55 lines
2.2 KiB
Markdown
55 lines
2.2 KiB
Markdown
# RAQ, a GAP System package for Racks And Quandles.
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* Website: code.studioinfinity.org/RAQ/wiki
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* Repository: code.studioinfinity.org/RAQ
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* Authors/maintainers of RAQ: Glen Whitney <glen@studioinfinity.org>
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<!--
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#! @Chapter Introduction
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#! @AutoDocPlainText -->
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The RAQ package provides a variety of facilities for constructing and
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computing with one-sided quasigroups, racks, and quandles in GAP.
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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 them 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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<!--@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.)
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<!--@BeginExampleSession --><pre>
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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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</pre><!--@EndExampleSession -->
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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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<!--@EndAutoDocPlainText -->
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