Semigroups, Monoids, and other Generalisations of Groups

These include

  • functions for calculating withtransformations,
  • functions for investigatingsemigroups, in particular transformation semigroups,monoids, andfinitely presented semigroups and monoids,
  • sets of basic functions formagmas andadditive magmas,
  • a package SONATA for investigating near rings,
  • a package XMod for crossed modules and cat-1 groups,
  • a package GPD for computation of finite groupoids,
  • a package Loops for various types of loops,
  • a package Semigroups (former Citrus) for computing with semigroups of transformations and partial permutations, or subsemigroups of regular Rees 0-matrix semigroups, and also with free inverse semigroups,
  • a package Smallsemi, providing a data library of all semigroups with at most 8 elements,
  • a package NumericalSgps for computations with numerical semigroups, and
  • a package SgpViz for semigroup visualization.