# Modules#

Sage provides modules of various kinds over various base rings.

## Free modules, submodules, and quotients#

## Modules with basis#

## Finitely generated modules over a PID#

## Finitely presented graded modules#

- Finitely generated free graded left modules over connected graded algebras
- Elements of finitely generated free graded left modules
- Homomorphisms of finitely generated free graded left modules
- Homsets of finitely generated free graded left modules
- Finitely presented graded modules
- Elements of finitely presented graded modules
- Homomorphisms of finitely presented graded modules
- Homsets of finitely presented graded modules
- Finitely presented graded modules over the Steenrod algebra
- Homomorphisms of finitely presented modules over the Steenrod algebra

## Special modules#

## Morphisms#

## Vectors#

- Vectors with integer entries
- File: sage/modules/vector_integer_sparse.pyx (starting at line 1)
- Vectors with elements in \(\GF{2}\)
- Vectors with integer mod \(n\) entries, with small \(n\)
- File: sage/modules/vector_modn_sparse.pyx (starting at line 1)
- Vectors with rational entries
- File: sage/modules/vector_rational_sparse.pyx (starting at line 1)
- Dense vectors over the symbolic ring
- Sparse vectors over the symbolic ring
- Vectors over callable symbolic rings
- Dense vectors using a NumPy backend
- Dense real double vectors using a NumPy backend
- Dense vectors using a NumPy backend.
- Dense integer vectors using a NumPy backend.
- Dense complex double vectors using a NumPy backend
- Pickling for the old CDF vector class
- Pickling for the old RDF vector class