63 lines
1.3 KiB
Julia
63 lines
1.3 KiB
Julia
module CapraceGroup
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using AbstractAlgebra
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using Groups
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###############################################################################
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#
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# Generating set
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#
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###############################################################################
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Comm(x,y) = x*y*x^-1*y^-1
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function generatingset()
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CapraceGroup = Groups.FPGroup(["x","y","z","t","r"]);
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x,y,z,t,r = gens(CapraceGroup)
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relations = [
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x^7,
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y^7,
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t^2,
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r^73,
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t*r*t*r,
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Comm(x,y)*z^-1,
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Comm(x,z),
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Comm(y,z),
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Comm(x^2*y*z^-1, t),
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Comm(x*y*z^3, t*r),
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Comm(x^3*y*z^2, t*r^17),
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Comm(x, t*r^-34),
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Comm(y, t*r^-32),
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Comm(z, t*r^-29),
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Comm(x^-2*y*z, t*r^-25),
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Comm(x^-1*y*z^-3, t*r^-19),
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Comm(x^-3*y*z^-2, t*r^-11)
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];
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(CapraceGroup, Dict(rel => CapraceGroup() for rel in relations))
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return CapraceGroup, gens(CapraceGroup)
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end
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function generatingset(parsed_args)
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return generatingset()
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end
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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function groupname(parsed_args)
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return groupname(), 0
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end
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groupname() = "CapraceGroup"
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end # of module CapraceGroup
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