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This is documentation for Sage version 10.9.beta6 for development purpose.

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Version 10.9.beta6 Reference Manual

Home - Modules

Tutorial: Using free modules and vector spaces

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

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

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

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

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

Space of pseudomorphisms of free modules
Pseudomorphisms of free modules

Vectors with integer entries
File: /home/runner/work/sage/sage/src/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: /home/runner/work/sage/sage/src/sage/modules/vector_modn_sparse.pyx (starting at line 1)
Vectors with rational entries
File: /home/runner/work/sage/sage/src/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

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

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File: /home/runner/work/sage/sage/src/sage/modules/vector_integer_sparse.pyx (starting at line 1)¶

Vectors with elements in \(\GF{2}\)

Vectors with integer entries

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