libsemigroups

Libsemigroups is a C++ library for semigroups and monoids; it is partly based on "Algorithms for computing finite semigroups", "Expository Slides", and Semigroupe 2.01 by Jean-Eric Pin. The libsemigroups library is used in the Semigroups package for GAP. Some of the features of Semigroupe 2.01 are not yet implemented in libsemigroups; this is a work in progress. Missing features include those for: - Green's relations, or classes - finding a zero - minimal ideal, principal left/right ideals, or indeed any ideals - inverses - local submonoids - the kernel - variety tests. These will be included in a future version. Libsemigroups performs roughly the same as Semigroupe 2.01 when there is a known upper bound on the size of the semigroup being enumerated, and this is used to initialize the data structures for the semigroup; see libsemigroups::Semigroup::reserve for more details. Note that in Semigroupe 2.01 it is always necessary to provide such an upper bound, but in libsemigroups it is not. Libsemigroups also has some advantages over Semigroupe 2.01: - there is a (hopefully) convenient C++ API, which makes it relatively easy to create and manipulate semigroups and monoids - there are some multithreaded methods for semigroups and their congruences - you do not have to know/guess the size of a semigroup or monoid before you begin - libsemigroups supports more types of elements than Semigroupe 2.01 - it is relatively straightforward to add support for further types of elements and semigroups - it is possible to enumerate a certain number of elements of a semigroup or monoid (say if you are looking for an element with a particular property), to stop, and then to start the enumeration again at a later point - you can instantiate as many semigroups and monoids as you can fit in memory - it is possible to add more generators after a semigroup or monoid has been constructed, without losing or having to recompute any information that was previously known - libsemigroups contains rudimentary implementations of the Todd-Coxeter and Knuth-Bendix algorithms for finitely presented semigroups, which can also be used to compute congruences of a (not necessarily finitely presented) semigroup or monoid.

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