From 77c788c62d66d031caa07a0f448a8a5be5a886ec Mon Sep 17 00:00:00 2001
From: Janika Peters <janika.peters@rwth-aachen.de>
Date: Thu, 19 Dec 2024 14:35:16 +0100
Subject: [PATCH] Fix reflection for negative roots

---
 experimental/LieAlgebras/src/LieAlgebras.jl      | 1 +
 experimental/LieAlgebras/src/RootSystem.jl       | 3 ++-
 experimental/LieAlgebras/test/RootSystem-test.jl | 4 ++--
 3 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl
index 020861f40d7..68550375088 100644
--- a/experimental/LieAlgebras/src/LieAlgebras.jl
+++ b/experimental/LieAlgebras/src/LieAlgebras.jl
@@ -80,6 +80,7 @@ import ..Oscar:
   parent_type,
   permutation_group,
   rank,
+  reflection,
   root,
   roots,
   sub,
diff --git a/experimental/LieAlgebras/src/RootSystem.jl b/experimental/LieAlgebras/src/RootSystem.jl
index 784dddbd9b2..908413a5fc2 100644
--- a/experimental/LieAlgebras/src/RootSystem.jl
+++ b/experimental/LieAlgebras/src/RootSystem.jl
@@ -1113,8 +1113,9 @@ function reflection(beta::RootSpaceElem)
 
   b, index_of_beta = is_positive_root_with_index(beta)
   if !b
-    index_of_beta = is_root_with_index(beta) - rk
+    b, index_of_beta = is_negative_root_with_index(beta)
   end
+  @req b "Not a root"
 
   found_simple_root = index_of_beta <= rk
   current_index = index_of_beta
diff --git a/experimental/LieAlgebras/test/RootSystem-test.jl b/experimental/LieAlgebras/test/RootSystem-test.jl
index 48c98252f99..e469a6d1c4e 100644
--- a/experimental/LieAlgebras/test/RootSystem-test.jl
+++ b/experimental/LieAlgebras/test/RootSystem-test.jl
@@ -380,11 +380,11 @@
       @test r * reflection(r) == -r
     end
 
-    R = root_system([(:A, 1), (:A, 1)])
+    R = root_system([(:B, 2), (:A, 2)])
     for r in roots(R)
       @test r * reflection(r) == -r
       for r2 in roots(R)
-        if r != r2 && r != -r2
+        if is_zero(dot(r, r2)) #roots are orthogonal
           @test r2 * reflection(r) == r2
         end
       end