Add tools to compute in mapping class groups

This commit is contained in:
kalmarek 2018-03-22 11:09:03 +01:00
parent e0d3cb607b
commit ed12d87b7a
2 changed files with 119 additions and 109 deletions

119
MCG.jl
View File

@ -27,7 +27,7 @@ function parse_commandline()
"--radius" "--radius"
help = "Radius of ball B_r(e,S) to find solution over" help = "Radius of ball B_r(e,S) to find solution over"
arg_type = Int arg_type = Int
default = 4 default = 2
"--warmstart" "--warmstart"
help = "Use warmstart.jl as the initial guess for SCS" help = "Use warmstart.jl as the initial guess for SCS"
action = :store_true action = :store_true
@ -38,113 +38,15 @@ end
const PARSEDARGS = parse_commandline() const PARSEDARGS = parse_commandline()
include("CPUselect.jl") include("CPUselect.jl")
# set_parallel_mthread(PARSEDARGS, workers=true) set_parallel_mthread(PARSEDARGS, workers=false)
include("FPGroups_GAP.jl")
module MCGrps
using Groups
using Nemo using Nemo
Comm(x,y) = x*y*x^-1*y^-1
function Group(N::Int)
if N == 2
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
S = Nemo.gens(MCGroup)
N = length(S)
A = prod(reverse(S))*prod(S)
relations = [
[Comm(S[i], S[j]) for i in 1:N for j in 1:N if abs(i-j) > 1]...,
[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:N-1]...,
(S[1]*S[2]*S[3])^4*inv(S[5])^2,
Comm(A, S[1]),
A^2
]
relations = [relations; [inv(rel) for rel in relations]]
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
return MCGroup
elseif N < 2
throw("Genus must be at least 2!")
end
MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
S = Nemo.gens(MCGroup)
a0 = S[1]
A = S[2:end]
k = length(A)
relations = [
[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
[Comm(a0, A[i]) for i in 1:k if i != 4]...,
[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
A[4]*a0*A[4]*inv(a0*A[4]*a0)
]
# 3-chain relation
c = prod(reverse(A[1:4]))*prod(A[1:4])
b0 = c*a0*inv(c)
push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
# Lantern relation
b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
u = inv(A[6]*A[5])*b1*(A[6]*A[5])
x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
b3 = x*a0*inv(x)
push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
# Hyperelliptic relation
X = prod(reverse(A))*prod(A)
function n(i::Int, b=b0)
if i == 1
return A[1]
elseif i == 2
return b
else
return w(i-2)*n(i-2)*w(i-2)
end
end
function w(i::Int)
(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
end
push!(relations, X*n(N)*inv(n(N)*X))
relations = [relations; [inv(rel) for rel in relations]]
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
@show MCGroup
return MCGroup
end
###############################################################################
#
# Misc
#
###############################################################################
function groupname(parsed_args)
N = parsed_args["N"]
return groupname(N), N
end
groupname(N::Int) = "MCG$(N)"
end #of module MCGrps
using SCS.SCSSolver using SCS.SCSSolver
using PropertyT using PropertyT
using Groups
include("FPGroups_GAP.jl")
include("groups/mappingclassgroup.jl")
function main(GROUP, parsed_args) function main(GROUP, parsed_args)
@ -157,12 +59,11 @@ function main(GROUP, parsed_args)
name, N = GROUP.groupname(parsed_args) name, N = GROUP.groupname(parsed_args)
isdir(name) || mkdir(name) isdir(name) || mkdir(name)
G = GROUP.Group(N) G, S = GROUP.generatingset(N)
S = Nemo.gens(G)
relations = [k*inv(v) for (k,v) in G.rels] relations = [k*inv(v) for (k,v) in G.rels]
prepare_pm_delta(name, GAP_groupcode(S, relations), radius) prepare_pm_delta(name, GAP_groupcode(S, relations), radius)
S = unique([S; [inv(s) for s in S]]) S = unique([S; inv.(S)])
Id = G() Id = G()
@ -178,10 +79,10 @@ function main(GROUP, parsed_args)
info(logger, "Threads: $(Threads.nthreads())") info(logger, "Threads: $(Threads.nthreads())")
info(logger, "Workers: $(workers())") info(logger, "Workers: $(workers())")
solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.9, acceleration_lookback=1) solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm) PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, radius, warm)
return 0 return 0
end end
main(MCGrps, PARSEDARGS) main(MappingClassGroups, PARSEDARGS)

109
groups/mappingclassgroup.jl Normal file
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@ -0,0 +1,109 @@
module MappingClassGroups
using Nemo
using Groups
###############################################################################
#
# Generating set
#
###############################################################################
Comm(x,y) = x*y*x^-1*y^-1
function generatingset(N::Int)
if N == 2
MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
S = Nemo.gens(MCGroup)
N = length(S)
A = prod(reverse(S))*prod(S)
relations = [
[Comm(S[i], S[j]) for i in 1:N for j in 1:N if abs(i-j) > 1]...,
[S[i]*S[i+1]*S[i]*inv(S[i+1]*S[i]*S[i+1]) for i in 1:N-1]...,
(S[1]*S[2]*S[3])^4*inv(S[5])^2,
Comm(A, S[1]),
A^2
]
relations = [relations; [inv(rel) for rel in relations]]
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
return MCGroup
elseif N < 2
throw("Genus must be at least 2!")
end
MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
S = Nemo.gens(MCGroup)
a0 = S[1]
A = S[2:end]
k = length(A)
relations = [
[Comm(A[i], A[j]) for i in 1:k for j in 1:k if abs(i-j) > 1]...,
[Comm(a0, A[i]) for i in 1:k if i != 4]...,
[A[i]*A[(i+1)]*A[i]*inv(A[i+1]*A[i]*A[i+1]) for i in 1:k-1]...,
A[4]*a0*A[4]*inv(a0*A[4]*a0)
]
# 3-chain relation
c = prod(reverse(A[1:4]))*prod(A[1:4])
b0 = c*a0*inv(c)
push!(relations, (A[1]*A[2]*A[3])^4*inv(a0*b0))
# Lantern relation
b1 = inv(A[4]*A[5]*A[3]*A[4])*a0*(A[4]*A[5]*A[3]*A[4])
b2 = inv(A[2]*A[3]*A[1]*A[2])*b1*(A[2]*A[3]*A[1]*A[2])
u = inv(A[6]*A[5])*b1*(A[6]*A[5])
x = prod(reverse(A[2:6]))*u*prod(inv.(A[1:4]))
b3 = x*a0*inv(x)
push!(relations, a0*b2*b1*inv(A[1]*A[3]*A[5]*b3))
# Hyperelliptic relation
X = prod(reverse(A))*prod(A)
function n(i::Int, b=b0)
if i == 1
return A[1]
elseif i == 2
return b
else
return w(i-2)*n(i-2)*w(i-2)
end
end
function w(i::Int)
(A[2i+4]*A[2i+3]*A[2i+2]* n(i+1))*(A[2i+1]*A[2i] *A[2i+2]*A[2i+1])*
(A[2i+3]*A[2i+2]*A[2i+4]*A[2i+3])*( n(i+1)*A[2i+2]*A[2i+1]*A[2i] )
end
push!(relations, X*n(N)*inv(n(N)*X))
relations = [relations; [inv(rel) for rel in relations]]
Groups.add_rels!(MCGroup, Dict(rel => MCGroup() for rel in relations))
return MCGroup, gens(MCGroup)
end
function generatingset(parsed_args)
N = parsed_args["N"]
return generatingset(N)
end
###############################################################################
#
# Misc
#
###############################################################################
function groupname(parsed_args)
N = parsed_args["N"]
return groupname(N), N
end
groupname(N::Int) = "MCG$(N)"
end #of module MappingClassGroups