The study and implementation of algorithms for the manipulation and calculation of semigroups. Computational applications in other branches of mathematics, such as the study of factorisations in integral domains, or the resolution of systems of equations and inequations with integral coefficients. As part of this section, other than the various publications concerning said algorithms, the numericalsgps freeware package for GAP has been implemented (this can be accessed and downloaded at www.gap-system.org). It is currently in version 0.97.