What should ApproxFun do with roots of periodic functions?

[eprovst]

Currently if you search for the roots of a periodic function the result, whilst correct, are sometimes somewhat unexpected:

julia> c = Fun(cos, Fourier())
Fun(Fourier(【0.0,6.283185307179586❫),[-5.622629982202156e-17, 1.2537963267703604e-16, 1.0])

julia> roots(c)
2-element Vector{Float64}:
 -1.5707963267948966
  1.570796326794897

In this example one of the roots is outside of the interval [0, 2π) and one of the roots within that interval (namely 3π/2) isn't returned. In general I think it would be preferable if roots searches within the 'base' interval and not outside of it. Another option would be to give some sort of 'infinite' vector, but that might unnecessarily overcomplicate things.

[dlfivefifty]

just a bug: roots is using -π..π as the "base interval". A PR fixing this would be appreciated.

[eprovst]

The bug seems to reside in ApproxFunFourier.jl/src/roots.jl.

[dlfivefifty]

It looks like tocanonical is broken:

julia> tocanonical(Circle(),-im)
-1.5707963267948966

In

https://github.com/JuliaApproximation/ApproxFunFourier.jl/blob/cd406eb7e001223d24865eefc75dc83344425c55/src/Domains/Circle.jl#L46

we probably want to add mod(..., 2convert(T,π))