A package of algorithms for solving hard problems in group theory.

摘要

In this thesis we developed some methods of a new emerging area of mathematics, which we call experimental algebra. We designed new algorithms, both deterministic and heuristic, aimed at hard problems in algebra. Using these algorithms we solved some open problems in groups and semigroups. These algorithms are implemented and organized in a package. In addition to implementations of stand-alone algorithms for solving particular problems, the package contains a variety of reusable components---tools that can be used to modify the behavior of existing algorithms, to form alternative strategies and to build new algorithms out of provided components.