initial adjust of GAPGroups files
This commit is contained in:
parent
02825a8ec0
commit
7f4824492c
@ -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
|
||||
|
||||
@ -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
|
||||
|
||||
@ -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
|
||||
|
||||
Loading…
Reference in New Issue
Block a user