# 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>

<!--
#! @Chapter Introduction
#! @AutoDocPlainText -->
The &RAQ; package provides a variety of facilities for constructing and
computing with one-sided quasigroups, racks, and quandles in &GAP;.

<!--@Section Installation
@AutoDocPlainText -->
&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 &GAP; installation, or perhaps the `.gap/pkg` subdirectory of
your home directory.

<!--@Acknowledgements
@AutoDocPlainText -->
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;.

<!--@Chapter Introduction
@Section A first spin
@AutoDocPlainText -->
Perhaps the following &GAP; 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.)
<!--@BeginExampleSession ``` -->
```
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):
```
<!--@EndExampleSession
@AutoDocPlainText -->

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.)
<!--@EndAutoDocPlainText -->