From eef13c9afa124da568f845c57f07212dbbe49881 Mon Sep 17 00:00:00 2001
From: Marek Kaluba <kalmar@amu.edu.pl>
Date: Wed, 7 Jul 2021 10:36:40 +0200
Subject: [PATCH] Since SMC act from the left(!) distinguish
 Aut(Left|Right)Perm

---
 src/groups/symplectic_twists.jl | 51 +++++++++++++++++++++++++++++++++
 src/groups/transvections.jl     | 14 ++++-----
 2 files changed, 58 insertions(+), 7 deletions(-)

diff --git a/src/groups/symplectic_twists.jl b/src/groups/symplectic_twists.jl
index 00e37af..74cd8ba 100644
--- a/src/groups/symplectic_twists.jl
+++ b/src/groups/symplectic_twists.jl
@@ -217,3 +217,54 @@ function evaluate!(
 
     return t
 end
+
+struct PermLeftAut <: GSymbol
+    perm::Vector{UInt8}
+
+    function PermLeftAut(p::AbstractVector{<:Integer})
+        @assert sort(p) == 1:length(p)
+        return new(p)
+    end
+end
+
+function Base.show(io::IO, p::PermLeftAut)
+    print(io, "σˡ")
+    join(io, (subscriptify(Int(i)) for i in p.perm))
+end
+
+Base.inv(p::PermLeftAut) = PermLeftAut(invperm(p.perm))
+
+Base.:(==)(p::PermLeftAut, q::PermLeftAut) = p.perm == q.perm
+Base.hash(p::PermLeftAut, h::UInt) = hash(p.perm, hash(PermLeftAut, h))
+
+function evaluate!(v::NTuple{T, N}, p::PermLeftAut, ::Alphabet, tmp=one(first(v))) where {T, N}
+
+    G = parent(first(v))
+    A = alphabet(G)
+    img = gens(G)[p.perm]
+    gens_idcs = Dict(A[A[first(word(im))]] => img[i] for (i,im) in enumerate(gens(G)))
+
+    for elt in v
+        copyto!(tmp, elt)
+        resize!(word(elt), 0)
+        for idx in word(tmp)
+            # @show idx
+            if haskey(gens_idcs, idx)
+                k = gens_idcs[idx]
+                append!(word(elt), word(k))
+            elseif haskey(gens_idcs, inv(A, idx))
+                k = inv(gens_idcs[inv(A, idx)])
+                append!(word(elt), word(k))
+            else
+                push!(word(elt), idx)
+            end
+        end
+        _setnormalform!(elt, false)
+        _setvalidhash!(elt, false)
+
+        normalform!(tmp, elt)
+        copyto!(elt, tmp)
+    end
+
+    return v
+end
diff --git a/src/groups/transvections.jl b/src/groups/transvections.jl
index e01d4fc..1b9a358 100644
--- a/src/groups/transvections.jl
+++ b/src/groups/transvections.jl
@@ -82,25 +82,25 @@ Base.@propagate_inbounds function evaluate!(v::NTuple{T, N}, t::Transvection, A:
     return v
 end
 
-struct PermAut <: GSymbol
+struct PermRightAut <: GSymbol
     perm::Vector{UInt8}
 
-    function PermAut(p::AbstractVector{<:Integer})
+    function PermRightAut(p::AbstractVector{<:Integer})
         @assert sort(p) == 1:length(p)
         return new(p)
     end
 end
 
-function Base.show(io::IO, p::PermAut)
+function Base.show(io::IO, p::PermRightAut)
     print(io, 'σ')
     join(io, (subscriptify(Int(i)) for i in p.perm))
 end
 
-Base.inv(p::PermAut) = PermAut(invperm(p.perm))
+Base.inv(p::PermRightAut) = PermRightAut(invperm(p.perm))
 
-Base.:(==)(p::PermAut, q::PermAut) = p.perm == q.perm
-Base.hash(p::PermAut, h::UInt) = hash(p.perm, hash(PermAut, h))
+Base.:(==)(p::PermRightAut, q::PermRightAut) = p.perm == q.perm
+Base.hash(p::PermRightAut, h::UInt) = hash(p.perm, hash(PermRightAut, h))
 
-Base.@propagate_inbounds function evaluate!(v::NTuple{T, N}, p::PermAut, ::Alphabet, tmp=one(first(v))) where {T, N}
+function evaluate!(v::NTuple{T, N}, p::PermRightAut, ::Alphabet, tmp=one(first(v))) where {T, N}
     return v[p.perm]
 end