GAP (computer algebra system): Difference between revisions

Revision as of 07:37, 11 July 2023

Revision as of 22:39, 4 November 2023

Line 25:

}}

'''GAP''' ([[Group (mathematics)|Groups]], [[Algorithm]]s and [[Computer programming|Programming]]) is aan [[open source]] [[computer algebra system]] for computational [[Discrete mathematics#Algebraic structures|discrete algebra]] with particular emphasis on [[computational group theory]].

==History==

GAP was developed at Lehrstuhl D für Mathematik (LDFM), [[RWTH Aachen University|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]].<ref>{{cite web|url=https://www.gap-system.org/Doc/History/history.html|title=Some history of GAP|website=Official GAP website|access-date=September 27, 2019}}</ref> 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, [[Braunschweig University of Technology|Technische Universität Braunschweig]], and [[Colorado State University]] at [[Fort Collins, Colorado|Fort Collins]]; in April 2020, a fifth GAP Centre located at the [[University of Kaiserslautern|TU Kaiserslautern]] was added.<ref>{{cite web|url=https://www.gap-system.org/Contacts/centres.html|title=GAP Centres|website=Official GAP website|access-date=April 18, 2020}}</ref>

==Features==

GAP contains a [[Procedural programming|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 group|Finite groups]] can be defined as [[Permutation group|groups of permutations]] and it is also possible to define [[Finitely-presented group|finitely presented groups]] by specifying generators and relations. Several databases of important finite groups are included. GAP also allows to work with [[Matrix (mathematics)|matrices]] and with [[Finite field|finite fields]] (which are represented using [[Conway polynomial (finite fields)|Conway polynomials]]). [[Ring (mathematics)|Rings]], [[Module (mathematics)|modules]] and [[Lie algebra|Lie algebras]] are also supported.

==Distribution==

Line 44 ⟶ 47:

gap> i:=IsomorphismPermGroup(G); # Find an isomorphism from G to a group of permutations.

<action isomorphism>

gap> Image(i,G); # TheGenerators for the image of G under Ii - thesewritten areas the generatorsproducts of imdisjoint Gcyclic 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.