RAQ, a GAP System package for Racks And Quandles.

• Website: http://code.studioinfinity.org/RAQ/wiki
• Repository: http://code.studioinfinity.org/RAQ
• Authors/maintainers of RAQ: Glen Whitney glen@studioinfinity.org

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

&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.)

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.)