Modules#
Sage provides modules of various kinds over various base rings.
Free modules, submodules, and quotients#
- Abstract base class for modules
- Free modules
ComplexDoubleVectorSpace_classEchelonMatrixKeyFreeModule()FreeModuleFactoryFreeModule_ambientFreeModule_ambient_domainFreeModule_ambient_fieldFreeModule_ambient_pidFreeModule_genericFreeModule_generic_domainFreeModule_generic_fieldFreeModule_generic_pidFreeModule_submodule_fieldFreeModule_submodule_pidFreeModule_submodule_with_basis_fieldFreeModule_submodule_with_basis_pidModule_free_ambientRealDoubleVectorSpace_classVectorSpace()basis_seq()element_class()is_FreeModule()span()
- Elements of free modules
FreeModuleElementFreeModuleElement_generic_denseFreeModuleElement_generic_sparsefree_module_element()is_FreeModuleElement()make_FreeModuleElement_generic_dense()make_FreeModuleElement_generic_dense_v1()make_FreeModuleElement_generic_sparse()make_FreeModuleElement_generic_sparse_v1()prepare()random_vector()vector()zero_vector()
- Submodules and subquotients of free modules
- Quotients of free modules
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#
- Discrete subgroups of \(\ZZ^n\)
- Free quadratic modules
FreeQuadraticModule()FreeQuadraticModule_ambientFreeQuadraticModule_ambient_domainFreeQuadraticModule_ambient_fieldFreeQuadraticModule_ambient_pidFreeQuadraticModule_genericFreeQuadraticModule_generic_fieldFreeQuadraticModule_generic_pidFreeQuadraticModule_submodule_fieldFreeQuadraticModule_submodule_pidFreeQuadraticModule_submodule_with_basis_fieldFreeQuadraticModule_submodule_with_basis_pidInnerProductSpace()QuadraticSpace()is_FreeQuadraticModule()
- Integral lattices
- Finite \(\ZZ\)-modules with bilinear and quadratic forms
- \(\ZZ\)-filtered vector spaces
- Multiple \(\ZZ\)-graded filtrations of a single vector space
Morphisms#
Vectors#
- Vectors with integer entries
- Vectors with elements in \(\GF{2}\)
- Vectors with integer mod \(n\) entries, with small \(n\)
- Vectors with rational entries
- 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 complex double vectors using a NumPy backend
- Pickling for the old CDF vector class
- Pickling for the old RDF vector class