RAQ, a GAP System package for Racks And Quandles.
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README.md

RAQ, a GAP System package for Racks And Quandles.

The &RAQ; package provides a variety of facilities for constructing and computing with one-sided quasigroups, racks, and quandles in ⪆. Highlights include:

  • Constructing quandles from operation tables, groups, or other quandles.
  • And more to come..

&RAQ; uses no external binaries, so installation consists only of placing its unpacked file tree in a directory in your package search path, e.g. the pkg directory of your ⪆ installation, or perhaps the .gap/pkg subdirectory of your home directory.

The authors of &RAQ; would like to acknowledge their debt to the creators of &RIG;, an earlier package for Racks in GAP; chief among whom is Leandro Vendramin. &RIG; was an inspiration for the creation of &RAQ;, and using and reading that package suggested many features needed in the development of &RAQ;.

Perhaps the following ⪆ interactive session, which constructs the conjugation quandle of the symmetric group on three elements and then performs a few simple computations on that quandle, will give the flavor of &RAQ;. (It is presumed that the &RAQ; package has already been loaded with LoadPackage("RAQ"); prior to these example commands being executed, and that remains true throughout the package documentation.)

gap> S3 := SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> Elements(S3);
[ (), (2,3), (1,2), (1,2,3), (1,3,2), (1,3) ]
gap> Q3 := ConjugationQuandle(S3);
<left quandle with 6 generators>
gap> elt := Elements(Q3); # the element ^p: below means conjugation by p in S3 
[ ^():, ^(2,3):, ^(1,2):, ^(1,2,3):, ^(1,3,2):, ^(1,3): ]
gap> elt[4]*elt[3]; # So this will produce (1,2,3)^{-1}(1,2)(1,2,3)
^(2,3):

Note in particular that &RAQ; generally, unless otherwise specifically requested, produces left quandles and racks. (That is to say, quandles in which for any fixed element $l$, the "left-multiplication by $l$" operation $x\mapsto l*x$ is a permutation of the quandle.)

&copyright; 2018 by Glen Whitney.

This package may be distributed under the terms and conditions of the GNU Public License version 3. See the LICENSE file in the package directory for details.