Monoid

Home Page

http://schmidt.ucg.ie/monoid

Description

MONOID is a package of GAP functions for transformation monoids and related objects. It contains functions that deal with

• (finite) transformations,
• transformation monoids,
• finite binary relations, and
• actions of monoids on various sorts of sets.

MONOID provides functions that determine the size of a transformation monoid M, can list the elements of M or decide membership of any transformation of degree n in M. Moreover, the Green class structure of M can be determined.

Relations can be multiplied, checked for properties like reflexive, symmetric, transitive, and closures can be formed. Relations of degree n can be used to generate a monoid.

The action of a transformation monoid on {1, . ., n} induces actions on tuples, subsets, ... which can be used to build new transformation monoids from given ones.

Authors

Steve Linton, sal@dcs.st-and.ac.uk,
Center for Interdisciplinary Research in Computational Algebra
University of St. Andrews
The North Haugh
St. Andrews, Fife, KY16 9SS
UK

Götz Pfeiffer, goetz@schmidt.ucg.ie
Department of Mathematics
University College Galway
Galway
Ireland

E. Robertson, edmund@dcs.st-and.ac.uk
Department of Computer Science
University of Otago
PO Box 56
Dunedin
New Zealand
and

Nik Ruskuc, nik@mcs.st-and.ac.uk
Department of Computer Science
University of Otago
PO Box 56
Dunedin
New Zealand
.