Piterman K.I., Vendramin L. Computer algebra with GAP

Monograph. — Publication details not specified, 2023. — 156 p.Implementing new algorithms and the ever-growing power of modern computers have a revolutionary impact on science. Mathematics, whose artistic and creative nature could have been thought to be a barrier to the influence of computers, does not escape the reach of this revolution. Much of the mathematics published nowadays makes extensive use of machine computations. Remarkably, a substantial part of the results could not be obtained without it or would take an unreasonable amount of time. This includes many outstanding theoretical results that depend on computers to verify a hypothesis or perform particular calculations while proving a theorem. The use of computers is also growing in teaching mathematics at all levels. Regarding abstract algebra, one computer algebra system that is hard to overlook is GAP (“Groups, Algorithms and Programming”). It is extensively used when teaching elementary algebra and in advanced scientific literature, testing and disproving conjectures. This is one motivation that led us to write this monograph. The first version of GAP was released in December 1988, named Version 2.4, and it was a project started by Joachim Beubüser in 1986 at the Lehrstuhl D für Mathematik, RWTH-Aachen University. Indeed, the system was officially presented during an Oberwolfach meeting in May 1988. The GAP system has a kernel written in C, and its interpreter for the programming language belongs to the family of Pascal languages. It may be regarded as an object-oriented and imperative programming language. It is important to remark that GAP is an open-source program.