fix: avoid duplicates in overorder computation

- Basis matrices of orders must always be in Hermite normal form,
  either because of (improved) index calculations or for faster
  comparisons of orders.
- Some places violated the implicit HNF rule
- Add assertions to the code

Project.toml

@@ -1,6 +1,6 @@
 name = "Hecke"
 uuid = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
-version = "0.30.5"
+version = "0.30.6"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"

src/NumFieldOrd/NfOrd/Overorders.jl

@@ -48,8 +48,8 @@ end
 
 # For convenience, there is a quotient constructor for an extension of orders.
 # The quotient will be represented as an abelian group.
-mutable struct GrpAbFinGenToNfOrdQuoNfOrd{T1, T2, S, U} <:
-              Map{FinGenAbGroup, T1, HeckeMap, GrpAbFinGenToNfOrdQuoNfOrd{T1, T2, S, U}}
+mutable struct GrpAbFinGenToNfOrdQuoNfOrd{T1, T2, S, U} <: Map{FinGenAbGroup, T2, HeckeMap, HeckeMap}
+              #Map{FinGenAbGroup, T2, HeckeMap, GrpAbFinGenToNfOrdQuoNfOrd{T1, T2, S, U}}
   domain::FinGenAbGroup
   codomain::T1
   bottom::T2
@@ -393,7 +393,7 @@ function _minimal_poverorders_in_ring_of_multipliers(O, P, excess = Int[0], use_
           excess[] = excess[] + 1
           continue
         end
-        L = Order(K, bL, check = false, cached = false)
+        L = Order(K, hnf!(bL, :lowerleft), check = false, cached = false)
         lQL = prime_ideals_over(L, P)
         if length(lQL) == 1 && norm(lQL[1]) == norm(P)^q
           push!(orders, L)
@@ -521,6 +521,7 @@ function _minimal_poverorders_at_2(O, P, excess = Int[])
           excess[] = excess[] + 1
           continue
         end
+        hnf!(bL, :lowerleft)
         L = Order(K, bL, check = false, cached = false)
         lQL = prime_ideals_over(L, P)
         if length(lQL) == 1 && norm(lQL[1]) == norm(P)^q
@@ -682,6 +683,7 @@ function pprimary_overorders(O, P)
         new = pprimary_overorders_bass(N, Q)
         for S in new
           H = basis_matrix(FakeFmpqMat, S, copy = false)
+          @hassert :AbsNumFieldOrder is_hnf(H.num, :lowerleft)
           ind = prod(H.num[i, i] for i in 1:degree(O))//(H.den)^degree(O)
           if haskey(current, ind)
             c = current[ind]
@@ -698,7 +700,7 @@ function pprimary_overorders(O, P)
         new = _minimal_poverorders_in_ring_of_multipliers(N, Q, excess)
         for S in new
           H = basis_matrix(FakeFmpqMat, S, copy = false)
-          #@assert is_hnf(H.num, :lowerleft)
+          @hassert :AbsNumFieldOrder is_hnf(H.num, :lowerleft)
           ind = prod(H.num[i, i] for i in 1:degree(O))//(H.den)^degree(O)
           if haskey(current, ind)
             c = current[ind]

test/NfOrd/Overorders.jl

@@ -58,4 +58,15 @@
   A = StructureConstantAlgebra(f)
   O = Order(A, basis(A))
   @test length(overorders(O)) == 2535
+
+  let # issue reported by M. Kirschmer
+    P, x = polynomial_ring(QQ)
+    K, a  = number_field(x^6 - x^5 - x^4 + 2*x^3 - x + 1)
+    R = ring_of_integers(K)
+    P = prime_ideals_over(R, 5)
+    OO = Order(K, basis(P[1]*P[2]^2))
+    X = overorders(OO);
+    S = Set([ basis_matrix(x) for x in X ]);
+    @test length(S) == length(X) == 29
+  end
 end