Use README.md for manual intro (initial working version)

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* Website: code.studioinfinity.org/RAQ/wiki * Website: code.studioinfinity.org/RAQ/wiki
* Repository: code.studioinfinity.org/RAQ * Repository: code.studioinfinity.org/RAQ
* Authors/maintainers of RAQ: Glen Whitney <glen@studioinfinity.org>
This package provides a variety of facilities for computing with one-sided
quasigroups, racks, and quandles in GAP.
It uses no external binaries, so installation consists only of placing the RAQ
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 #! @Chapter Introduction
#! @AutoDocPlainText --> #! @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 The authors of RAQ would like to acknowledge their debt to the creators of
RIG, an earlier package for Racks in GAP; chief among them is Leandro RIG, an earlier package for Racks in GAP; chief among them is Leandro
Vendramin. RIG was an inspiration for the creation of RAQ, and using and Vendramin. RIG was an inspiration for the creation of RAQ, and using and
reading that package suggested many features needed in the development of reading that package suggested many features needed in the development of
RAQ. RAQ.
<!--@EndAutoDocPlainText -->
Authors/maintainers of RAQ: Glen Whitney <glen@studioinfinity.org> <--@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 -->
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 -->