passagemath-modules

=========================================================================================================================================================================================================== passagemath: Vectors, matrices, tensors, vector spaces, affine spaces, modules and algebras, additive groups, quadratic forms, root systems, homology, coding theory, matroids

About SageMath

"Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB"

Copyright (C) 2005-2024 The Sage Development Team

https://www.sagemath.org

SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

About this pip-installable source distribution

This pip-installable source distribution sagemath-modules is a distribution of a part of the Sage Library. It provides a small subset of the modules of the Sage library ("sagelib", sagemath-standard).

What is included

• Vectors, Vector Spaces, Modules <https://doc.sagemath.org/html/en/reference/modules/index.html>_

• Matrices and Spaces of Matrices <https://doc.sagemath.org/html/en/reference/matrices/index.html>_

• Fields of real and complex numbers in arbitrary precision floating point arithmetic (using MPFR, GSL, mpmath, MPC)

• Free Modules with Combinatorial Bases <https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/free_module.html>_

• Tensor Modules <https://doc.sagemath.org/html/en/reference/tensor_free_modules/index.html>_

• Additive Abelian Groups <https://doc.sagemath.org/html/en/reference/groups/sage/groups/additive_abelian/additive_abelian_group.html>_

• Matrix and Affine Groups <https://doc.sagemath.org/html/en/reference/groups/index.html#matrix-and-affine-groups>_

• Root Systems <https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/root_system/all.html#sage-combinat-root-system-all>_

• Quadratic Forms <https://doc.sagemath.org/html/en/reference/quadratic_forms/index.html>_

• Ring Extensions <https://doc.sagemath.org/html/en/reference/rings/sage/rings/ring_extension.html>_ and Derivations <https://doc.sagemath.org/html/en/reference/rings/sage/rings/derivation.html>_

• Clifford, Exterior <https://doc.sagemath.org/html/en/reference/algebras/sage/algebras/clifford_algebra.html>, and Weyl Algebras <https://doc.sagemath.org/html/en/reference/algebras/sage/algebras/weyl_algebra.html>

• Chain Complexes, Homology <https://doc.sagemath.org/html/en/reference/homology/index.html>, Free Resolutions <https://doc.sagemath.org/html/en/reference/resolutions/index.html>

• Matroid Theory <https://doc.sagemath.org/html/en/reference/matroids/index.html>_

• Coding Theory <https://doc.sagemath.org/html/en/reference/coding/index.html>_

• Cryptography <https://doc.sagemath.org/html/en/reference/cryptography/index.html>_

• Probability Spaces and Distributions <https://doc.sagemath.org/html/en/reference/probability/index.html>, Statistics <https://doc.sagemath.org/html/en/reference/stats/index.html>

Examples

A quick way to try it out interactively::

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-modules[test]" ipython

In [1]: from sage.all__sagemath_modules import *

In [2]: M = matroids.Wheel(5); M
Out[2]: Wheel(5): Regular matroid of rank 5 on 10 elements with 121 bases

In [3]: M.representation()
Out[3]:
[ 1  0  0  0  0  1  0  0  0 -1]
[ 0  1  0  0  0 -1  1  0  0  0]
[ 0  0  1  0  0  0 -1  1  0  0]
[ 0  0  0  1  0  0  0 -1  1  0]
[ 0  0  0  0  1  0  0  0 -1  1]

Available as extras, from other distributions

pip install "sagemath-modules[RDF,CDF]" Linear algebra over fields of real and complex numbers using NumPy

pip install "sagemath-modules[RBF,CBF]" Linear algebra over fields of real and complex numbers with ball arithmetic using FLINT/arb

pip install "sagemath-modules[GF,GF2,GF2e,GFpn]" Linear algebra over finite fields (various implementations)

pip install "sagemath-modules[QQbar,NumberField,CyclotomicField]" Linear algebra over the algebraic numbers or number fields

pip install "sagemath-modules[flint,fpylll,linbox]" Lattice basis reduction (LLL, BKZ)::

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-modules[flint,fpylll,linbox,test]" ipython

In [1]: from sage.all__sagemath_modules import *

In [2]: M = matrix(ZZ, [[1,2,3],[31,41,51],[101,201,301]])

In [3]: A = M.LLL(); A
Out[3]:
[ 0  0  0]
[-1  0  1]
[ 1  1  1]

pip install "sagemath-modules[padics]" Linear algebra over p-adic rings and fields

pip install "sagemath-modules[combinat]" Modules and algebras with combinatorial bases; algebraic combinatorics

pip install "sagemath-modules[invariant]" Submodules invariant under group actions

pip install "sagemath-modules[standard]" All related features as in a standard installation of SageMath

Development

::

$ git clone --origin passagemath https://github.com/passagemath/passagemath.git
$ cd passagemath
passagemath $ ./bootstrap
passagemath $ python3 -m venv modules-venv
passagemath $ source modules-venv/bin/activate
(modules-venv) passagemath $ pip install -v -e pkgs/sagemath-modules