passagemath-modules 10.5.49

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

passagemath is open source mathematical software in Python, released under the GNU General Public Licence GPLv2+.

It is a fork of SageMath, which has been developed 2005-2025 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork was created in October 2024 with the following goals:

• providing modularized installation with pip, thus completing a major project started in 2020 in the Sage codebase,

• establishing first-class membership in the scientific Python ecosystem,

• giving clear attribution of upstream projects,

• providing independently usable Python interfaces to upstream libraries,

• providing platform portability and integration testing services to upstream projects,

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

• developing a port to Pyodide for serverless deployment with Javascript,

• developing a native Windows port.

Full documentation is available online.

passagemath attempts to support all major Linux distributions and recent versions of macOS. Use on Windows currently requires the use of Windows Subsystem for Linux or virtualization.

Complete sets of binary wheels are provided on PyPI for Python versions 3.9.x-3.12.x. Python 3.13.x is also supported, but some third-party packages are still missing wheels, so compilation from source is triggered for those.

About this pip-installable distribution package

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[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