From 605b26050540a6c90178d1e5c3b89e5b24291b4e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Felix=20R=C3=B6hrich?= <roehrich@art.rwth-aachen.de>
Date: Sat, 7 Dec 2024 14:20:23 +0100
Subject: [PATCH] revert orientation of G2

---
 experimental/LieAlgebras/src/CartanMatrix.jl  | 8 ++++----
 experimental/LieAlgebras/src/DynkinDiagram.jl | 2 +-
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/experimental/LieAlgebras/src/CartanMatrix.jl b/experimental/LieAlgebras/src/CartanMatrix.jl
index 46f26c2594cf..f53afac4924b 100644
--- a/experimental/LieAlgebras/src/CartanMatrix.jl
+++ b/experimental/LieAlgebras/src/CartanMatrix.jl
@@ -72,7 +72,7 @@ function cartan_matrix(fam::Symbol, rk::Int)
   elseif fam == :F
     mat = matrix(ZZ, [2 -1 0 0; -1 2 -1 0; 0 -2 2 -1; 0 0 -1 2])
   elseif fam == :G
-    mat = matrix(ZZ, [2 -1; -3 2])
+    mat = matrix(ZZ, [2 -3; -1 2])
   else
     error("Unreachable")
   end
@@ -204,7 +204,7 @@ function cartan_symmetrizer(gcm::ZZMatrix; check::Bool=true)
       d[i] = d[i + 1] = 2
       i += rk
     elseif fam == :G
-      d[i] = 3
+      d[i + 1] = 3
       i += rk
     else
       error("unreachable")
@@ -337,10 +337,10 @@ function cartan_type_with_ordering(gcm::ZZMatrix; check::Bool=true)
         push!(ord, v0, v1)
       elseif gcm[v0, v1] == -3
         push!(type, (:G, 2))
-        push!(ord, v1, v0)
+        push!(ord, v0, v1)
       elseif gcm[v1, v0] == -3
         push!(type, (:G, 2))
-        push!(ord, v0, v1)
+        push!(ord, v1, v0)
       else
         error("unreachable")
       end
diff --git a/experimental/LieAlgebras/src/DynkinDiagram.jl b/experimental/LieAlgebras/src/DynkinDiagram.jl
index 81e033d97777..5aea2acc34be 100644
--- a/experimental/LieAlgebras/src/DynkinDiagram.jl
+++ b/experimental/LieAlgebras/src/DynkinDiagram.jl
@@ -100,7 +100,7 @@ function show_dynkin_diagram(fam::Symbol, rk::Int, labels::AbstractVector{Int})
     D = "$(labels[1]) - $(labels[2]) >=> $(labels[3]) - $(labels[4])"
   elseif fam == :G
     @assert rk == 2
-    D = "$(labels[1]) >>> $(labels[2])"
+    D = "$(labels[1]) <<< $(labels[2])"
   end
   isempty(D) && error("Unreachable")
   print(D)