2.2 KiB
RAQ, a GAP System package for Racks And Quandles.
- Website: code.studioinfinity.org/RAQ/wiki
- Repository: 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 GAP.
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.
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 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.
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@Section A first spin
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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):
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.)
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