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# RAQ, a GAP System package for Racks And Quandles.
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2018-08-19 17:44:57 +00:00
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* Website: http://code.studioinfinity.org/RAQ/wiki
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* Repository: http://code.studioinfinity.org/RAQ
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2018-08-19 06:48:21 +00:00
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* Authors/maintainers of RAQ: Glen Whitney <glen@studioinfinity.org>
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2018-08-17 04:12:38 +00:00
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2018-08-19 05:34:13 +00:00
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<!--
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#! @Chapter Introduction
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#! @AutoDocPlainText -->
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2018-08-21 19:33:38 +00:00
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The &RAQ; package provides a variety of facilities for constructing and
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2018-09-01 15:12:31 +00:00
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computing with one-sided quasigroups, racks, and quandles in &GAP;. Highlights
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include:
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* Constructing quandles from operation tables, groups, or other quandles.
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* And more to come..
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<!--@Section Installation
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@AutoDocPlainText -->
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&RAQ; uses no external binaries, so installation consists only of placing its
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unpacked file tree in a directory in your package search path, e.g. the `pkg`
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directory of your &GAP; installation, or perhaps the `.gap/pkg` subdirectory of
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your home directory.
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<!--@Acknowledgements
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@AutoDocPlainText -->
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The authors of &RAQ; would like to acknowledge their debt to the creators of
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&RIG;, an earlier package for Racks in GAP; chief among whom is Leandro
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Vendramin. &RIG; was an inspiration for the creation of &RAQ;, and using and
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reading that package suggested many features needed in the development of
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&RAQ;.
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2018-08-19 06:52:42 +00:00
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<!--@Chapter Introduction
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@Section A first spin
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@AutoDocPlainText -->
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Perhaps the following &GAP; interactive session, which constructs the
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conjugation quandle of the symmetric group on three elements and then performs
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a few simple computations on that quandle, will give the flavor of &RAQ;. (It is
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presumed that the &RAQ; package has already been loaded with
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`LoadPackage("RAQ");` prior to these example commands being executed, and that
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remains true throughout the package documentation.)
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<!--@BeginExampleSession ``` -->
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```
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gap> S3 := SymmetricGroup(3);
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Sym( [ 1 .. 3 ] )
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gap> Elements(S3);
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[ (), (2,3), (1,2), (1,2,3), (1,3,2), (1,3) ]
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gap> Q3 := ConjugationQuandle(S3);
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<left quandle with 6 generators>
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gap> elt := Elements(Q3); # the element ^p: below means conjugation by p in S3
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[ ^():, ^(2,3):, ^(1,2):, ^(1,2,3):, ^(1,3,2):, ^(1,3): ]
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gap> elt[4]*elt[3]; # So this will produce (1,2,3)^{-1}(1,2)(1,2,3)
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^(2,3):
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```
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<!--@EndExampleSession
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@AutoDocPlainText -->
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2018-08-19 07:24:35 +00:00
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2018-08-21 19:33:38 +00:00
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Note in particular that &RAQ; generally, unless otherwise specifically
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requested, produces __left__ quandles and racks. (That is to say, quandles in
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which for any fixed element $l$, the "left-multiplication by $l$" operation
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$x\mapsto l*x$ is a permutation of the quandle.)
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2018-09-01 15:12:31 +00:00
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<!--@Copyright
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@AutoDocPlainText -->
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©right; 2018 by Glen Whitney.
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This package may be distributed under the terms and conditions of the GNU
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Public License version 3. See the <C>LICENSE</C> file in the package directory
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for details.
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2018-08-19 06:52:42 +00:00
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<!--@EndAutoDocPlainText -->
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