Fix reflection for negative roots

experimental/LieAlgebras/src/LieAlgebras.jl

@@ -80,6 +80,7 @@ import ..Oscar:
   parent_type,
   permutation_group,
   rank,
+  reflection,
   root,
   roots,
   sub,

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

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