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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.