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PEAL: PErmutation groups and ALgorithms

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PEAL: Permutation groups and algorithms

PEAL is an organisation that hosts a collection of tools for computing with permutation groups.

Here we list the people that have been directly involved in PEAL so far, our projects within PEAL, and our associated written publications.

People

Each of the following projects has its own collection of authors, maintainers, and contributors. Here, we simply list the union of these people, i.e. everyone who has directly contributed to PEAL’s tools, in one way or another. So far, we have all come to be associated with PEAL by our connections with the AI Research Group at the School of Computer Science of the University of St Andrews.

Projects

★ Vole

Vole is a GAP package written in Rust that aims to provide a high-performance implementation of the graph backtracking algorithm of the paper “Permutation group algorithms based on directed graphs”. Vole also implements new tools for canonising in arbitrary finite permutation groups, whose underlying theory is in preparation for publication.

★ GraphBacktracking

GraphBacktracking is a GAP package that provides a proof-of-concept implementation of the graph backtracking algorithm of the paper “Permutation group algorithms based on directed graphs”. The GraphBacktracking package was used for the experiments described in that paper, and is not intended to have high performance.

★ BacktrackKit

BacktrackKit is a GAP package that aims to provide a reference implementation of the partition backtracking algorithm of Jeffrey Leon. It is not intended to have high performance.

★ DirectDisjointProdDecomposition

DirectDisjointProdDecomposition is a collection of GAP code that includes an implementation of the algorithm described in the paper “Disjoint direct product decompositions of permutation groups”, along with the code that was used for the experiments in that paper. This algorithm decomposes a permutation group that is a direct product, whose factors act on disjoint sets of points, into those factors.

DirectDisjointProdDecomposition was created by Mun See Chang and Christopher Jefferson.

★ GrpLib

GrpLib is a library of problems in computational group theory, along with a library of families of permutation groups. These groups are provided in a format that allows them to be easily used in computations.

GrpLib is maintained by Ruth Hoffmann and Christopher Jefferson.

Associated PEAL publications