Add SOut generating set

AutFN.jl

@@ -46,6 +46,19 @@ function generating_set_of_OutF(N::Int)
     return Vector{AutWord}(unique(S)), one(AutWord)
 end
 
+function generating_set_of_SOutF(N::Int)
+    indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
+    ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
+    λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
+
+    S = ϱs
+    push!(S, λs...)
+    push!(S,[inv(g) for g in S]...)
+
+    return Vector{AutWord}(unique(S)), one(AutWord)
+end
+
+
 function generating_set_of_Sym(N::Int)
     σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
 
@@ -137,7 +150,6 @@ function ΔandSDPconstraints(identity::AutWord, S::Vector{AutWord})
     end
 
     @show length(B₄_images)
-    # @assert length(B₄_images) == 3425657
 
     println("Creating product matrix...")
     @time pm = create_product_matrix(B₂, B₄_images)
@@ -217,9 +229,9 @@ function main()
     N = parsed_args["N"]
     upper_bound = parsed_args["upper-bound"]
 
-    name = "OutF$N"
+    name = "SOutF$N"
     name = name*"-$(string(upper_bound))"
-    S() = generating_set_of_OutF(N)
+    S() = generating_set_of_SOutF(N)
 
     if parsed_args["cpus"] ≠ nothing
         if parsed_args["cpus"] > cpuinfo_physicalcores()