GAP (software)

GAP (software)
Name	GAP
Developer	University of St Andrews, Mathematical Sciences Research Institute, University of Sydney, University of Bordeaux
Released	1986
Programming language	C (programming language), GAP language
Operating system	Linux, Microsoft Windows, macOS
License	GNU General Public License

GAP (software) is a computer algebra system focused on computational discrete algebra with particular emphasis on computational group theory, representation theory, and combinatorics. Originating in the mid-1980s, it provides an interactive environment, a high-level interpreted language, an extensive library of algorithms, and a rich collection of data libraries. GAP is used by researchers and educators affiliated with institutions such as University of St Andrews, University of Sydney, University of Bordeaux, RWTH Aachen University and research institutes including Mathematical Sciences Research Institute.

Overview

GAP serves as a platform for computations in areas associated with groups, semigroups, rings, modules, algebras, and combinatorial objects. The system integrates algorithmic developments influenced by work at Institut des Hautes Études Scientifiques, Max Planck Institute for Mathematics, Princeton University, Harvard University, and University of Cambridge. Core capabilities include manipulation of permutation groups, matrix groups, polycyclic groups, character tables, and design theory, reflecting contributions from researchers linked to Erlangen-Nürnberg, Moscow State University, and University of Warwick.

Features and Functionality

GAP offers functionality spanning algorithmic group theory, representation theory, and combinatorics. Key features include: - Group and semigroup constructions supporting operations derived from methodologies used at Kurt Gödel Research Center, Steklov Institute of Mathematics, and University of Oxford. - Character table computations influenced by techniques from École Normale Supérieure, University of Illinois at Urbana–Champaign, and University of Michigan. - Permutation group algorithms used in projects at Los Alamos National Laboratory, Bell Labs, and Lawrence Berkeley National Laboratory. - Data libraries containing group catalogs, character tables, and small groups contributed by teams at University of Sydney, University of St Andrews, University of Szeged, and University of Padua. - An extensible package system enabling extensions analogous to packages developed at Rutherford Appleton Laboratory, KTH Royal Institute of Technology, and University of Oxford.

Architecture and Implementation

GAP is implemented as a hybrid system combining a kernel written in C (programming language) with an interpreter for the native GAP language. This architecture mirrors approaches from projects at University of California, Berkeley, ETH Zurich, and Massachusetts Institute of Technology. The kernel provides memory management, low-level data structures, and bindings to external libraries, while the interpreter supports pattern matching, lazy evaluation, and first-class functions similar to paradigms explored at Carnegie Mellon University and Stanford University. Data libraries are stored in formats designed for efficient lookup, reflecting database techniques from University of Illinois at Urbana–Champaign.

Interfacing facilities allow integration with systems and languages from diverse research centers such as SageMath project collaborators, PARI/GP contributors at Université Bordeaux 1, and numeric libraries originating at Numerical Algorithms Group. The package mechanism supports modular contributions from groups at Technische Universität München and University of Münster.

History and Development

Development began in 1986 with principal contributors affiliated with University of St Andrews and collaborators from University of Sydney and University of Cologne. Early development incorporated algorithmic advances produced by researchers associated with University of Cambridge, Moscow State University, and University of Birmingham. Over successive releases, the project incorporated data and algorithms influenced by work at Max Planck Institute for Mathematics, École Polytechnique, and Institut des Hautes Études Scientifiques. Major milestones include the establishment of the GAP Group, the release of extensive small groups libraries, and the emergence of specialized packages authored by teams across Europe, North America, and Australia.

Community and Ecosystem

The GAP ecosystem comprises academic contributors, package authors, and user communities centered at research institutions such as University of St Andrews, University of Sydney, RWTH Aachen University, and Max Planck Institute for Mathematics. Mailing lists, workshops, and conferences connect users from European Mathematical Society meetings, Association for Symbolic Logic events, and workshops at Mathematical Sciences Research Institute. The package repository hosts contributions from groups at University of Oxford, KU Leuven, Aalto University, and University of Bordeaux, fostering collaboration with projects like SageMath project and integrations with systems developed at University of Cambridge.

Applications and Use Cases

GAP is applied in research, education, and software development across many institutions. Use cases include classification problems pursued at University of Birmingham, computational investigations in representation theory at University of Illinois at Urbana–Champaign, and combinatorial design computations used by researchers at University of Auckland and University of Waterloo. It supports thesis work and curriculum at universities such as University of St Andrews, University of Sydney, and ETH Zurich and has been employed in collaborative research involving Max Planck Institute for Mathematics, Princeton University, and Harvard University.

Licensing and Availability

GAP is distributed under the GNU General Public License, enabling redistribution and modification in line with free software practices championed by organizations like the Free Software Foundation. Binary builds and source distributions are maintained by the GAP Group and contributed to by nodes at University of St Andrews, University of Sydney, and University of Bordeaux. Packages maintained by contributors at RWTH Aachen University, KTH Royal Institute of Technology, and University of Oxford are available through the central package index for research and teaching use.

Category:Computer algebra systems