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

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 "passagemath-modules[RDF,CDF]"

Linear algebra over fields of real and complex numbers using NumPy

pip install "passagemath-modules[RBF,CBF]"

Linear algebra over fields of real and complex numbers with ball arithmetic using FLINT/arb

pip install "passagemath-modules[GF,GF2,GF2e,GFpn]"

Linear algebra over finite fields (various implementations)

pip install "passagemath-modules[QQbar,NumberField,CyclotomicField]"

Linear algebra over the algebraic numbers or number fields

pip install "passagemath-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 "passagemath-modules[padics]"

Linear algebra over p-adic rings and fields

pip install "passagemath-modules[combinat]"

Modules and algebras with combinatorial bases; algebraic combinatorics

pip install "passagemath-modules[invariant]"

Submodules invariant under group actions

pip install "passagemath-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

Type¶

standard

Dependencies¶

• $(PYTHON)

• $(PYTHON_TOOLCHAIN)

• cysignals: Interrupt and signal handling for Cython

• cython: C-Extensions for Python, an optimizing static compiler

• gmpy2: Python interface to GMP/MPIR, MPFR, and MPC

• gsl: The GNU Scientific Library

• mpc: Arithmetic of complex numbers with arbitrarily high precision and correct rounding

• mpfr: Multiple-precision floating-point computations with correct rounding

• mpmath: Pure Python library for multiprecision floating-point arithmetic

• numpy: Package for scientific computing with Python

• pkgconfig: Python interface to pkg-config

• python_build: A simple, correct PEP517 package builder

• sage-setup: Build system of the Sage library

• sagemath_categories: Sage categories, basic rings, polynomials, functions

• sagemath_environment: System and software environment

Version Information¶

package-version.txt:

10.6.3

version_requirements.txt:

passagemath-modules ~= 10.6.3.0

Equivalent System Packages¶

(none known)