38 lines
749 B
Julia
38 lines
749 B
Julia
struct CapraceGroup <: GAPGroup
|
|
args::Dict{String,Any}
|
|
end
|
|
|
|
name(G::CapraceGroup) = "CapraceGroup"
|
|
|
|
function group(G::CapraceGroup)
|
|
|
|
caprace_group = Groups.FPGroup(["x","y","z","t","r"])
|
|
|
|
x,y,z,t,r = gens(caprace_group)
|
|
|
|
relations = [
|
|
x^7,
|
|
y^7,
|
|
t^2,
|
|
r^73,
|
|
t*r*t*r,
|
|
Comm(x,y)*z^-1,
|
|
Comm(x,z),
|
|
Comm(y,z),
|
|
Comm(x^2*y*z^-1, t),
|
|
Comm(x*y*z^3, t*r),
|
|
Comm(x^3*y*z^2, t*r^17),
|
|
Comm(x, t*r^-34),
|
|
Comm(y, t*r^-32),
|
|
Comm(z, t*r^-29),
|
|
Comm(x^-2*y*z, t*r^-25),
|
|
Comm(x^-1*y*z^-3, t*r^-19),
|
|
Comm(x^-3*y*z^-2, t*r^-11)
|
|
];
|
|
|
|
relations = [relations; [inv(rel) for rel in relations]]
|
|
|
|
Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations))
|
|
return caprace_group
|
|
end
|