Polynomials.jl

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This is possibly a silly question, but is related to the previous issue #308 .

Admitedly we have an empty polynomial matrix, created for example with the command:

julia> a=Polynomial.(rand(0,0))
0×0 Array{Polynomial{Float64},2}

julia> eltype(a)
Polynomial{Float64}

how it is possible to determine the type of coefficients (in the above case Float64). For a nonempty matrix, this is easy

julia> a=Polynomial.(rand(1,1))
1×1 Array{Polynomial{Float64},2}:
 Polynomial(0.8736304322844237)

julia> eltype(a[1])
Float64

I think I'd suggest eltype(eltype(a)). But I'm not getting the same thing as you (though I'm on a new branch where the symbol is part of the type):

julia> a = Polynomial.(rand(0,0))
0×0 Array{Any,2}

julia> eltype(a)
Any

Whereas:

julia> p = Polynomial([1,2,3])
Polynomial(1 + 2*x + 3*x^2)

julia> a = [p p^2; -p^2 1]
2×2 Array{Polynomial{Int64,:x},2}:
 Polynomial(1 + 2*x + 3*x^2)                     …  Polynomial(1 + 4*x + 10*x^2 + 12*x^3 + 9*x^4)
 Polynomial(-1 - 4*x - 10*x^2 - 12*x^3 - 9*x^4)     Polynomial(1)

julia> eltype(eltype(a))
Int64

I am working with Julia 1.5. eltype(eltype(a)) does not work! Is this a new feature in Julia 1.6?

john verzani [email protected] schrieb am Sa., 6. Feb. 2021, 19:05:

I think I'd suggest eltype(eltype(a)). But I'm not getting the same thing as you (though I'm on a new branch where the symbol is part of the type):

julia> a = Polynomial.(rand(0,0))

0×0 Array{Any,2}

julia> eltype(a)

Any

Whereas:

julia> p = Polynomial([1,2,3])

Polynomial(1 + 2x + 3x^2)

julia> a = [p p^2; -p^2 1]

2×2 Array{Polynomial{Int64,:x},2}:

Polynomial(1 + 2x + 3x^2) … Polynomial(1 + 4x + 10x^2 + 12x^3 + 9x^4)

Polynomial(-1 - 4x - 10x^2 - 12x^3 - 9x^4) Polynomial(1)

julia> eltype(eltype(a))

Int64

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I'm not certain I am answering the question you are getting at, but that construct is just applying the function eltype twice (once to get that eltype of the array and again to get that of the polynomial).

I think this issue can be closed. However, I wonder if the following is in the current version correct:

a=Polynomial.(rand(0,0))
0×0 Matrix{Any}

In an earlier version (see my first entry) it was

a=Polynomial.(rand(0,0))
0×0 Array{Polynomial{Float64},2}

Yeah, I'm not sure why this changed. I thought maybe a change to broadcasting, but the behaviour is there under v1.0 too. Must be a change to the constructor. I was about to type you just need to specify the type, as in Polynomial{Float64}.(rand(0,0)), but even that failed. You need to put in the symbol too: Polynomial{Float64,:x}.(rand(0,0)).