Semigroups, Monoids, and other Generalisations of Groups

These include

• functions for calculating with transformations,
  
  
• functions for investigating semigroups, in particular transformation semigroups, monoids, and finitely presented semigroups and monoids,
  
  
• sets of basic functions for magmas and additive 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.