GAP computer algebra system
Encyclopedia
GAP is a computer algebra system
for computational discrete algebra with particular emphasis on computational group theory
.
, Germany from 1986 to 1997. After the retirement of J. 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
. In the summer of 2005 coordination was transferred to an equal partnership of 4 `GAP Centres', located at University of St. Andrews; RWTH Aachen
; the Technische Universität Braunschweig
; and Colorado State University
at Fort Collins
.
" 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). To run GAP, 128 MB of RAM is sufficient.
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. , there are 58 packages distributed with GAP, of which approximately 35 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 Sage.
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.
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) ]
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
for computational discrete algebra with particular emphasis on computational group theory
Computational group theory
In mathematics, computational group theory is the study ofgroups by means of computers. It is concernedwith designing and analysing algorithms anddata structures to compute information about groups...
.
History
GAP was developed at Lehrstuhl D für Mathematik (LDFM), RWTH AachenRWTH Aachen
RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....
, Germany from 1986 to 1997. After the retirement of J. 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
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
. In the summer of 2005 coordination was transferred to an equal partnership of 4 `GAP Centres', located at University of St. Andrews; RWTH Aachen
RWTH Aachen
RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....
; the Technische Universität Braunschweig
Technische Universität Braunschweig
The TU Braunschweig is the oldest University of Technology in Germany. It was founded in 1745 as Collegium Carolinum and is a member of TU9, an incorporated society of the most renowned and largest German Institutes of Technology. Today it has about 13,000 students, making it the third largest...
; and Colorado State University
Colorado State University
Colorado State University is a public research university located in Fort Collins, Colorado. The university is the state's land grant university, and the flagship university of the Colorado State University System.The enrollment is approximately 29,932 students, including resident and...
at Fort Collins
Fort Collins, Colorado
Fort Collins is a Home Rule Municipality situated on the Cache La Poudre River along the Colorado Front Range, and is the county seat and most populous city of Larimer County, Colorado, United States. Fort Collins is located north of the Colorado State Capitol in Denver. With a 2010 census...
.
Distribution
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 "copyleftCopyleft
Copyleft is a play on the word copyright to describe the practice of using copyright law to offer the right to distribute copies and modified versions of a work and requiring that the same rights be preserved in modified versions of the work...
" conditions. GAP runs on any Unix
Unix
Unix is a multitasking, multi-user computer operating system originally developed in 1969 by a group of AT&T employees at Bell Labs, including Ken Thompson, Dennis Ritchie, Brian Kernighan, Douglas McIlroy, and Joe Ossanna...
system, under Windows
Microsoft Windows
Microsoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...
, and on Macintosh systems. The standard distribution requires about 300 MB (about 400 MB if all the packages are loaded). To run GAP, 128 MB of RAM is sufficient.
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
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...
, hopefully improving the quality of the final packages, and providing recognition akin to an academic publication for their authors. , there are 58 packages distributed with GAP, of which approximately 35 have been through this process.
An interface is available for using the SINGULAR
SINGULAR
SINGULAR is a computer algebra system for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory. SINGULAR is free software released under the GNU General Public License. Problems in non-commutative algebra can be tackled with...
computer algebra system from within GAP. GAP is also included in the mathematical software system Sage.
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.
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.
(1,5,3,7,2,6,4,8), (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
- Comparison of computer algebra systems