Untangle different factor functions

[lgoettgens]

There is Hecke.factor and AbstractAlgebra/Nemo.factor.
Both of them have the other one as a fallback, see:

Hecke.jl/src/Hecke.jl

Line 223 in bb9dbe6

AbstractAlgebra.factor(x::RingElement) = factor(x)

Hecke.jl/src/Misc/Integer.jl

Line 179 in f96fb3b

factor(a...; b...) = Nemo.factor(a...; b...)

This has the drawback that for types, where factor is not supported (e.g. QQBarElem), one gets a StackOverflowError instead of the expected MethodError.

Maybe related: #1110

[fieker]

Just be very careful.

• the tangle also involves the weired interaction between root(s) of polynomials and factor
• the key reason for introducing this "monstrosity" was integer factorisation: the Hecke version is much more powerful, in general, than Nemo(=flint)
• several of this are related to imprecise type parameters, sometimes deliberate to not unneccessaryly exclude, and sometimes by exident.
• support for the AA-Int and Rat types is scetchy - and never was our priority or interest

[fingolfin]

In triage it was just discussed whether moving the integer factorisation from Hecke to Nemo might help. At least @fieker and @thofma seemed to be OK with it.