Silly example of a non-simple number field

[fagu]

Creating the number field $\mathbb Q[x_1,x_2]/(x_1-1,x_2)$ crashes:

julia> R,x=polynomial_ring(QQ);
julia> K,_=number_field([x-1,x])[1]
ERROR: Requires nonzero constant coefficient
Stacktrace:
  [1] polynomial_to_power_sums(f::QQPolyRingElem, n::Int64)
    @ AbstractAlgebra ~/.julia/packages/AbstractAlgebra/zuBl1/src/Poly.jl:2890
  [2] (::Hecke.var"#1576#1577"{QQPolyRing})(f::QQMPolyRingElem)
    @ Hecke ./none:0
  [3] iterate
    @ ./generator.jl:47 [inlined]
  [4] collect_to!
    @ ./array.jl:840 [inlined]
  [5] collect_to_with_first!
    @ ./array.jl:818 [inlined]
  [6] collect(itr::Base.Generator{Vector{QQMPolyRingElem}, Hecke.var"#1576#1577"{QQPolyRing}})
    @ Base ./array.jl:792
  [7] trace_assure
    @ ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:1047 [inlined]
  [8] tr(a::NfAbsNSElem)
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:1067
  [9] minpoly_via_trace(a::NfAbsNSElem)
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:1092
 [10] minpoly
    @ ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:567 [inlined]
 [11] _check_consistency(K::NfAbsNS)
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NonSimpleNumField/Field.jl:121
 [12] number_field(f::Vector{QQPolyRingElem}, S::Vector{Symbol}; cached::Bool, check::Bool)
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:936
 [13] number_field
    @ ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:927 [inlined]
 [14] number_field(f::Vector{QQPolyRingElem}, s::String; cached::Bool, check::Bool)
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:919
 [15] number_field
    @ ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:912 [inlined]
 [16] number_field(f::Vector{QQPolyRingElem})
    @ Hecke ~/.julia/packages/Hecke/D2kay/src/NumField/NfAbs/NonSimple.jl:912
 [17] top-level scope
    @ REPL[8]:1

[fagu]

And maybe the following example doesn't terminate. (At least it has been running for more than 5 minutes on my laptop.)

R,x=polynomial_ring(QQ);
Q,_=number_field(x);
S,y=polynomial_ring(Q);
K,_=number_field([y]);
absolute_primitive_element(K)