The Howdy Glossary

GAP is a computer algebra system tailored for computational discrete algebra, featuring a high-level programming language and specialized commands to work with groups, rings, fields, and algebras. It optimizes algorithms based on theoretical insights into these structures to efficiently handle large computational problems. Users can interact with GAP through command-line and scripting capabilities, making it an effective tool for working with complex algebraic computations.

The development of GAP began in the mid-1980s under Professor Joachim Neubüser at RWTH Aachen University in Germany. Over the years, it has evolved thanks to contributions from a global community of developers. GAP's design focus is on providing researchers and mathematicians with an optimized environment for handling algebraic structures efficiently by leveraging theory-informed algorithms.

GAP competes with other computational algebra systems like Magma, SageMath, and Mathematica. While GAP excels in computational discrete algebra through its specialized commands and algorithm optimization for groups, rings, fields, and algebras, Magma focuses on algebra and number theory computations. SageMath offers broader mathematical computing tools encompassing symbolic and numerical computations as well as discrete mathematics. Mathematica provides comprehensive capabilities across various mathematical domains including symbolic algebra and visualization. Each of these systems has unique strengths tailored to different aspects of mathematical computation needs.