Add `roots_with_multiplicity` ?

[fingolfin]

Feature request by @laurentbartholdi from issue #2112:

Also, I don't think it's so useful to return many times a root; just as factor(100) returns an iterable [2 => 2, 5 => 2], it would certainly be useful to return roots with their multiplicity in the same format?

Rough implementation:

gcd_quo(a::PolyRingElem{T},b::PolyRingElem{T}) where T = let g = gcd(a,b)
    g,divexact(a,g),divexact(b,g)
end

function yun_algorithm(callback::Function,f)
    g, c, d = gcd_quo(f,derivative(f))
    d -= derivative(c)
    i = 1
    while !isone(c)
        g, c, d = gcd_quo(c,d)
        d -= derivative(c)
        callback(g,i)
        i += 1
    end
end

function roots_with_multiplicity(p::PolyRingElem{T}) where T
    r = Pair{T,Int}[]
    yun_algorithm(p) do g, i
        degree(g)>0 && for w=roots(g)
            push!(r,w=>i)
        end
    end
    r
end

[fieker]

the questin is what do we want, ie is useful. The documentation of roots is refreshingly vague and, in most cases, does not promise too much
However it would be breaking