Yes, sorry about that. Using tuples for large polynomials is not a good idea but it does allow the type system to reason about degrees. I'm not sure how useful having the compiler reason about degrees really is though.
> On May 3, 2014, at 8:15 PM, andrew cooke <and...@acooke.org> wrote: > > see the discussion at https://github.com/JuliaLang/julia/issues/5857 (search > for NTuple). it seems that NTuple currently is not a contiguous block of > memory, but a collection of pointers to its contents. it also seems that > this will change... > > andrew > > >> On Saturday, 3 May 2014 18:58:09 UTC-4, Andrea Pagnani wrote: >> Strange behavior >> >> I define Type Polynomial according to Stefan definition and >> >> julia> a = tuple(rand(500,1)...); b = tuple(rand(500,1)...); >> julia> @time P1=Polynomial(a); >> elapsed time: 24.441438322 seconds (614490296 bytes allocated) >> julia> @time P2=Polynomial(b); >> elapsed time: 2.4303e-5 seconds (7296 bytes allocated) >> julia> @time P1 + P2; >> elapsed time: 0.001270669 seconds (1037376 bytes allocated) >> >> >> I tried with a tuple of 1000 random elements on my macBook Pro 4 Giga and it >> takes forever (and starts swapping). It seems that the compiler does not >> handle very well this Type (after the first round type definition for P1, >> creating P2 is super fast, and uses a reasonable amount of memory). >> >> Of course one can use other strategies for polynomials, but the behaviour is >> somehow surprising. >> >> >> >> >>> On Friday, May 2, 2014 5:55:50 PM UTC+2, Stefan Karpinski 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 <albee...@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 >>>
