Producing actions from binary functions.

Computing Cayley-graphs.

Chains in partially ordered sets given by their Hasse diagrams.
A Hasse diagram  is a hash-map from elements to the set of related elements.

Chain semigroups based on a skeleton.

Combinatorics stuff that is not readily available in
the contrib package.

Abstract functions for calculating conjugate elements, conjugacy classes,
and representatives.

Functions for transferring data between GAP and kigen.

Constructing isomorphisms/embeddings between semigroups given  by generators.
In other words, searching for an isomorphisms of Cayley-graphs.
The elements of both semigroups are fully enumerated.
The source semigroup is converted to generator table (partial multiplication
table containing all the images of right multiplication by generators).
The elements of target semigroups are classified by their index-periods in
order to find possible targets for generators.

Independent sets of semigroups represented by multiplication tables.

Information about memory usage.

Constructing morphisms and morphic relations.
input: two multiplication tables (source, target)
output: vectors describing morphisms, index i -> image

These functions are relatively inefficient (compared to generator table
methods). More for reference purposes, not for the high-end computations.

This is a reference implementation for the paper:
Finite Computational Structures and Implementations: Semigroups and
Morphic Relations
International Journal of Networking and Computing,
Volume 7, Number 2, pages 318–335, July 2017

Functions for dealing with abstract multiplication tables of semigroups.
The multiplicative elements are represented by their indices in a
given sequence. The tables are vectors of vectors (the rows of the table),
so multiplication is just a constant-time look up.
Functionality for multiplying subsets of elements and computing closures
and thus enumerating subsemigroups. The subsemigroups can be stored in
efficient int-sets.

partitioned binary relations stored as maps: integers -> set of integers
e.g. {1 #{1 2}, 2 #{2}}
for degree n, domain is 1..n, codomain is n+1..2n
e.g. degree 3, domain is {1,2,3}, codomain is {4,5,6}

Computing partially ordered sets. Ways of defining binary relations:
1. elements and a relation function (implicit)
2. a map: element x -> set of related elements (explicit)

Getting the indices of elements in vectors by giving a predicate
or by equality.

Strongly connected components of digraphs.

General functions for semigroups. Black box style, the element(s)
and the operation need to be supplied.

Skeleton of a transformation semigroup given by a set of  generators.

General functions for computing subsemigroups.
Black box style, the element(s) and the operation need to be supplied.

Transformations and permutations simply representated as vectors.

'Native' conjugacy class representative calculation.Transformations are
separated into single point mappings. A permutation is constructed by finding
the minimal relabeling of a transformation.

Transformations and permutations embedded into partitioned
binary relations.