On Fri, Sep 25, 2020 at 03:15:06PM +0000, Christopher Jefferson wrote: > Just to extend on Leonard's comments, > > The paper New refiners for permutation group search [Christopher > Jefferson, Markus Pfeiffer, Rebecca Waldecker] gives a brief overview > of partitions, while extending it. "Permutation group algorithms based > on directed graphs" gives a new, more general framework, which uses > directed graphs. > > If you are happy looking at code, > https://www.github.com/gap-packages/ferret gives a (reasonably) clean > reimplementation in C++, while https://github.com/peal/backtrackkit > gives a simple, very low-performance implementation (it aims to > produce the "right partitions", but does so in a very simple but > inefficient way). > > I also recently gave a brief overview on the topic at the Newtown > Institute: https://www.newton.ac.uk/seminar/20200131113012201 , which > you may (or may not) find helpful. I'm also happy to answer any > questions, particularly about Leon's paper which myself and my > co-authors are fairly sure we understand.
I like to thanks all of you for all the references, I have started to read them. In fact, I am interested in the computation of automorphisms groups of Euclidean lattices. There is a published algorithm by Plesken and Souvignier (1997) which uses backtracking and the randomized Schreier-Sims algorithm. Prof Souvignier published a C implementation of this algorithm which is widely used. MAGMA uses a faster but unpublished algorithm whose source code is not public. The documentation says: The computation of the automorphism group of a lattice (i.e. the largest matrix group that acts on the lattice) and the testing of lattices for isometry is performed within Magma using orthogonal decomposition (due to Gabi Nebe) and a backtrack search designed by Bill Unger in 2009. The backtrack search is based on the Plesken-Souvignier backtrack algorithm [PS97] together with ordered partition methods due to Leon. So I am left trying to understand what is the ordered partition method and how it can be used. Cheers, Bill _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
