Fix bug in power_mod and is_zero(::Ideal) (#1273)

(Found by M. Kirschmer)
thofma · Nov 4, 2023 · f83ab8e · f83ab8e
1 parent c4b9e50
commit f83ab8e
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Showing 4 changed files with 19 additions and 3 deletions.
diff --git 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
@@ -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
@@ -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
@@ -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