Re: [julia-users] How can Julia recognise the degree of a polynomial?

[Stefan Karpinski]

There isn't a built-in polynomial type, but it's pretty easy to make one.
If the type of the polynomial depends on its degree, then you can dispatch
on it. For example, you could do something like this:

immutable Polynomial{n,T<:Number}
  a::NTuple{n,T}
end
Polynomial(a::Number...) = Polynomial(promote(a...))

function +{d1,d2}(p1::Polynomial{d1}, p2::Polynomial{d2})
    d1 <= d2 || return p2 + p1
    a = ntuple(d2) do k
        k <= d1 ? p1.a[k] + p2.a[k] : p2.a[k]
    end
    Polynomial(promote(a...))
end

julia> p1 = Polynomial(1,2,3)
Polynomial{3,Int64}((1,2,3))

julia> p2 = Polynomial(1,2)
Polynomial{2,Int64}((1,2))

julia> p3 = Polynomial(1,1.5)
Polynomial{2,Float64}((1.0,1.5))

julia> p1 + p2
Polynomial{3,Int64}((2,4,3))

julia> p1 + p3
Polynomial{3,Float64}((2.0,3.5,3.0))

julia> p3 + p1
Polynomial{3,Float64}((2.0,3.5,3.0))

julia> p3 + p2
Polynomial{2,Float64}((2.0,3.5))


Since the degree of the polynomial is part of the type, you can dispatch
based on it. I'm not sure that's necessary though. You could always just
check what the degree of a polynomial is and choose between algorithms
explicitly.


On Fri, May 2, 2014 at 11:25 AM, Albert Díaz <albeert....@gmail.com> wrote:

> We are trying to develop a program to find the different roots of a nth
> degree polynomial using a few quite simple methods (fixed-point, bisection,
> newton..) and we would like to know how, when given a function, to
> recognise it's degree in order to choose between different root-finding
> methods.
>
>
> Thanks
>