Plans regarding enumeration of quasigroups.
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Detailed Description
Plans regarding enumeration of quasigroups.
 Todo:
 Enumeration and classification

For small order (say, n <= 5) it should be possible to enumerate all (isomorphism types) of quasigroups (and also the total count is interesting), and providing a catalogue.

Of course, we also need the numbers (total and nonisomorphic) of unital quasigroups, groups, commutative quasigroups, unital commutative quasigroups, and commutative groups.

Implement enumeration functions according to "All isomorphism types of
small groupoids" in ComputerAlgebra/Algebra/Lisp/Groupoids/plans/Enumeration.hpp.

What is the relation to the module for latin squares (see ComputerAlgebra/CombinatorialMatrices/Lisp/LatinSquares/plans/general.hpp)?

The general idea would be that here we enumerate everything with an "algebraic flavour", while there we handle everything with a "combinatorial flavour".
 Todo:
 Random generation of quasigroups and unital quasigroups

Producing random quasigroups and random unital quasigroups of bigger order must have been studied in the literature.

One could run a (generalised) SAT solver, for sampling the solutions of the condition "(unital) quasigroup".

Given a quasigroup, one can consider random isotopic images (choosing three random permutations); in this way one can sample the isotopy class.
Definition in file Enumeration.hpp.