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The St Andrews GAP semigroup package ------------------------------------------------------------

At St Andrews we are developing a GAP semigroup package.

Our code is not yet ready to distribute but it is intended

that this will be available with a futurerelease of GAP V4.

We have two semigroup enumerators based on Todd-Coxeter

which enumerate semigroups given by a finite presentation.

One of these is a C program which enumerates the semigroup

and returns the "coset table" to GAP. The second is written

in the GAP language.

We have a number of functions written in GAP to investigate

algebraic properties of a semigroup once it has been

enumerated. These functions find idempotents, find left

or right or two-sided ideals, R-classes, L-classes and D-

classes.

In addition we have implemented in GAP a program to

compute the semigroup given by a finite set of

transformations. Here is an abstract of a paper we are

writing on this part of the software.

Computing transformation monoids

Authors:

S.A. Linton, G. Pfeiffer, E.F. Robertson and N. Ruskuc

Abstract: Efficient computational methods are available for

computing with finite groups of permutations. In this paper we

utilise such methods in developing an algorithm to compute

the order and algebraic structure of finite transformation

monoids. We start from an algorithm due to Lallement and

McFadden and develop some theoretical improvements. The

underlying strategy is to translate computations in the

transformation monoid into computations in some

permutation groups.

Abstracts of some other relevant publications are

available on the WWW at the URL

http://www-groups.dcs.st-and.ac.uk/~nik/publ.html

and

http://www-groups.dcs.st-and.ac.uk/~edmund/publications.html

Although we intend a Todd-Coxeter and the transformation

monoid program to be the basic tools of the GAP semigroups

package, we are going to develop many more functions to

allow semigroups computed with these basic tools to be

investigated.

We have developed theoretically a number of other T-C

type algorithms for semigroups which we have not

yet implemented.

Nik Ruskuc Edmund Robertson 1 Aug 1996

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