Bug in Horner's scheme

[aytekinar]

Description

Horner's scheme as it is implemented now gives wrong results.

Observed Behaviour

julia> using Polynomials
julia> p1 = Poly([Inf, Inf])
Poly(Inf + Inf⋅x)
julia> p1(Inf)
NaN
julia> p1(-Inf)
NaN
julia> p1(0)
NaN
julia> p2 = Poly([0, Inf])
Poly(Inf⋅x)
julia> p2(-Inf)
NaN

Desired Behaviour

julia> using Polynomials
julia> p1 = Poly([Inf, Inf])
Poly(Inf + Inf⋅x)
julia> p1(Inf)
Inf
julia> p1(-Inf)
NaN
julia> p1(0)
NaN
julia> p2 = Poly([0, Inf])
Poly(Inf⋅x)
julia> p2(-Inf)
-Inf

[aytekinar]

Moreover, without the bugfix, we currently have

julia> using Polynomials
julia> p = Poly([1])
Poly(1)
julia> p(Inf)
NaN
julia> p(NaN)
NaN

both of which should give 1.0, I suppose, as the polynomial is a constant polynomial.

[jverzani]

Yes, this is how SymPy handles these cases.