See also loladiro's Polynomials.jl package, which would accept pull
requests for alternative root finding methods to be added (there's an open
issue on my original fork to add a realroots function, at minimum)
On Friday, May 2, 2014, Stefan Karpinski <ste...@karpinski.org> wrote:
> 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<javascript:_e(%7B%7D,'cvml','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
>>
>
>
