passagemath-gap 10.8.4

passagemath: Computational Group Theory with GAP

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 2005-2026 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork uses the motto “Creating a Free Passage Between the Scientific Python Ecosystem and Mathematical Software Communities.” It was created in October 2024 with the following goals:

• providing modularized installation with pip from binary wheels, - this major project was started in May 2020 in the Sage codebase and completed in passagemath 10.5.29 (May 2025),

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

• giving clear attribution of upstream projects,

• providing independently usable Python interfaces to upstream libraries,

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

• inviting collaborations with upstream projects,

• building a professional, respectful, inclusive community,

• empowering Sage users to participate in the scientific Python ecosystem by publishing packages,

• developing a port to WebAssembly (Pyodide, emscripten-forge) for serverless deployment with Javascript,

• developing a native Windows port - passagemath 10.6.1 (July 2025) published the first pip-installable wheel packages for native Windows on x86_64, - passagemath packages became available in the [MSYS2 software distribution](https://packages.msys2.org/search?t=pkg&q=passagemath) in November 2025.

Moreover, the passagemath project:

• provides a stable, frequently updated version of the Sage distribution,

• integrates additional mathematical software, notably Macaulay2, a full set of GAP packages, and the Combinatorial Matrix Recognition library,

• curates a library of Sage user packages.

Full documentation is available online.

passagemath attempts to support and provides binary wheels suitable for all major Linux distributions and recent versions of macOS.

Binary wheels for native Windows (x86_64, ARM) are are available for a subset of the passagemath distributions. Use of the full functionality of passagemath on Windows currently requires the use of Windows Subsystem for Linux (WSL) or virtualization.

The supported Python versions in the passagemath-10.8.x series are 3.11.x-3.14.x; the passagemath-10.6.x series (EOL 2026-10) still supports Python 3.10.x.

About this pip-installable distribution package

This pip-installable distribution passagemath-gap is a small distribution that provides modules that depend on the GAP system.

What is included

• Cython interface to libgap

• Pexpect interface to GAP

• numerous modules with build-time dependencies on GAP, see MANIFEST

• the binary wheels on PyPI ship a prebuilt copy of GAP and at least the following GAP packages:

  • atlasrep: Interface to the Atlas of Group Representations

  • autodoc: Generate documentation from GAP source code

  • autpgrp: Computing the automorphism group of a p-group

  • cohomolo: Cohomology groups of finite groups on finite modules

  • corelg: Computing with real Lie algebras

  • crime: Group cohomology and Massey products

  • crisp: Computing with radicals, injectors, Schunck classes and projectors

  • crypting: Hashes and crypto

  • datastructures: Collection of standard data structures

  • design: Constructing, classifying, partitioning, and studying block designs

  • digraphs: Graphs, digraphs, and multidigraphs

  • factint: Advanced methods for factoring integers

  • fga: Free group algorithms

  • gapdoc: Meta package for GAP documentation

  • gbnp: Gröbner bases of noncommutative polynomials

  • genss: Generic Schreier-Sims

  • grape: GRaph Algorithms using PErmutation groups

  • guava: Computing with error-correcting codes

  • hecke: Calculating decomposition matrices of Hecke algebras

  • images: Minimal and canonical images

  • jupyterviz: Visualization Tools for Jupyter and the GAP REPL

  • io: Bindings for low level C library I/O routines

  • json: Reading and Writing JSON

  • laguna: Lie AlGebras and UNits of group Algebras

  • liealgdb: Database of Lie algebras

  • liepring: Database and algorithms for Lie p-rings

  • liering: Computing with finitely presented Lie rings

  • lins: Computing the normal subgroups of a finitely presented group

  • loops: Computing with quasigroups and loops

  • mapclass: Mapping class orbit computation

  • orb: Methods to enumerate orbits

  • packagemanager: Easily download and install GAP packages

  • primgrp: Primitive permutation groups library

  • quagroup: Computations with quantum groups

  • qpa: Quivers and path algebras

  • repsn: Constructing representations of finite groups

  • sla: Simple Lie algebras

  • smallgrp: The GAP Small Groups Library

  • sonata: System of nearrings and their applications

  • sophus: Computing in nilpotent Lie algebras

  • toric: Toric varieties and some combinatorial geometry computations

  • utils: Utility functions

  • uuid: RFC 4122 UUIDs

  • ZeroMQInterface: ZeroMQ bindings

• the binary wheels on PyPI ship a prebuilt copy of the native Jupyter kernel for GAP

Examples

Running GAP from the command line:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-gap" sage -gap
 ┌───────┐   GAP 4.14.0 of 2024-12-05
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-apple-darwin22-default64-kv9
 Configuration:  gmp 6.3.0, GASMAN, readline
 Loading the library and packages ...
 Packages:   GAPDoc 1.6.7, PrimGrp 3.4.4, SmallGrp 1.5.4, TransGrp 3.6.5
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap>

Using the library interface from Python:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-gap[test]" IPython

In [1]: from passagemath_modules import *

In [2]: from passagemath_gap import *

In [3]: G = libgap.eval("Group([(1,2,3), (1,2)(3,4), (1,7)])")

In [4]: CG = G.ConjugacyClasses()

In [5]: gamma = CG[2]

In [6]: g = gamma.Representative()

In [7]: CG; gamma; g
[ ()^G, (4,7)^G, (3,4,7)^G, (2,3)(4,7)^G, (2,3,4,7)^G, (1,2)(3,4,7)^G, (1,2,3,4,7)^G ]
(3,4,7)^G
(3,4,7)

Available as extras, from other distributions

Jupyter kernel spec

pip install "passagemath-gap[jupyterkernel]"

installs the kernel spec for use in the Jupyter notebook and JupyterLab

pip install "passagemath-gap[notebook]"

installs the kernel spec and the Jupyter notebook

pip install "passagemath-gap[jupyterlab]"

installs the kernel spec and JupyterLab

GAP packages

pip install "passagemath-gap[4ti2interface]"

installs 4ti2interface

pip install "passagemath-gap[aclib]"

installs aclib: Almost crystallographic groups

pip install "passagemath-gap[agt]"

installs agt

pip install "passagemath-gap[alnuth]"

installs alnuth: Algebraic number theory, interface to PARI/GP

pip install "passagemath-gap[caratinterface]"

installs caratinterface

pip install "passagemath-gap[corefreesub]"

installs corefreesub

pip install "passagemath-gap[cryst]"

installs cryst: Computing with crystallographic groups

pip install "passagemath-gap[crystcat]"

installs crystcat: Crystallographic groups catalog

pip install "passagemath-gap[ctbllib]"

installs ctbllib: The GAP Character Table Library

pip install "passagemath-gap[cubefree]"

installs cubefree

pip install "passagemath-gap[cddinterface]"

installs cddinterface

pip install "passagemath-gap[curlinterface]"

installs curlinterface

pip install "passagemath-gap[deepthought]"

installs deepthought

pip install "passagemath-gap[difsets]"

installs difsets

pip install "passagemath-gap[float]"

installs float

pip install "passagemath-gap[fr]"

installs fr

pip install "passagemath-gap[fwtree]"

installs fwtree

pip install "passagemath-gap[grpconst]"

installs grpconst

pip install "passagemath-gap[guarana]"

installs guarana

pip install "passagemath-gap[hap]"

installs hap: Homological algebra programming

pip install "passagemath-gap[hapcryst]"

installs hapcryst: HAP extension for crystallographic groups

pip install "passagemath-gap[help]"

installs help

pip install "passagemath-gap[irredsol]"

installs irredsol: Library of irreducible soluble linear groups over finite fields and of finite primivite soluble groups

pip install "passagemath-gap[lpres]"

installs lpres

pip install "passagemath-gap[modisom]"

installs modisom

pip install "passagemath-gap[nilmat]"

installs nilmat

pip install "passagemath-gap[nq]"

installs nq: Nilpotent quotients of finitely presented groups

pip install "passagemath-gap[numericalsgps]"

installs numericalsgps

pip install "passagemath-gap[polenta]"

installs polenta: Polycyclic presentations for matrix groups

pip install "passagemath-gap[polycyclic]"

installs polycyclic: Computation with polycyclic groups

pip install "passagemath-gap[polymaking]"

installs polymaking: Interfacing the geometry software polymake

pip install "passagemath-gap[radiroot]"

installs radiroot: Roots of a polynomial as radicals

pip install "passagemath-gap[rcwa]"

installs rcwa

pip install "passagemath-gap[resclasses]"

installs resclasses: Set-theoretic computations with residue classes

pip install "passagemath-gap[semigroups]"

installs semigroups

pip install "passagemath-gap[sglppow]"

installs sglppow

pip install "passagemath-gap[simpcomp]"

installs simpcomp

pip install "passagemath-gap[singular]"

installs singular: Interface to Singular

pip install "passagemath-gap[smallsemi]"

installs smallsemi

pip install "passagemath-gap[sonata]"

installs sonata

pip install "passagemath-gap[symbcompcc]"

installs symbcompcc

pip install "passagemath-gap[tomllib]"

installs tomlib: The GAP Library of Tables of Marks

pip install "passagemath-gap[transgrp]"

installs transgrp: Transitive Groups Library

pip install "passagemath-gap[xmod]"

installs xmod

pip install "passagemath-gap[unitlib]"

installs unitlib

pip install "passagemath-gap[yangbaxter]"

installs yangbaxter

Collections

pip install "passagemath-gap[standard]"

installs all GAP packages present in a standard installation of Sage and their dependencies

pip install "passagemath-gap[full]"

installs the full set of GAP packages shipped by the GAP distribution and their dependencies