StackOverflowError when computing roots over Puiseux series field

[YueRen]

This is related to #4007, and found together with @VictoriaSchleis @APMS04

julia> K,t = puiseux_series_field(QQ,10,"t")
(Puiseux series field in t over QQ, t + O(t^11))

julia> R,x = K["x"]
(Univariate polynomial ring in x over K, x)

julia> roots(x-1)
ERROR: StackOverflowError:
Stacktrace:
     [1] factor(a::AbstractAlgebra.Generic.Poly{AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}})
       @ Hecke ~/.julia/packages/Hecke/x2Cxg/src/Misc/Integer.jl:179
     [2] factor(x::AbstractAlgebra.Generic.Poly{AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}})
       @ Hecke ~/.julia/packages/Hecke/x2Cxg/src/Hecke.jl:202
     [3] factor(a::AbstractAlgebra.Generic.Poly{AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}}; b::@Kwargs{})
       @ Hecke ~/.julia/packages/Hecke/x2Cxg/src/Misc/Integer.jl:179
--- the last 2 lines are repeated 26659 more times ---
 [53322] factor(x::AbstractAlgebra.Generic.Poly{AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}})
       @ Hecke ~/.julia/packages/Hecke/x2Cxg/src/Hecke.jl:202

@thofma Is computing roots over puiseux_series_field currently supported? Roots over PadicFields seem to work.

[thofma]

No, not possible. Even the roots over PadicFields have some issues.

I will change the error messages to "Not implemented yet" or something like that.

[lgoettgens]

I think this stack overflow is here instead of a MethodError: no method matching factor(::AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}) due to thofma/Hecke.jl#1394

[fingolfin]

With thofma/Hecke.jl#1701 we finally don't get a stack overflow but at least a sensible error:

julia> roots(x-1)
ERROR: function factor is not implemented for argument
AbstractAlgebra.Generic.Poly{AbstractAlgebra.Generic.PuiseuxSeriesFieldElem{QQFieldElem}}: x - 1 + O(t^10)

[YueRen]

That is good enough for me, happy to close the issue once that is merged!