear transformations)
 
 AUTHOR:
 

src/sage/modules/vector_space_morphism.py

@@ -1,5 +1,5 @@
 r"""
-Vector Space Morphisms (aka Linear Transformations)
+Morphisms of vector spaces (linear transformations)
 
 AUTHOR:
 
@@ -139,7 +139,7 @@
     sage: phi.is_surjective()
     False
 
-Restrictions and Representations
+Restrictions and representations
 --------------------------------
 
 It is possible to restrict the domain and codomain of a linear

src/sage/modules/with_basis/__init__.py

@@ -1,5 +1,5 @@
 r"""
-Concrete classes related to modules with a distinguished basis.
+Concrete classes related to modules with a distinguished basis
 
 This module provides concrete classes for various constructions
 related to modules with a distinguished basis:

src/sage/modules/with_basis/cell_module.py

@@ -1,5 +1,5 @@
 r"""
-Cell Modules
+Cell modules
 """
 #*****************************************************************************
 #       Copyright (C) 2015-2018 Travis Scrimshaw <tcscrims at gmail.com>

src/sage/modules/with_basis/indexed_element.pyx

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 r"""
-An element in an indexed free module.
+An element in an indexed free module
 
 AUTHORS:
 

src/sage/modules/with_basis/morphism.py

@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
 r"""
-Module with basis morphisms
+Morphisms of modules with a basis
 
 This module contains a hierarchy of classes for morphisms of modules
 with a basis (category :class:`Modules.WithBasis`):

src/sage/modules/with_basis/representation.py

@@ -1,10 +1,12 @@
 """
-Representations Of A Semigroup
+Representations of a semigroup
 
 AUTHORS:
 
-- Travis Scrimshaw (2015-11-21): Initial version
-- Siddharth Singh  (2020-03-21): Signed Representation
+- Travis Scrimshaw (2015-11-21): initial version
+
+- Siddharth Singh  (2020-03-21): signed representation
+
 """
 
 ##############################################################################
@@ -315,19 +317,19 @@ def __init__(self, semigroup, module, on_basis, side="left", **kwargs):
             pass
 
         category = kwargs.pop('category', Modules(module.base_ring()).WithBasis())
-        
+
         if side not in ["left", "right"]:
             raise ValueError('side must be "left" or "right"')
-        
+
         self._left_repr = (side == "left")
         self._on_basis = on_basis
         self._module = module
-        
+
         indices = module.basis().keys()
-        
+
         if 'FiniteDimensional' in module.category().axioms():
             category = category.FiniteDimensional()
-        
+
         Representation_abstract.__init__(self, semigroup, module.base_ring(), indices,
                                          category=category, **module.print_options())
 
@@ -449,10 +451,10 @@ def product_by_coercion(self, left, right):
             ...
             TypeError: unsupported operand parent(s) for *:
              'Representation of The Klein 4 group of order 4, as a permutation
-             group indexed by Subsets of {0, 1, 2, 3} over Rational Field' and 
-             'Representation of The Klein 4 group of order 4, as a permutation 
+             group indexed by Subsets of {0, 1, 2, 3} over Rational Field' and
+             'Representation of The Klein 4 group of order 4, as a permutation
              group indexed by Subsets of {0, 1, 2, 3} over Rational Field'
-            
+
             sage: from sage.categories.algebras import Algebras
             sage: category = Algebras(QQ).FiniteDimensional().WithBasis()
             sage: T = Representation(G, E, on_basis, category=category)
@@ -963,13 +965,13 @@ class SignRepresentationPermgroup(SignRepresentation_abstract):
     def _default_sign(self, elem):
         """
         Return the sign of the element
-        
+
         INPUT:
-      
+
         - ``elem`` -- the element of the group
 
         EXAMPLES::
-        
+
             sage: G = groups.permutation.PGL(2, 3)
             sage: V = G.sign_representation()
             sage: elem = G.an_element()

src/sage/modules/with_basis/subquotient.py

@@ -1,5 +1,5 @@
 r"""
-Quotients of Modules With Basis
+Quotients of modules with basis
 """
 # ****************************************************************************
 #  Copyright (C) 2010-2015 Florent Hivert <Florent.Hivert@univ-mlv.fr>