Modules

Sage provides modules of various kinds over various base rings.

• Tutorial: Using free modules and vector spaces

Free modules, submodules, and quotients

• Abstract base class for modules
• Free modules
• Elements of free modules
• Submodules and subquotients of free modules
• Quotients of free modules

See also sage.tensor.modules.finite_rank_free_module.

Modules with basis

• Concrete classes related to modules with a distinguished basis
• Cell modules
• An element in an indexed free module
• Invariant modules
• Morphisms of modules with a basis
• Quotients of modules with basis
• Representations of a semigroup

Finitely generated modules over a PID

• Finitely generated modules over a PID
• Elements of finitely generated modules over a PID
• Morphisms between 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

• Discrete subgroups of \(\ZZ^n\)
• Free quadratic modules
• Integral lattices
• Finite \(\ZZ\)-modules with bilinear and quadratic forms
• \(\ZZ\)-filtered vector spaces
• Multiple \(\ZZ\)-graded filtrations of a single vector space

Morphisms

• Space of morphisms of vector spaces (linear transformations)
• Morphisms of vector spaces (linear transformations)
• Homspaces between free modules
• Morphisms of free modules
• Morphisms defined by a matrix

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

Misc

• Diamond cutting implementation
• Helper classes to implement tensor operations
• Iterators over finite submodules of a \(\ZZ\)-module
• Miscellaneous module-related functions

Indices and Tables

• Index

• Module Index

• Search Page