.. _spkg_sagemath_gap:

=====================================================================================================
sagemath_gap: Computational Group Theory with GAP
=====================================================================================================


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


Type
----

standard


Dependencies
------------

- $(PYTHON)
- $(PYTHON_TOOLCHAIN)
- :ref:`spkg_cysignals`
- :ref:`spkg_cython`
- :ref:`spkg_dot2tex`
- :ref:`spkg_gap`
- :ref:`spkg_gmp`
- :ref:`spkg_gmpy2`
- :ref:`spkg_memory_allocator`
- :ref:`spkg_mpc`
- :ref:`spkg_mpfr`
- :ref:`spkg_pexpect`
- :ref:`spkg_pkgconf`
- :ref:`spkg_pkgconfig`
- :ref:`spkg_sage_conf`
- :ref:`spkg_sage_setup`
- :ref:`spkg_sagemath_categories`
- :ref:`spkg_sagemath_environment`
- :ref:`spkg_sagemath_gap_pkg_factint_data`
- :ref:`spkg_sagemath_gap_pkg_primgrp_data`
- :ref:`spkg_sagemath_gap_pkg_smallgrp_data`
- :ref:`spkg_sagemath_modules`
- :ref:`spkg_sagemath_repl`
- :ref:`spkg_setuptools`

Version Information
-------------------

package-version.txt::

    10.6.47

version_requirements.txt::

    passagemath-gap ~= 10.6.47.0

Installation commands
---------------------

.. tab:: PyPI:

   .. CODE-BLOCK:: bash

       $ pip install passagemath-gap~=10.6.47.0

.. tab:: Sage distribution:

   .. CODE-BLOCK:: bash

       $ sage -i sagemath_gap


However, these system packages will not be used for building Sage
because ``spkg-configure.m4`` has not been written for this package;
see :issue:`27330` for more information.
