Make AutSymbol and AutWord callable via fmap and imap

src/automorphism_groups.jl

@@ -7,19 +7,31 @@ immutable AutSymbol <: GSymbol
     gen::String
     pow::Int
     ex::Expr
+    fmap::Function
+    imap::Function
+end
+
+function (f::AutSymbol){T}(v::Vector{GWord{T}})
+    if f.pow > 0
+        map = f.fmap
+    else
+        map = f.imap
+    end
+    for i in 1:abs(f.pow)
+         v::Vector{GWord{T}} = map(v)
+    end
+    return v
 end
 
 (==)(s::AutSymbol, t::AutSymbol) = s.gen == t.gen && s.pow == t.pow
 hash(s::AutSymbol, h::UInt) = hash(s.gen, hash(s.pow, hash(:AutSymbol, h)))
 
-IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(IdAutomorphism(N)))
+IdSymbol(::Type{AutSymbol}) = AutSymbol("(id)", 0, :(Id(N)), v -> Vector{GWord}(v), v -> Vector{GWord}(v))
 
 function change_pow(s::AutSymbol, n::Int)
-
     if n == 0
         return one(s)
     end
-
     symbol = s.ex.args[1]
     if symbol == :ɛ
         return flip_AutSymbol(s.ex.args[2], pow=n)
@@ -29,29 +41,58 @@ function change_pow(s::AutSymbol, n::Int)
         return rmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
     elseif symbol == :λ
         return lmul_AutSymbol(s.ex.args[2], s.ex.args[3], pow=n)
-    elseif symbol == :IdAutomorphism
+    elseif symbol == :Id
         return s
     else
         warn("Changing an unknown type of symbol! $s")
-        return AutSymbol(s.gen, n, s.ex)
+        return AutSymbol(s.gen, n, s.ex, s.fmap, s.imap)
     end
 end
 
 inv(f::AutSymbol) = change_pow(f, -f.pow)
 
+function ϱ(i,j)
+    # @assert i ≠ j
+    return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]) for k in eachindex(v)]
+end
+
+function ϱ_inv(i,j)
+    # @assert i ≠ j
+    return v -> [(k!=i ? GWord(v[k]) : v[i]*v[j]^-1) for k in eachindex(v)]
+end
+
+
+function λ(i,j)
+    # @assert i ≠ j
+    return v -> ([(k!=i ? GWord(v[k]) : v[j]*v[i]) for k in eachindex(v)])
+end
+
+function λ_inv(i,j)
+    # @assert i ≠ j
+    return v -> ([(k!=i ? GWord(v[k]) : v[j]^-1*v[i]) for k in eachindex(v)])
+end
+
+
+ɛ(i) = v -> [(k!=i ? GWord(v[k]) : v[k]^-1) for k in eachindex(v)]
+
+function σ(perm)
+    # @assert sort(perm) == collect(1:length(perm))
+    return v -> [GWord(v[perm[k]]) for k in eachindex(v)]
+end
+
 function rmul_AutSymbol(i,j; pow::Int=1)
     gen = string('ϱ',Char(8320+i), Char(8320+j)...)
-    return AutSymbol(gen, pow, :(ϱ($i,$j)))
+    return AutSymbol(gen, pow, :(ϱ($i,$j)), ϱ(i,j), ϱ_inv(i,j))
 end
 
 function lmul_AutSymbol(i,j; pow::Int=1)
     gen = string('λ',Char(8320+i), Char(8320+j)...)
-    return AutSymbol(gen, pow, :(λ($i,$j)))
+    return AutSymbol(gen, pow, :(λ($i,$j)), λ(i,j), λ_inv(i,j))
 end
 
 function flip_AutSymbol(j; pow::Int=1)
     gen = string('ɛ', Char(8320 + j))
-    return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)))
+    return AutSymbol(gen, (2+ pow%2)%2, :(ɛ($j)), ɛ(j), ɛ(j))
 end
 
 function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
@@ -59,11 +100,12 @@ function symmetric_AutSymbol(perm::Vector{Int}; pow::Int=1)
     ord = order(perm)
     pow = pow % ord
     perm = perm^pow
-    if array(perm) == collect(1:length(perm))
+    p = array(perm)
+    if p == collect(1:length(p))
         return one(AutSymbol)
     else
-        gen = string('σ', [Char(8320 + i) for i in array(perm)]...)
+        gen = string('σ', [Char(8320 + i) for i in p]...)
-        return AutSymbol(gen, 1, :(σ($(array(perm)))))
+        return AutSymbol(gen, 1, :(σ($p)), σ(p), σ(array(inv(perm))))
     end
 end
 
@@ -77,6 +119,13 @@ end
 
 typealias AutWord GWord{AutSymbol}
 
+function (F::AutWord)(v)
+    for f in F.symbols
+        v = f(v)
+    end
+    return v
+end
+
 convert(::Type{AutWord}, s::AutSymbol) = GWord(s)
 
 function simplify_perms!(W::AutWord)