From abb8fd98056e38970928371e3d81e8755738efba Mon Sep 17 00:00:00 2001
From: Tommy Hofmann <thofma@gmail.com>
Date: Thu, 21 Sep 2023 05:41:36 +0200
Subject: [PATCH] Fix automorphism group of non-simple field

---
 src/Map/automorphisms.jl     |  4 ++--
 test/NumField/NfAbs/NfAbs.jl | 10 ++++++++++
 2 files changed, 12 insertions(+), 2 deletions(-)

diff --git a/src/Map/automorphisms.jl b/src/Map/automorphisms.jl
index 07bd180f77..d8d550fba7 100644
--- a/src/Map/automorphisms.jl
+++ b/src/Map/automorphisms.jl
@@ -10,7 +10,7 @@ export absolute_automorphism_list, absolute_automorphism_group
 
 
 function _automorphisms(K::NfAbsNS; is_abelian::Bool = false)
-  pols = QQPolyRingElem[is_univariate(x)[2] for x in K.pol]
+  pols = QQPolyRingElem[to_univariate(Globals.Qx, x) for x in K.pol]
   rt = Vector{Vector{NfAbsNSElem}}(undef, length(pols))
   for i = 1:length(pols)
     rt[i] = roots(K, pols[i])
@@ -19,7 +19,7 @@ function _automorphisms(K::NfAbsNS; is_abelian::Bool = false)
   ind = 1
   I = cartesian_product_iterator([1:length(x) for x in rt], inplace = true)
   for i in I
-    auts[ind] = hom(K, K, elem_type(K)[rt[i[j]] for j = 1:length(pols)])
+    auts[ind] = hom(K, K, elem_type(K)[rt[j][i[j]] for j = 1:length(pols)])
     ind += 1
   end
   return auts
diff --git a/test/NumField/NfAbs/NfAbs.jl b/test/NumField/NfAbs/NfAbs.jl
index d4cc4a8af3..7d6248e073 100644
--- a/test/NumField/NfAbs/NfAbs.jl
+++ b/test/NumField/NfAbs/NfAbs.jl
@@ -66,3 +66,13 @@ end
  K, a = number_field(f)
  @test length(factor(K, f).fac) == 4
 end
+
+@testset "automorphisms" begin
+  Qx, x = QQ["x"]
+  K, a = number_field([x^2 - 2, x^2 - 3], "a", cached = false)
+  @test is_normal(K)
+  @test length(automorphism_list(K)) == 4
+  K, a = number_field([x^2 - 2, x^3 - 2], "a", cached = false)
+  @test !is_normal(K)
+  @test length(automorphism_list(K)) == 2
+end