From 60a055cf6d9a54784a3dca18e56c090b20282e50 Mon Sep 17 00:00:00 2001
From: Tommy Hofmann <thofma@gmail.com>
Date: Tue, 14 Nov 2023 22:31:16 +0100
Subject: [PATCH] Fix preimage map of residue field (#1285)

---
 src/Map/NfOrd.jl           |  6 +++++-
 test/NfOrd/ResidueField.jl | 16 ++++++++++++++++
 2 files changed, 21 insertions(+), 1 deletion(-)

diff --git a/src/Map/NfOrd.jl b/src/Map/NfOrd.jl
index 27f5d97a3e..ca70dc8877 100644
--- a/src/Map/NfOrd.jl
+++ b/src/Map/NfOrd.jl
@@ -604,7 +604,11 @@ function NfOrdToFqFieldMor(O::NfOrd, P::NfOrdIdl)
     for i in 2:d
       add!(zz.elem_in_nf, zz.elem_in_nf, powers[i - 1] * lift(ZZ, coeff(y, i - 1)))
     end
-    zz.elem_in_nf = mod(zz.elem_in_nf, p)
+    if is_defining_polynomial_nice(nf(O)) && contains_equation_order(O)
+      zz.elem_in_nf = mod(zz.elem_in_nf, p)
+    else
+      zz = mod(zz, p)
+    end
     @assert _image(zz) == y
     return zz
   end
diff --git a/test/NfOrd/ResidueField.jl b/test/NfOrd/ResidueField.jl
index 95da76f115..08055b039c 100644
--- a/test/NfOrd/ResidueField.jl
+++ b/test/NfOrd/ResidueField.jl
@@ -50,5 +50,21 @@
       @test (mF3\(a4) - b) in P
     end
   end
+
+  # 1284
+
+  P, x = polynomial_ring(ZZ)
+  K, a = number_field(x^5 + x^3 - x^2 - x - 1)
+  M = Order(K, [1, 121*a, a^2 - 17*a, a^3 - 72*a, a^4 - 76*a])
+  P = prime_ideals_over(M, 11)
+
+  for i in 1:1000
+    for p in P
+      k, h = residue_field(M, p, false)
+      y = Hecke.primitive_element(k)
+      tmp = preimage(h, y)
+      @test h(tmp) == y
+    end
+  end
 end