From f6a4083ac545fe0a91830f54fb3d2146c148aec1 Mon Sep 17 00:00:00 2001
From: Tommy Hofmann <thofma@gmail.com>
Date: Sat, 4 Nov 2023 11:03:05 +0100
Subject: [PATCH] Fix bug in power_mod and is_zero(::Ideal)

(Found by M. Kirschmer)
---
 src/AlgAssAbsOrd/ICM.jl       |  2 +-
 src/HeckeTypes.jl             |  6 ++++++
 src/NumFieldOrd/NfOrd/Elem.jl |  3 +--
 test/NfOrd/Ideal.jl           | 11 +++++++++++
 4 files changed, 19 insertions(+), 3 deletions(-)

diff --git a/src/AlgAssAbsOrd/ICM.jl b/src/AlgAssAbsOrd/ICM.jl
index df070c6599..761e8e459b 100644
--- a/src/AlgAssAbsOrd/ICM.jl
+++ b/src/AlgAssAbsOrd/ICM.jl
@@ -86,7 +86,7 @@ function is_isomorphic(I::T, J::T) where { T <: Union{ NfAbsOrdIdl, NfOrdFracIdl
 end
 
 function ring_of_multipliers(I::NfOrdFracIdl)
-  return ring_of_multipliers(numerator(I, copy = false)*denominator(I, copy = false))
+  return ring_of_multipliers(numerator(I, copy = false))
 end
 
 ###############################################################################
diff --git a/src/HeckeTypes.jl b/src/HeckeTypes.jl
index 71f35d208b..51c6e51e77 100644
--- a/src/HeckeTypes.jl
+++ b/src/HeckeTypes.jl
@@ -1042,6 +1042,9 @@ const NfAbsOrdIdlSetID = Dict{NfAbsOrd, NfAbsOrdIdlSet}()
     C.princ_gen_fac_elem = FacElem(nf(O)(x))
     C.is_principal = 1
     C.princ_gen_special = (1, abs(x), ZZRingElem(0))
+    if is_zero(x)
+      C.iszero = 1
+    end
     C.gen_one = ZZRingElem(x)
     C.gen_two = O(x)
     C.norm = ZZRingElem(abs(x))^degree(O)
@@ -1059,6 +1062,9 @@ const NfAbsOrdIdlSetID = Dict{NfAbsOrd, NfAbsOrdIdlSet}()
     C.princ_gen_fac_elem = FacElem(nf(O)(x))
     C.is_principal = 1
     C.princ_gen_special = (2, Int(0), abs(x))
+    if is_zero(x)
+      C.iszero = 1
+    end
     C.gen_one = x
     C.gen_two = O(x)
     C.norm = abs(x)^degree(O)
diff --git a/src/NumFieldOrd/NfOrd/Elem.jl b/src/NumFieldOrd/NfOrd/Elem.jl
index 432141f211..8f4b386d00 100644
--- a/src/NumFieldOrd/NfOrd/Elem.jl
+++ b/src/NumFieldOrd/NfOrd/Elem.jl
@@ -290,8 +290,7 @@ end
 
 function powermod(a::NfAbsOrdElem, i::ZZRingElem, p::ZZRingElem)
 
-  #if contains_equation_order(parent(a))#This doesn't work!
-  if is_defining_polynomial_nice(nf(parent(a)))
+  if is_defining_polynomial_nice(nf(parent(a))) && contains_equation_order(parent(a))
     return powermod_fast(a, i, p)
   else
     return powermod_gen(a, i, p)
diff --git a/test/NfOrd/Ideal.jl b/test/NfOrd/Ideal.jl
index 95e23ea361..b4c85cc634 100644
--- a/test/NfOrd/Ideal.jl
+++ b/test/NfOrd/Ideal.jl
@@ -36,6 +36,9 @@
     Ib = basis(I2)
     II = ideal(O2, Ib)
     @test I2 == II
+
+    @test is_zero(ideal(O1, 0))
+    @test is_zero(ideal(O1, ZZ(0)))
   end
 
   I = ideal(O1, -17)
@@ -189,6 +192,14 @@
   @testset "p-Radical" begin
     I = @inferred pradical(O1, 2)
     @test I == ideal(O1, FlintZZ[2 0 0; 0 1 0; 0 0 1])
+
+    # An order which does not contain the equation order
+    P, x = polynomial_ring(QQ)
+    f = x^5 + x^3 - x^2 - x - 1
+    K, a = number_field(f)
+    R = maximal_order(K)
+    OO = Order(K, basis(5*R))
+    pradical(OO, 2)
   end
 
   @testset "Prime Decomposition" begin