parametrize PropertyTGroups types by N

groups/autfreegroup.jl

@@ -1,21 +1,12 @@
-struct SpecialAutomorphismGroup <: SymmetrizedGroup
-    args::Dict{String,Any}
+struct SpecialAutomorphismGroup{N} <: SymmetrizedGroup
     group::AutGroup
-    N::Int
 
     function SpecialAutomorphismGroup(args::Dict)
-        N = args["SAut"]
-        return new(args, AutGroup(FreeGroup(N), special=true), N)
+        return new{args["SAut"]}(AutGroup(FreeGroup(N), special=true))
     end
 end
 
-function name(G::SpecialAutomorphismGroup)
-    if haskey(G.args, "nosymmetry") && G.args["nosymmetry"]
-        return "SAutF$(G.N)"
-    else
-        return "oSAutF$(G.N)"
-    end
-end
+name(G::SpecialAutomorphismGroup{N}) where N = "SAutF$(N)"
 
 group(G::SpecialAutomorphismGroup) = G.group
 
@@ -24,8 +15,8 @@ function generatingset(G::SpecialAutomorphismGroup)
     return unique([S; inv.(S)])
 end
 
-function autS(G::SpecialAutomorphismGroup)
-    return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
+function autS(G::SpecialAutomorphismGroup{N}) where N
+    return WreathProduct(PermutationGroup(2), PermutationGroup(N))
 end
 
 ###############################################################################

groups/mappingclassgroup.jl

@@ -1,17 +1,14 @@
-struct MappingClassGroup <: GAPGroup
-    args::Dict{String,Any}
-    N::Int
+struct MappingClassGroup{N} <: GAPGroup end
 
-    MappingClassGroup(args) = new(args, args["MCG"])
-end
+MappingClassGroup(args::Dict) = MappingClassGroup{args["MCG"]}()
 
-name(G::MappingClassGroup) = "MCG($(G.N))"
+name(G::MappingClassGroup{N}) where N = "MCG(N)"
 
-function group(G::MappingClassGroup)
+function group(G::MappingClassGroup{N}) where N
 
-    if G.N < 2
+    if N < 2
         throw("Genus must be at least 2!")
-    elseif G.N == 2
+    elseif N == 2
         MCGroup = Groups.FPGroup(["a1","a2","a3","a4","a5"]);
         S = gens(MCGroup)
 
@@ -31,7 +28,7 @@ function group(G::MappingClassGroup)
        return MCGroup
 
     else
-        MCGroup = Groups.FPGroup(["a$i" for i in 0:2G.N])
+        MCGroup = Groups.FPGroup(["a$i" for i in 0:2N])
         S = gens(MCGroup)
 
         a0 = S[1]
@@ -76,7 +73,7 @@ function group(G::MappingClassGroup)
            (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(G.N)*inv(n(G.N)*X))
+        # 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))

groups/speciallinear.jl

@@ -1,60 +1,44 @@
-struct SpecialLinearGroup <: SymmetrizedGroup
-    args::Dict{String,Any}
+struct SpecialLinearGroup{N} <: SymmetrizedGroup
     group::AbstractAlgebra.Group
-    N::Int
+    p::Int
+    X::Bool
 
     function SpecialLinearGroup(args::Dict)
-        n = args["SL"]
+        N = args["SL"]
         p = args["p"]
         X = args["X"]
 
         if p == 0
-            G = MatrixSpace(Nemo.ZZ, n, n)
+            G = MatrixSpace(Nemo.ZZ, N, N)
         else
             R = Nemo.NmodRing(UInt(p))
-            G = MatrixSpace(R, n, n)
+            G = MatrixSpace(R, N, N)
         end
-        return new(args, G, n)
+        return new{N}(G, p, X)
     end
 end
 
-function name(G::SpecialLinearGroup)
-    p = G.args["p"]
-    X = G.args["X"]
-
-    if p == 0
-       R = (X ? "Z[x]" : "Z")
+function name(G::SpecialLinearGroup{N}) where N
+    if G.p == 0
+       R = (G.X ? "Z[x]" : "Z")
     else
-       R = "F$p"
-    end
-    if haskey(G.args, "nosymmetry") && G.args["nosymmetry"]
-        return "SL($(G.N),$R)"
-    else
-        return "oSL($(G.N),$R)"
+       R = "F$(G.p)"
     end
+    return SL($(G.N),$R)
 end
 
 group(G::SpecialLinearGroup) = G.group
 
-function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
-    @assert i≠j
-    m = one(M)
-    m[i,j] = val
-    return m
-end
-
-function generatingset(G::SpecialLinearGroup)
-    p = G.args["p"]
-    X = G.args["X"]
-    p > 0 && X && throw("SL(n, F_p[x]) not implemented")
+function generatingset(G::SpecialLinearGroup{N}) where N
+    G.p > 0 && G.X && throw("SL(n, F_p[x]) not implemented")
     SL = group(G)
-    r = G.args["radius"]
-    return generatingset(SL, r, X)
+    return generatingset(SL, G.X)
 end
 
+# r is the injectivity radius of
+# SL(n, Z[X]) -> SL(n, Z) induced by X -> 100
 
-function generatingset(SL::MatSpace, radius::Integer, X::Bool=false)
-
+function generatingset(SL::MatSpace, X::Bool=false, r=5)
     n = SL.cols
     indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
 
@@ -66,8 +50,15 @@ function generatingset(SL::MatSpace, radius::Integer, X::Bool=false)
     return unique([S; inv.(S)])
 end
 
-function autS(G::SpecialLinearGroup)
-    return WreathProduct(PermutationGroup(2), PermutationGroup(G.N))
+function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
+    @assert i≠j
+    m = one(M)
+    m[i,j] = val
+    return m
+end
+
+function autS(G::SpecialLinearGroup{N}) where N
+    return WreathProduct(PermutationGroup(2), PermutationGroup(N))
 end
 
 ###############################################################################