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GAP ( Groups , Algorithm s and Programming ) is a Computer Algebra System for computational discrete algebra 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 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 St Andrews; LDFM; the Technical University of Braunschweig and Colorado State University at Fort Collins . 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 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 August 2005 there are 50 packages distributed with GAP, of which approximately 30 have been through this process. The current version is 4.4.6, as of September 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. 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) ] EXTERNAL LINKS
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