Test and fix norm_equation for RelNumFieldOrder

src/NumberTheory/NmbThy.jl

@@ -129,7 +129,7 @@ norm_equation(R::AbsNumFieldOrder, k::Base.Integer; abs::Bool = false) = norm_eq
 function norm_equation_fac_elem(R::Hecke.RelNumFieldOrder{AbsSimpleNumFieldElem,Hecke.AbsSimpleNumFieldOrderFractionalIdeal}, a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem})
 
   @assert Hecke.is_maximal(R)
-  Ka, mKa, mkK = absolute_field(Hecke.nf(R))
+  Ka, mKa, mkK = Hecke.absolute_field(Hecke.nf(R))
   Ra = maximal_order(Ka)
   class_group(Ra)
   k = Hecke.nf(parent(a))

test/NumberTheory/nmbthy.jl

@@ -4,22 +4,35 @@ using Test
 function evalu(x::Fac)
   return x.unit * prod(p*k for (p,k) = x.fac)
 end
-@testset "Polymake.factorizations" begin
+
+@testset "factorizations" begin
   k, a = quadratic_field(-5)
   zk = maximal_order(k)
   f = factorizations(zk(6))
   @test length(f) == 2
   @test all(x -> evalu(x) == 6, f)
 end
 
-@testset "Polymake.norm_equation" begin
+@testset "norm_equation.absolute" begin
   k, a = wildanger_field(3, 13)
   zk = maximal_order(k)
   na = norm(rand(zk, 1:10))
   s = norm_equation(zk, na)
   @test all(x->norm(x) == na, s)
 end
 
+@testset "norm_equation.relative" begin
+  L, _ = quadratic_field(-1)
+  _, x = L[:x]
+  f = x^12 - 34734*x^11 + 401000259*x^10 - 1456627492885*x^9 - 2537142937228035*x^8 + 18762072755679375516*x^7 - 812368636358864062944*x^6 - 70132863629758257512231931*x^5 + 25834472514893102332821062085*x^4 + 76623280610352450247247939584745*x^3 - 45080885015422662132515763499758450*x^2 - 2070499552240812214288316981071818900*x - 550505759097778545485364826246753544;
+  k, _ = number_field(f)
+
+  zk = maximal_order(k)
+  na = norm(rand(zk, 10))
+  s = norm_equation(zk, na)
+  @test all(x->norm(x) == na, s)
+end
+
 @testset "DiscreteLog" begin
 
   F = GF(3,4);