initial adjust of GAPGroups files
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@ -1,20 +1,14 @@
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module CapraceGroup
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struct CapraceGroup <: GAPGroup
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args::Dict{String,Any}
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end
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using AbstractAlgebra
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using Groups
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name(G::CapraceGroup) = "CapraceGroup"
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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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function group(G::CapraceGroup)
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Comm(x,y) = x*y*x^-1*y^-1
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caprace_group = Groups.FPGroup(["x","y","z","t","r"])
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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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x,y,z,t,r = gens(caprace_group)
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relations = [
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x^7,
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@ -38,25 +32,6 @@ function generatingset()
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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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Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations))
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return caprace_group
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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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@ -1,49 +1,24 @@
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module HigmanGroup
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struct HigmanGroup <: GAPGroup
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args::Dict{String,Any}
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end
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using AbstractAlgebra
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using Groups
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name(G::HigmanGroup) = "HigmanGroup"
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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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function group(G::HigmanGroup)
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Comm(x,y) = x*y*x^-1*y^-1
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higman_group = Groups.FPGroup(["a","b","c","d"]);
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function generatingset()
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HigmanGr = Groups.FPGroup(["a","b","c","d"]);
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a,b,c,d = gens(HigmanGr)
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a,b,c,d = gens(higman_group)
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relations = [
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b^-1*Comm(b,a),
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c^-1*Comm(c,b),
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d^-1*Comm(d,c),
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a^-1*Comm(a,d)
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b^-1*Comm(b,a),
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c^-1*Comm(c,b),
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d^-1*Comm(d,c),
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a^-1*Comm(a,d)
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];
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(HigmanGr, Dict(rel => HigmanGr() for rel in relations))
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return HigmanGr, gens(HigmanGr)
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Groups.add_rels!(higman_group, Dict(rel => HigmanGr() for rel in relations))
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return higman_group
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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() = "HigmanGroup"
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end # of module CapraceGroup
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@ -1,17 +1,14 @@
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module MappingClassGroups
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struct MappingClassGroup <: GAPGroup
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args::Dict{String,Any}
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end
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using AbstractAlgebra
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using Groups
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function name(G::MappingClassGroup)
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N = G.args["N"]
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return "MCG($(N))"
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end
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###############################################################################
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#
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# Generating set
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#
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###############################################################################
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Comm(x,y) = x*y*x^-1*y^-1
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function generatingset(N::Int)
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function group(G::MappingClassGroup)
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N = G.args["N"]
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if N < 2
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throw("Genus must be at least 2!")
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elseif N == 2
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@ -33,77 +30,57 @@ function generatingset(N::Int)
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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return MCGroup
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end
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else
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MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
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S = gens(MCGroup)
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MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
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S = gens(MCGroup)
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a0 = S[1]
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A = S[2:end]
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k = length(A)
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a0 = S[1]
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A = S[2:end]
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k = length(A)
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relations = [
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[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
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[Comm(a0, A[i]) for i in 1:k if i != 4]...,
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[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
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A[4]*a0*A[4]*inv(a0*A[4]*a0)
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]
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relations = [
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[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
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[Comm(a0, A[i]) for i in 1:k if i != 4]...,
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[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
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A[4]*a0*A[4]*inv(a0*A[4]*a0)
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]
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# 3-chain relation
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c = prod(reverse(A[1:4]))*prod(A[1:4])
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b0 = c*a0*inv(c)
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push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
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# 3-chain relation
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c = prod(reverse(A[1:4]))*prod(A[1:4])
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b0 = c*a0*inv(c)
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push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
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# Lantern relation
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b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
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b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
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u = inv(A[6]*A[5])*b1*(A[6]*A[5])
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x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
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b3 = x*a0*inv(x)
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push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
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# Lantern relation
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b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
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b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
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u = inv(A[6]*A[5])*b1*(A[6]*A[5])
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x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
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b3 = x*a0*inv(x)
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push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
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# Hyperelliptic relation
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X = prod(reverse(A))*prod(A)
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# Hyperelliptic relation
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X = prod(reverse(A))*prod(A)
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function n(i::Int, b=b0)
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if i == 1
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return A[1]
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elseif i == 2
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return b
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else
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return w(i-2)*n(i-2)*w(i-2)
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function n(i::Int, b=b0)
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if i == 1
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return A[1]
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elseif i == 2
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return b
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else
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return w(i-2)*n(i-2)*w(i-2)
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end
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end
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function w(i::Int)
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(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
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(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
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end
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# push!(relations, X*n(N)*inv(n(N)*X))
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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return MCGroup
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end
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function w(i::Int)
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(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
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(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
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end
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# push!(relations, X*n(N)*inv(n(N)*X))
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
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return MCGroup, gens(MCGroup)
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end
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function generatingset(parsed_args)
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N = parsed_args["N"]
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return generatingset(N)
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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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N = parsed_args["N"]
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return groupname(N), N
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end
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groupname(N::Int) = "MCG$(N)"
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end #of module MappingClassGroups
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