passagemath-modules 10.4.59

passagemath: Vectors, matrices, tensors, vector spaces, affine spaces, modules and algebras, additive groups, quadratic forms, 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

• Matrices and Spaces of Matrices

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

• Free Modules with Combinatorial Bases

• Tensor Modules

• Additive Abelian Groups

• Matrix and Affine Groups

• Root Systems

• Quadratic Forms

• Ring Extensions and Derivations

• Clifford, Exterior, and Weyl Algebras

• Chain Complexes, Homology, Free Resolutions

• Matroid Theory

• Coding Theory

• Cryptography

• Probability Spaces and Distributions, Statistics

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[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