GAP (

Groups A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

Algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s and Programming) is a

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The d ...

for computational discrete algebra with particular emphasis on

computational group theory In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because f ...

History

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 (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

Scotland Scotland (, ) is a Countries of the United Kingdom, country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a Anglo-Scottish border, border with England to the southeast ...

. In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the

University of St Andrews (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

, RWTH Aachen,

Technische Universität Braunschweig The Technische Universität Braunschweig (unofficially University of Braunschweig – Institute of Technology), commonly referred to as TU Braunschweig, is the oldest ' (comparable to an institute of technology in the American system) in Germany. ...

, and Colorado State University at

Fort Collins A fortification is a military construction or building designed for the defense of territories in warfare, and is also used to establish rule in a region during peacetime. The term is derived from Latin ''fortis'' ("strong") and ''facere'' ...

; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added.

Distribution

GAP and its sources, including packages (sets of user contributed programs), data library (including a

list of small groups The following list in mathematics contains the finite groups of small order up to group isomorphism. Counts For ''n'' = 1, 2, … the number of nonisomorphic groups of order ''n'' is : 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5 ...

) and the manual, are distributed freely, subject to "

copyleft Copyleft is the legal technique of granting certain freedoms over copies of copyrighted works with the requirement that the same rights be preserved in derivative works. In this sense, ''freedoms'' refers to the use of the work for any purpose ...

" conditions. GAP runs on any

Unix Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, an ...

system, under

Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for ser ...

, and on

Macintosh The Mac (known as Macintosh until 1999) is a family of personal computers designed and marketed by Apple Inc. Macs are known for their ease of use and minimalist designs, and are popular among students, creative professionals, and software en ...

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 Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer revie ...

, hopefully improving the quality of the final packages, and providing recognition akin to an academic publication for their authors. , 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 SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, numbe ...

Sample session

gap> G:=SmallGroup(8,1); # Set G to be a group of order 8. gap> i:=IsomorphismPermGroup(G); # Find an isomorphism from G to a group of permutations. gap> Image(i,G); # The image of G under I - these are the generators of im G. gap> Elements(Image(i,G)); # All the elements of im G.

References

External links

* * {{DEFAULTSORT:Gap Computer Algebra System Computer algebra system software for Linux Computer algebra system software for macOS Computer algebra system software for Windows Free computer algebra systems

History

Distribution

Sample session

See also

References

External links