passagemath-gap 10.8.1
passagemath: Computational Group Theory with GAP
Requires Python: <3.15,>=3.11

=============================================================================
 passagemath: Computational Group Theory with GAP
=============================================================================

`passagemath <https://github.com/passagemath/passagemath>`__ is open
source mathematical software in Python, released under the GNU General
Public Licence GPLv2+.

It is a fork of `SageMath <https://www.sagemath.org/>`__, 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 <https://groups.google.com/g/sage-devel/c/6HO1HEtL1Fs/m/G002rPGpAAAJ>`__,

-  providing independently usable Python interfaces to upstream
   libraries,

-  offering `platform portability and integration testing
   services <https://github.com/passagemath/passagemath/issues/704>`__
   to upstream projects,

-  inviting collaborations with upstream projects,

-  `building a professional, respectful, inclusive
   community <https://groups.google.com/g/sage-devel/c/xBzaINHWwUQ>`__,

-  `empowering Sage users to participate in the scientific Python ecosystem
   <https://github.com/passagemath/passagemath/issues/248>`__ by publishing packages,

-  developing a port to WebAssembly (`Pyodide <https://pyodide.org/en/stable/>`__, 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 <https://passagemath.org/docs/latest/html/en/index.html>`__ 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 <https://www.gap-system.org>`_.


What is included
----------------

- `Cython interface to libgap <https://passagemath.org/docs/latest/html/en/reference/libs/sage/libs/gap/libgap.html>`_

- `Pexpect interface to GAP <https://passagemath.org/docs/latest/html/en/reference/interfaces/sage/interfaces/gap.html>`_

- numerous modules with build-time dependencies on GAP, see `MANIFEST <https://github.com/passagemath/passagemath/blob/main/pkgs/sagemath-gap/MANIFEST.in>`_

- the binary wheels on PyPI ship a prebuilt copy of GAP and at least the following `GAP packages <https://www.gap-system.org/packages>`__:

  - `atlasrep <https://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep>`__: Interface to the Atlas of Group Representations
  - `autodoc <https://gap-packages.github.io/AutoDoc>`__: Generate documentation from GAP source code
  - `autpgrp <https://gap-packages.github.io/autpgrp/>`__: Computing the automorphism group of a p-group
  - `cohomolo <https://gap-packages.github.io/cohomolo>`__: Cohomology groups of finite groups on finite modules
  - `corelg <https://gap-packages.github.io/corelg/>`__: Computing with real Lie algebras
  - `crime <https://gap-packages.github.io/crime/>`__: Group cohomology and Massey products
  - `crisp <http://www.icm.tu-bs.de/~bhoeflin/crisp/index.html>`__: Computing with radicals, injectors, Schunck classes and projectors
  - `crypting <https://gap-packages.github.io/crypting/>`__: Hashes and crypto
  - `datastructures <https://gap-packages.github.io/datastructures>`__: Collection of standard data structures
  - `design <https://gap-packages.github.io/design>`__: Constructing, classifying, partitioning, and studying block designs
  - `digraphs <https://digraphs.github.io/Digraphs>`__: Graphs, digraphs, and multidigraphs
  - `factint <https://gap-packages.github.io/FactInt>`__: Advanced methods for factoring integers
  - `fga <https://gap-packages.github.io/fga/>`__: Free group algorithms
  - `gapdoc <https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc>`__: Meta package for GAP documentation
  - `gbnp <https://gap-packages.github.io/gbnp/>`__: Gröbner bases of noncommutative polynomials
  - `genss <https://gap-packages.github.io/genss>`__: Generic Schreier-Sims
  - `grape <https://gap-packages.github.io/grape>`__: GRaph Algorithms using PErmutation groups
  - `guava <https://gap-packages.github.io/guava>`__: Computing with error-correcting codes
  - `hecke <https://gap-packages.github.io/hecke/>`__: Calculating decomposition matrices of Hecke algebras
  - `images <https://gap-packages.github.io/images/>`__: Minimal and canonical images
  - `jupyterviz <https://nathancarter.github.io/jupyterviz>`__: Visualization Tools for Jupyter and the GAP REPL
  - `io <https://gap-packages.github.io/io>`__: Bindings for low level C library I/O routines
  - `json <https://gap-packages.github.io/json/>`__: Reading and Writing JSON
  - `laguna <https://gap-packages.github.io/laguna>`__: Lie AlGebras and UNits of group Algebras
  - `liealgdb <https://gap-packages.github.io/liealgdb/>`__: Database of Lie algebras
  - `liepring <https://gap-packages.github.io/liepring/>`__: Database and algorithms for Lie p-rings
  - `liering <https://gap-packages.github.io/liering/>`__: Computing with finitely presented Lie rings
  - `lins <https://gap-packages.github.io/LINS/>`__: Computing the normal subgroups of a finitely presented group
  - `loops <https://gap-packages.github.io/loops/>`__: Computing with quasigroups and loops
  - `mapclass <https://gap-packages.github.io/MapClass>`__: Mapping class orbit computation
  - `orb <https://gap-packages.github.io/orb>`__: Methods to enumerate orbits
  - `packagemanager <https://gap-packages.github.io/PackageManager/>`__: Easily download and install GAP packages
  - `primgrp <https://gap-packages.github.io/primgrp/>`__: Primitive permutation groups library
  - `quagroup <https://gap-packages.github.io/quagroup/>`__: Computations with quantum groups
  - `qpa <https://folk.ntnu.no/oyvinso/QPA/>`__: Quivers and path algebras
  - `repsn <https://gap-packages.github.io/repsn/>`__: Constructing representations of finite groups
  - `sla <https://gap-packages.github.io/sla/>`__: Simple Lie algebras
  - `smallgrp <https://gap-packages.github.io/smallgrp/>`__: The GAP Small Groups Library
  - `sonata <https://gap-packages.github.io/sonata/>`__: System of nearrings and their applications
  - `sophus <https://gap-packages.github.io/sophus/>`__: Computing in nilpotent Lie algebras
  - `toric <https://gap-packages.github.io/toric>`__: Toric varieties and some combinatorial geometry computations
  - `utils <https://gap-packages.github.io/utils>`__: Utility functions
  - `uuid <https://gap-packages.github.io/uuid/>`__: RFC 4122 UUIDs
  - `ZeroMQInterface <https://gap-packages.github.io/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 <https://gap-packages.github.io/4ti2interface/>`__

``pip install "passagemath-gap[aclib]"``
 installs `aclib <https://gap-packages.github.io/aclib/>`__: Almost crystallographic groups

``pip install "passagemath-gap[agt]"``
 installs `agt <https://gap-packages.github.io/agt/>`__

``pip install "passagemath-gap[alnuth]"``
 installs `alnuth <https://gap-packages.github.io/alnuth>`__: Algebraic number theory, interface to PARI/GP

``pip install "passagemath-gap[caratinterface]"``
 installs `caratinterface <https://gap-packages.github.io/caratinterface/>`__

``pip install "passagemath-gap[corefreesub]"``
 installs `corefreesub <https://gap-packages.github.io/corefreesub/>`__

``pip install "passagemath-gap[cryst]"``
 installs `cryst <https://www.math.uni-bielefeld.de/~gaehler/gap/packages.php>`__: Computing with crystallographic groups

``pip install "passagemath-gap[crystcat]"``
 installs `crystcat <https://www.math.uni-bielefeld.de/~gaehler/gap/packages.php>`__: Crystallographic groups catalog

``pip install "passagemath-gap[ctbllib]"``
 installs `ctbllib <https://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib>`__: The GAP Character Table Library

``pip install "passagemath-gap[cubefree]"``
 installs `cubefree <https://gap-packages.github.io/cubefree/>`__

``pip install "passagemath-gap[cddinterface]"``
 installs `cddinterface <https://gap-packages.github.io/cddinterface/>`__

``pip install "passagemath-gap[curlinterface]"``
 installs `curlinterface <https://gap-packages.github.io/curlinterface/>`__

``pip install "passagemath-gap[deepthought]"``
 installs `deepthought <https://gap-packages.github.io/deepthought/>`__

``pip install "passagemath-gap[difsets]"``
 installs `difsets <https://gap-packages.github.io/difsets>`__

``pip install "passagemath-gap[float]"``
 installs `float <https://gap-packages.github.io/float>`__

``pip install "passagemath-gap[fr]"``
 installs `fr <https://gap-packages.github.io/fr/>`__

``pip install "passagemath-gap[fwtree]"``
 installs `fwtree <https://gap-packages.github.io/fwtree/>`__

``pip install "passagemath-gap[grpconst]"``
 installs `grpconst <https://gap-packages.github.io/grpconst/>`__

``pip install "passagemath-gap[guarana]"``
 installs `guarana <https://gap-packages.github.io/guarana/>`__

``pip install "passagemath-gap[hap]"``
 installs `hap <https://gap-packages.github.io/hap>`__: Homological algebra programming

``pip install "passagemath-gap[hapcryst]"``
 installs `hapcryst <https://gap-packages.github.io/hapcryst/>`__: HAP extension for crystallographic groups

``pip install "passagemath-gap[help]"``
 installs `help <https://gap-packages.github.io/help/>`__

``pip install "passagemath-gap[irredsol]"``
 installs `irredsol <http://www.icm.tu-bs.de/~bhoeflin/irredsol/index.html>`__: Library of irreducible soluble linear groups over finite fields and of finite primivite soluble groups

``pip install "passagemath-gap[lpres]"``
 installs `lpres <https://gap-packages.github.io/lpres/>`__

``pip install "passagemath-gap[modisom]"``
 installs `modisom <https://gap-packages.github.io/modisom/>`__

``pip install "passagemath-gap[nilmat]"``
 installs `nilmat <https://gap-packages.github.io/nilmat/>`__

``pip install "passagemath-gap[nq]"``
 installs `nq <https://gap-packages.github.io/nq/>`__: Nilpotent quotients of finitely presented groups

``pip install "passagemath-gap[numericalsgps]"``
 installs `numericalsgps <https://gap-packages.github.io/numericalsgps/>`__

``pip install "passagemath-gap[polenta]"``
 installs `polenta <https://gap-packages.github.io/polenta/>`__: Polycyclic presentations for matrix groups

``pip install "passagemath-gap[polycyclic]"``
 installs `polycyclic <https://gap-packages.github.io/polycyclic/>`__: Computation with polycyclic groups

``pip install "passagemath-gap[polymaking]"``
 installs `polymaking <https://gap-packages.github.io/polymaking/>`__: Interfacing the geometry software polymake

``pip install "passagemath-gap[radiroot]"``
 installs `radiroot <https://gap-packages.github.io/radiroot/>`__: Roots of a polynomial as radicals

``pip install "passagemath-gap[rcwa]"``
 installs `rcwa <https://gap-packages.github.io/rcwa/>`__

``pip install "passagemath-gap[resclasses]"``
 installs `resclasses <https://gap-packages.github.io/resclasses/>`__: Set-theoretic computations with residue classes

``pip install "passagemath-gap[semigroups]"``
 installs `semigroups <https://semigroups.github.io/Semigroups/>`__

``pip install "passagemath-gap[sglppow]"``
 installs `sglppow <https://gap-packages.github.io/sglppow/>`__

``pip install "passagemath-gap[simpcomp]"``
 installs `simpcomp <https://gap-packages.github.io/simpcomp/>`__

``pip install "passagemath-gap[singular]"``
 installs `singular <https://gap-packages.github.io/singular/>`__: Interface to Singular

``pip install "passagemath-gap[smallsemi]"``
 installs `smallsemi <https://gap-packages.github.io/smallsemi/>`__

``pip install "passagemath-gap[sonata]"``
 installs `sonata <https://gap-packages.github.io/sonata/>`__

``pip install "passagemath-gap[symbcompcc]"``
 installs `symbcompcc <https://gap-packages.github.io/symbcompcc/>`__

``pip install "passagemath-gap[tomllib]"``
 installs `tomlib <https://gap-packages.github.io/tomlib>`__: The GAP Library of Tables of Marks

``pip install "passagemath-gap[transgrp]"``
 installs `transgrp <https://www.math.colostate.edu/~hulpke/transgrp>`__: Transitive Groups Library

``pip install "passagemath-gap[xmod]"``
 installs `xmod <https://gap-packages.github.io/xmod/>`__

``pip install "passagemath-gap[unitlib]"``
 installs `unitlib <https://gap-packages.github.io/unitlib/>`__

``pip install "passagemath-gap[yangbaxter]"``
 installs `yangbaxter <https://gap-packages.github.io/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