Jump to content

GAP (computer algebra system)

From Wikipedia, the free encyclopedia

GAP
Developer(s)
Initial release1988
Stable release
4.14.0[1] / 5 December 2024; 0 days ago (5 December 2024)
Repository
Written inC
Operating systemCross-platform
TypeComputer algebra system
LicenseGNU General Public License
Websitewww.gap-system.org

GAP (Groups, Algorithms and Programming) is an open source computer algebra system for computational discrete algebra with particular emphasis on computational group theory.

History

[edit]

GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to 1997. After the retirement of Joachim Neubüser from the chair of LDFM, the development and maintenance of GAP was coordinated by the School of Mathematical and Computational Sciences at the University of St Andrews, Scotland.[2] In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the University of St Andrews, RWTH Aachen, Technische Universität Braunschweig, and Colorado State University at Fort Collins; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added.[3]

Features

[edit]

GAP contains a procedural programming language and a large collection of functions to create and manipulate various mathematical objects. It supports integers and rational numbers of arbitrary size, memory permitting. Finite groups can be defined as groups of permutations and it is also possible to define finitely presented groups by specifying generators and relations. Several databases of important finite groups are included. GAP also allows to work with matrices and with finite fields (which are represented using Conway polynomials). Rings, modules and Lie algebras are also supported.

Distribution

[edit]

GAP and its sources, including packages (sets of user contributed programs), data library (including a list of small groups) and the manual, are distributed freely, subject to "copyleft" conditions. GAP runs on any Unix system, under Windows, and on Macintosh systems. The standard distribution requires about 300 MB (about 400 MB if all the packages are loaded).

The user contributed packages are an important feature of the system, adding a great deal of functionality. GAP offers package authors the opportunity to submit these packages for a process of peer review, hopefully improving the quality of the final packages, and providing recognition akin to an academic publication for their authors. As of March 2021, there are 151 packages distributed with GAP, of which approximately 71 have been through this process.

An interface is available for using the SINGULAR computer algebra system from within GAP. GAP is also included in the mathematical software system SageMath.

Sample session

[edit]
gap> G:=SmallGroup(8,1); # Set G to be the 1st group (in GAP catalogue) of order 8.
<pc group of size 8 with 3 generators>
gap> i:=IsomorphismPermGroup(G); # Find an isomorphism from G to a group of permutations.
<action isomorphism>
gap> Image(i,G); # Generators for the image of G under i - written as products of disjoint cyclic permutations.
Group([ (1,5,3,7,2,6,4,8), (1,3,2,4)(5,7,6,8), (1,2)(3,4)(5,6)(7,8) ])
gap> Elements(Image(i,G)); # All the elements of im G.
[ (), (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,4,2,3)(5,8,6,7),
  (1,5,3,7,2,6,4,8), (1,6,3,8,2,5,4,7), (1,7,4,5,2,8,3,6), (1,8,4,6,2,7,3,5) ]

See also

[edit]

References

[edit]
  1. ^ "Release 4.14.0". 5 December 2024. Retrieved 5 December 2024.
  2. ^ "Some history of GAP". Official GAP website. Retrieved 27 September 2019.
  3. ^ "GAP Centres". Official GAP website. Retrieved 18 April 2020.
[edit]