diff --git a/groups/caprace.jl b/groups/caprace.jl index 48d6b31..980421d 100644 --- a/groups/caprace.jl +++ b/groups/caprace.jl @@ -1,20 +1,14 @@ -module CapraceGroup +struct CapraceGroup <: GAPGroup + args::Dict{String,Any} +end -using AbstractAlgebra -using Groups +name(G::CapraceGroup) = "CapraceGroup" -############################################################################### -# -# Generating set -# -############################################################################### +function group(G::CapraceGroup) -Comm(x,y) = x*y*x^-1*y^-1 + caprace_group = Groups.FPGroup(["x","y","z","t","r"]) -function generatingset() - - CapraceGroup = Groups.FPGroup(["x","y","z","t","r"]); - x,y,z,t,r = gens(CapraceGroup) + x,y,z,t,r = gens(caprace_group) relations = [ x^7, @@ -38,25 +32,6 @@ function generatingset() relations = [relations; [inv(rel) for rel in relations]] - Groups.add_rels!(CapraceGroup, Dict(rel => CapraceGroup() for rel in relations)) - - return CapraceGroup, gens(CapraceGroup) + Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations)) + return caprace_group end - -function generatingset(parsed_args) - return generatingset() -end - -############################################################################### -# -# Misc -# -############################################################################### - -function groupname(parsed_args) - return groupname(), 0 -end - -groupname() = "CapraceGroup" - -end # of module CapraceGroup diff --git a/groups/higman.jl b/groups/higman.jl index 041a015..74b0af2 100644 --- a/groups/higman.jl +++ b/groups/higman.jl @@ -1,49 +1,24 @@ -module HigmanGroup +struct HigmanGroup <: GAPGroup + args::Dict{String,Any} +end -using AbstractAlgebra -using Groups +name(G::HigmanGroup) = "HigmanGroup" -############################################################################### -# -# Generating set -# -############################################################################### +function group(G::HigmanGroup) -Comm(x,y) = x*y*x^-1*y^-1 + higman_group = Groups.FPGroup(["a","b","c","d"]); -function generatingset() - - HigmanGr = Groups.FPGroup(["a","b","c","d"]); - a,b,c,d = gens(HigmanGr) + a,b,c,d = gens(higman_group) relations = [ - b^-1*Comm(b,a), - c^-1*Comm(c,b), - d^-1*Comm(d,c), - a^-1*Comm(a,d) + b^-1*Comm(b,a), + c^-1*Comm(c,b), + d^-1*Comm(d,c), + a^-1*Comm(a,d) ]; relations = [relations; [inv(rel) for rel in relations]] - Groups.add_rels!(HigmanGr, Dict(rel => HigmanGr() for rel in relations)) - - return HigmanGr, gens(HigmanGr) + Groups.add_rels!(higman_group, Dict(rel => HigmanGr() for rel in relations)) + return higman_group end - -function generatingset(parsed_args) - return generatingset() -end - -############################################################################### -# -# Misc -# -############################################################################### - -function groupname(parsed_args) - return groupname(), 0 -end - -groupname() = "HigmanGroup" - -end # of module CapraceGroup diff --git a/groups/mappingclassgroup.jl b/groups/mappingclassgroup.jl index ea44aff..500dceb 100644 --- a/groups/mappingclassgroup.jl +++ b/groups/mappingclassgroup.jl @@ -1,17 +1,14 @@ -module MappingClassGroups +struct MappingClassGroup <: GAPGroup + args::Dict{String,Any} +end -using AbstractAlgebra -using Groups +function name(G::MappingClassGroup) + N = G.args["N"] + return "MCG($(N))" +end -############################################################################### -# -# Generating set -# -############################################################################### - -Comm(x,y) = x*y*x^-1*y^-1 - -function generatingset(N::Int) +function group(G::MappingClassGroup) + N = G.args["N"] if N < 2 throw("Genus must be at least 2!") elseif N == 2 @@ -33,77 +30,57 @@ function generatingset(N::Int) Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations)) return MCGroup - end + else + MCGroup = Groups.FPGroup(["a$i" for i in 0:2N]) + S = gens(MCGroup) - MCGroup = Groups.FPGroup(["a$i" for i in 0:2N]) - S = gens(MCGroup) + a0 = S[1] + A = S[2:end] + k = length(A) - a0 = S[1] - A = S[2:end] - k = length(A) + relations = [ + [Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]..., + [Comm(a0, A[i]) for i in 1:k if i != 4]..., + [A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]..., + A[4]*a0*A[4]*inv(a0*A[4]*a0) + ] - relations = [ - [Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]..., - [Comm(a0, A[i]) for i in 1:k if i != 4]..., - [A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]..., - A[4]*a0*A[4]*inv(a0*A[4]*a0) - ] + # 3-chain relation + c = prod(reverse(A[1:4]))*prod(A[1:4]) + b0 = c*a0*inv(c) + push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0)) - # 3-chain relation - c = prod(reverse(A[1:4]))*prod(A[1:4]) - b0 = c*a0*inv(c) - push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0)) + # Lantern relation + b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4]) + b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2]) + u = inv(A[6]*A[5])*b1*(A[6]*A[5]) + x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4])) + b3 = x*a0*inv(x) + push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3)) - # Lantern relation - b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4]) - b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2]) - u = inv(A[6]*A[5])*b1*(A[6]*A[5]) - x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4])) - b3 = x*a0*inv(x) - push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3)) + # Hyperelliptic relation + X = prod(reverse(A))*prod(A) - # Hyperelliptic relation - X = prod(reverse(A))*prod(A) - - function n(i::Int, b=b0) - if i == 1 - return A[1] - elseif i == 2 - return b - else - return w(i-2)*n(i-2)*w(i-2) + function n(i::Int, b=b0) + if i == 1 + return A[1] + elseif i == 2 + return b + else + return w(i-2)*n(i-2)*w(i-2) + end end + + function w(i::Int) + (A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])* + (A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] ) + end + + # push!(relations, X*n(N)*inv(n(N)*X)) + + relations = [relations; [inv(rel) for rel in relations]] + Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations)) + + return MCGroup end - - function w(i::Int) - (A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])* - (A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] ) - end - - # push!(relations, X*n(N)*inv(n(N)*X)) - - relations = [relations; [inv(rel) for rel in relations]] - Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations)) - - return MCGroup, gens(MCGroup) end - -function generatingset(parsed_args) - N = parsed_args["N"] - return generatingset(N) -end - -############################################################################### -# -# Misc -# -############################################################################### - -function groupname(parsed_args) - N = parsed_args["N"] - return groupname(N), N -end - -groupname(N::Int) = "MCG$(N)" - -end #of module MappingClassGroups