Practical computation with linear groups over infinite domains

TL;DR

This paper reviews recent advances in algorithms for finitely generated linear groups over infinite fields, emphasizing practical implementation and experimental validation of these computational methods.

Contribution

It introduces a methodology for practical computation with linear groups over infinite domains and discusses its implementation and experimental results.

Findings

Algorithms successfully implemented and tested

Extensive computer experiments conducted

Advances facilitate practical computations in linear groups

Abstract

We survey recent progress in computing with finitely generated linear groups over infinite fields, describing the mathematical background of a methodology applied to design practical algorithms for these groups. Implementations of the algorithms have been used to perform extensive computer experiments.