generalize MCG to all FP GAP groups

MCGn.jl

@@ -20,10 +20,6 @@ function parse_commandline()
         help = "Set number of cpus used by solver (default: auto)"
         arg_type = Int
         required = false
-    "-N"
-        help = "Consider mapping class group of surface of genus N"
-        arg_type = Int
-        default = 2
     "--radius"
         help = "Radius of ball B_r(e,S) to find solution over"
         arg_type = Int
@@ -31,58 +27,43 @@ function parse_commandline()
     "--warmstart"
         help = "Use warmstart.jl as the initial guess for SCS"
         action = :store_true
+    "-MCG"
+        help = "Compute for mapping class group of surface of genus N"
+        arg_type = Int
+        required = false
+    "--Higman"
+        help = "Compute for Higman Group"
+        action = :store_true
+    "--Caprace"
+        help = "Compute for Higman Group"
+        action = :store_true
     end
 
     return parse_args(args)
 end
 const PARSEDARGS = parse_commandline()
 
-include("CPUselect.jl")
-set_parallel_mthread(PARSEDARGS, workers=false)
-
-using Nemo
-using SCS.SCSSolver
+using AbstractAlgebra
 using PropertyT
 using Groups
 
-include("FPGroups_GAP.jl")
+include("CPUselect.jl")
+set_parallel_mthread(PARSEDARGS, workers=false)
+
+include("main_gapgroup.jl")
+
+if PARSEDARGS["Caprace"]
+    include("groups/caprace.jl")
+    main(CapraceGroup, PARSEDARGS)
+
+elseif PARSEDARGS["Higman"]
+    include("groups/higman.jl")
+    main(HigmanGroup, PARSEDARGS)
+
+elseif PARSEDARGS["N"] != nothing
     include("groups/mappingclassgroup.jl")
-
-function main(GROUP, parsed_args)
-
-    radius = parsed_args["radius"]
-    tol = parsed_args["tol"]
-    iterations = parsed_args["iterations"]
-    upper_bound = parsed_args["upper-bound"]
-    warm = parsed_args["warmstart"]
-
-    name, N = GROUP.groupname(parsed_args)
-    isdir(name) || mkdir(name)
-
-    G, S = GROUP.generatingset(N)
-    relations = [k*inv(v) for (k,v) in G.rels]
-    prepare_pm_delta(name, GAP_groupcode(S, relations), radius)
-
-    S = unique([S; inv.(S)])
-
-    Id = G()
-
-    logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"))
-
-    info(logger, "Group:       $name")
-    info(logger, "Iterations:  $iterations")
-    info(logger, "Precision:   $tol")
-    info(logger, "Upper bound: $upper_bound")
-    info(logger, "Radius:      $radius")
-    info(logger, G)
-    info(logger, "Symmetric generating set of size $(length(S))")
-    info(logger, "Threads:     $(Threads.nthreads())")
-    info(logger, "Workers:     $(workers())")
-
-    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)
-    return 0
-end
-
     main(MappingClassGroups, PARSEDARGS)
+
+else
+    warn("You need to specify one of the --Higman, --Caprace, -MCG N")
+end

groups/caprace.jl

@@ -0,0 +1,62 @@
+module CapraceGroup
+
+using AbstractAlgebra
+using Groups
+
+###############################################################################
+#
+#  Generating set
+#
+###############################################################################
+
+Comm(x,y) = x*y*x^-1*y^-1
+
+function generatingset()
+
+   CapraceGroup = Groups.FPGroup(["x","y","z","t","r"]);
+   x,y,z,t,r = gens(CapraceGroup)
+
+   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!(CapraceGroup, Dict(rel => CapraceGroup() for rel in relations))
+
+   return CapraceGroup, gens(CapraceGroup)
+end
+
+function generatingset(parsed_args)
+   return generatingset()
+end
+
+###############################################################################
+#
+#  Misc
+#
+###############################################################################
+
+function groupname(parsed_args)
+    return groupname(), 0
+end
+
+groupname() = "CapraceGroup"
+
+end # of module CapraceGroup

groups/higman.jl

@@ -0,0 +1,49 @@
+module HigmanGroup
+
+using AbstractAlgebra
+using Groups
+
+###############################################################################
+#
+#  Generating set
+#
+###############################################################################
+
+Comm(x,y) = x*y*x^-1*y^-1
+
+function generatingset()
+
+   HigmanGr = Groups.FPGroup(["a","b","c","d"]);
+   a,b,c,d = gens(HigmanGr)
+
+   relations = [
+      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)
+end
+
+function generatingset(parsed_args)
+   return generatingset()
+end
+
+###############################################################################
+#
+#  Misc
+#
+###############################################################################
+
+function groupname(parsed_args)
+    return groupname(), 0
+end
+
+groupname() = "HigmanGroup"
+
+end # of module CapraceGroup

groups/mappingclassgroup.jl

@@ -12,9 +12,11 @@ using Groups
 Comm(x,y) = x*y*x^-1*y^-1
 
 function generatingset(N::Int)
-    if N == 2
+    if N < 2
+        throw("Genus must be at least 2!")
+    elseif N == 2
         MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
-        S = Nemo.gens(MCGroup)
+        S = gens(MCGroup)
 
         N = length(S)
         A = prod(reverse(S))*prod(S)
@@ -31,12 +33,10 @@ function generatingset(N::Int)
        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)
+    S = gens(MCGroup)
 
     a0 = S[1]
     A = S[2:end]

main_gapgroup.jl

@@ -0,0 +1,40 @@
+using SCS.SCSSolver
+# using Mosek
+# using CSDP
+# using SDPA
+
+include("FPGroups_GAP.jl")
+
+function main(GROUP, parsed_args)
+
+    radius = parsed_args["radius"]
+    tol = parsed_args["tol"]
+    iterations = parsed_args["iterations"]
+    upper_bound = parsed_args["upper-bound"]
+    warm = parsed_args["warmstart"]
+
+    name, N = GROUP.groupname(parsed_args)
+    G, S = GROUP.generatingset(N)
+
+    isdir(name) || mkdir(name)
+    logger = PropertyT.setup_logging(joinpath(name, "$(upper_bound)"), :fulllog)
+
+    relations = [k*inv(v) for (k,v) in G.rels]
+    prepare_pm_delta(name, GAP_groupcode(S, relations), radius)
+
+    S = unique([S; inv.(S)])
+
+    info(logger, "Group:       $name")
+    info(logger, "Iterations:  $iterations")
+    info(logger, "Precision:   $tol")
+    info(logger, "Upper bound: $upper_bound")
+    info(logger, "Radius:      $radius")
+    info(logger, "Threads:     $(Threads.nthreads())")
+    info(logger, "Workers:     $(workers())")
+    info(logger, G)
+    info(logger, "Symmetric generating set of size $(length(S))")
+
+    solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct, alpha=1.95, acceleration_lookback=1)
+
+    return PropertyT.check_property_T(name, S, G(), solver, upper_bound, tol, radius, warm)
+end