fix: don't use polynomial rings over zero rings

src/FunField/HessQR.jl

@@ -111,6 +111,8 @@
                               expressify(a.g, context = context)))
 end
 
+Hecke.characteristic(::HessQR) = 0
+
 function Hecke.integral_split(a::Generic.RationalFunctionFieldElem{QQFieldElem}, S::HessQR)
   if iszero(a)
     return zero(S), one(S)

src/Misc/nmod_poly.jl

@@ -199,6 +199,9 @@ function resultant_ideal_pp(f::PolyRingElem{T}, g::PolyRingElem{T}) where T <: R
       s = gcd(lift(res), pn)
       if !isone(s)
         new_pn = divexact(pn, s)
+        if is_one(new_pn)
+          return zero(R)
+        end
         R1 = residue_ring(ZZ, S(new_pn), cached = false)[1]
         R1t = polynomial_ring(R1, "y", cached = false)[1]
         f2 = R1t(T[R1(lift(coeff(f, i))) for i = 0:degree(f)])

src/NumField/NfAbs/Elem.jl

@@ -157,6 +157,8 @@ end
 
 #In this version, n is supposed to be a prime power
 function is_norm_divisible_pp(a::AbsSimpleNumFieldElem, n::ZZRingElem)
+  Main.a = a
+  Main.n = n
   K = parent(a)
   if !is_coprime(denominator(K.pol), n)
     na = norm(a)

src/NumFieldOrd/NfOrd/Ideal/Ideal.jl

@@ -1053,6 +1053,9 @@ function _minmod_easy(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
 end
 
 function _minmod_easy_pp(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
+  if isone(a)
+    return one(a)
+  end
   Zk = parent(b)
   k = number_field(Zk)
   if fits(Int, a)

src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl

@@ -741,6 +741,7 @@ function _decomposition(O::AbsNumFieldOrder, I::AbsNumFieldOrderIdeal, Ip::AbsNu
           Ba = basis(P, copy = false)
           for i in 1:degree(O)
             if !is_norm_divisible_pp((v*Ba[i] + u).elem_in_nf, modulo)
+              @assert !is_zero(mod(ZZ(norm((v*Ba[i] + u).elem_in_nf)), modulo))
               u = v*Ba[i] + u
               break
             end