sagemath_gap: Computational Group Theory with GAP¶

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 the following GAP packages:

  • aclib: Almost crystallographic groups

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

  • 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

  • cryst: Computing with crystallographic groups

  • crystcat: Crystallographic groups catalog

  • 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

  • hap: Homological algebra programming

  • hapcryst: HAP extension for crystallographic groups

  • 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

  • nq: Nilpotent quotients of finitely presented groups

  • orb: Methods to enumerate orbits

  • packagemanager: Easily download and install GAP packages

  • polenta: Polycyclic presentations for matrix groups

  • polycyclic: Computation with polycyclic groups

  • polymaking: Interfacing the geometry software polymake

  • primgrp: Primitive permutation groups library

  • quagroup: Computations with quantum groups

  • qpa: Quivers and path algebras

  • radiroot: Roots of a polynomial as radicals

  • repsn: Constructing representations of finite groups

  • resclasses: Set-theoretic computations with residue classes

  • singular: Interface to Singular

  • 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¶

A quick way to try it out interactively:

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

In [1]: from sage.all__sagemath_modules import *

In [2]: from sage.all__sagemath_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¶

Type¶

standard

Dependencies¶

• $(PYTHON)

• $(PYTHON_TOOLCHAIN)

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

• gap: Groups, Algorithms, Programming - a system for computational discrete algebra

• pkgconfig: Python interface to pkg-config

• sage-setup: Build system of the Sage library

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

• sagemath_environment: System and software environment

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

Version Information¶

package-version.txt:

10.6.3

version_requirements.txt:

passagemath-gap ~= 10.6.3.0

Equivalent System Packages¶

(none known)