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Dear GAP-forum,

Thierry Dana-Picard's question provoked two immediate replies by Peter

Webb and Martin Wursthorn which both stated: I have written GAP

routines ... . I enjoyed seeing this, I think it shows that the

GAP-forum serves its purpose.However I would like to take this instance to appeal to use the

GAP-forum also for informally informing others of the existence of

such routines without waiting for a question. This aspect has not been

emphazised when the function of the GAP-forum was explained in the

README file with the announcement of GAP, but I think as time proceeds

there will be more such "hidden treasures" which might be useful for

others as well if one knows of them. So please tell in the GAP-forum

about routines that you have written (and hopefully are willing to

share) as well as about interesting applications. It should be clear

that since the GAP-forum is unrefereed this does in no way conflict

with formal publications.Joachim Neubueser

Not being very well-versed in group theory, I have used GAP mainly for

combinatorial problems and finite relation algebras (including

polygroups, hypergraphs and a library of small examples). I find it a

very convenient language to write little routines that test

conjectures on these finite structures, and recently I have started

putting it together as a structured domain. However there is a big

difference between code written for private research and a public

package with documentation and extensive comments.

If other forum members are interested in the areas mentioned above, I

will gladly share what I've got. I'm certainly interested in feedback,

and on whether other GAP users are applying GAP outside group theory.

I realise that the developers are mainly commited to supporting

algorithms related to groups, but I think they have come up with a

nice, clean development system (and are giving it away free!) that

could be a basis for several other areas of abstract algebra and

discrete mathematics. Have other users of GAP implemented algorithms

and structures for universal algebra or related areas?

At this point I am only aware of GRAPE by Leonard Soicher for

graphs. Some of my routines would greatly benefit from his approach

but at the moment small finite polygroups are represented by a domain

that contains a list of all elements (records) and an operation table.

Most simple minded algorithms in this area loop of all subsets

of elements, so the complexity very bad and they won't work for larger

structures anyway. Relations are implemented as boolean matrices, but

it is simple to convert them to GRAPE format and then use the

interface to Brendan McKay's 'nauty' to get a more compact description

of the relation. In the near future I will also interface to some

c-code of my own, that searches for finite counter examples and

applies some theorem proving techniques for relation algebras.

BTW does anyone know of a program that tests finitary relational

structures for isomorphism (e.g. nauty does it for binary relational

structures)?

Peter Jipsen

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