Hack to "improve" (?) printing of vectors of ring/field/module elements

[fingolfin]

summary(io::IO, a::AbstractArray{<:RingElem}) = oscar_array_summary(io, a, axes(a))
function oscar_array_summary(io::IO, a, inds::Tuple{Vararg{OneTo}})
    print(io, Base.dims2string(length.(inds)), " ")
    showarg(io, a, true)
end

Before:

julia> v
2-element Vector{AbstractAlgebra.Generic.MPoly{nf_elem}}:
 x^2 - 3*y
 1//4*x^2 - 1//2*sqrt(3)*x*y + 3//2*sqrt(3)*x + 3//4*y^2 + 3//2*y

Apply this hack (?):

function Base.showarg(io::IO, x::Vector{<:RingElem}, toplevel::Bool)
    if toplevel
      print(io, "Vector of ring elements")
      return
    end
    # original code follows
    toplevel || print(io, "::")
    print(io, typeof(x))
end

After:

julia> v
2-element Vector of ring elements:
 x^2 - 3*y
 1//4*x^2 - 1//2*sqrt(3)*x*y + 3//2*sqrt(3)*x + 3//4*y^2 + 3//2*y

Of course one could do something similar for FieldElem, ModuleElem, etc.
and the output could be refined, e.g. it could print the parent (though I'd
not do this for now, as it raises many questions: handle empty vectors; should
it check that all entries have the same parent; and if not, what then? etc.)

Questions:

1. Is this type piracy? Vector is not our type, but RingElem is...
2. Would this be useful for improving our printing situation?
3. Where else is using showarg? If the above is too broad, we could also
   instead override summary(io::IO, x::Vector{<:RingElem}).

[thofma]

I understand the reason why one would one want this.

1. I always had the impression, that this is something hacky and could break julia internals in some inpredictable way? See Consider deleting custom show methods for types PainterQubits/Unitful.jl#321, Redefining show for Type{Foo{T}} breaks display of any MethodError JuliaLang/julia#13306, Remove show for Type{<:Pullback} FluxML/Zygote.jl#1356. I know it is a bit different, but maybe the same problems could arise in theory?
2. How do I print the the type of the vector? @show typeof(x) will not work anymore.
3. It makes debugging much harder if someone just gives me some output of a session.

[simonbrandhorst]

@HechtiDerLachs
At some point in the future something like this might help with the very long types in schemes.