GAP computer algebra system
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- This article is about a software package. For other uses see Gap (disambiguation).
GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra similar to Mathematica with particular emphasis on, but not restricted to, computational group theory. GAP was developed at Lehrstuhl D für Mathematik (LDFM), RWTH Aachen, Germany from 1986 to 1997. After the retirement of J. Neubüser from the chair of LDFM, the development and maintenance of GAP is coordinated by the School of Mathematical and Computational Sciences at the University of St. Andrews, Scotland.
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. It requires a minimum of 32 MB disk space; the full distribution takes about 300 MB. To run GAP one needs a minimum of 20 MB of main memory - for most purposes 128 MB are sufficient.
The current version is 4.4.5, as of May 2005. GAP 3 (last release: 3.4.4) is still available but no longer supported.
An interface is available for using the SINGULAR computer algebra system from within GAP.
Sample session
gap> G:=SmallGroup(8,1); # Set G to be a group 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); # 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) ]
External links
- GAP official site (http://www.gap-system.org): Details about the system, the software itself and instructions how to obtain and to install it.
- The interface from GAP to Singular (http://www-math.science.unitn.it/~costanti/#singular)