GAP 3 Share Package "monoid"

The MONOiD package

Share package since September 1997, communicated by Derek F. Holt, Warwick.
Corresponding GAP 4 package: GAP 4 package "monoid" (thanks to James Mitchell). Some of its functionality is also available in the main GAP 4 library.

Authors

Steve Linton, Götz Pfeiffer, Edmund Robertson, and Nik Ruskuc.

Implementation

Language: GAP 3
Operating system: Any
Current version: 2.4 (available here)

Description

MONOiD is a package of GAP 3 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.

Home Page (including manual)

http://schmidt.ucg.ie/monoid.

See also:

• a talk by Götz Pfeiffer at the Oberwolfach conference 1997, and
• a talk by Steve Linton at a conference on semigroups, July 1997, available in LaTeX, DVI, and PostScript.

Contact addresses

Steve Linton
School of Computer Science
University of St. Andrews
The North Haugh
St. Andrews, Fife, KY16 9SS
UK
email: sal@dcs.st-and.ac.uk

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

Edmund Robertson
School of Mathematics and Statistics
University of St. Andrews
The North Haugh
St. Andrews, Fife, KY16 9SS
UK
email: edmund@mcs.st-and.ac.uk

Nik Ruskuc
School of Mathematics and Statistics
University of St. Andrews
The North Haugh
St. Andrews, Fife, KY16 9SS
UK
email: nik@mcs.st-and.ac.uk