Gradients for polynomials in `Polynomials.jl`

[manuelbb-upb]

Zygote does not work with polynomials made with Polynomials.jl.
This is probably due to a missing Base.similar function and an index-shift in evalpoly.
I found this issue in discourse, see my comment here.

mwe:

using Zygote
using Polynomials
p = Polynomial( [0.0, 1.0] )  # 0 * x^0 + 1 * x^1 = x_1
gradient(p, 1.0)

errors with

MethodError: no method matching similar(::Polynomial{Float64, :x}, ::Type{Float64}, ::Int64)

After defining

Base.similar( :: Polynomial, etype = eltype(p), len = length(p.coeffs)) = similar( p.coeffs, etype, len )

the error is gone, but the result is wrong, gradient(p,1.0) evaluates to 0.0 instead of 1.0.
Also, for q = Polynomial( [0.0,] ) errors with

BoundsError: attempt to access 0-element Vector{Float64} at index [1]

which leads me to believe the error is due to the fact, that _evalpoly_intermediate(x,p) assumes p to be a Tuple with indexing starting at 1 whilst Polynomials.jl starts at 0 (as the first coefficient is for x^0).

[oxinabox]

Maybe we need to use a eachindex or axes somewhere there for that?