David P. Sanders
David P. Sanders
I probably shouldn't be doing this like this but I'm trying to create a polynomial with complex coefficients: ```jl julia> x = Fun(identity, (-100)..100) Fun(Chebyshev(-100..100),[0.0, 100.0]) julia> f = im*x...
```jl julia> x = Fun(identity, big(-100)..100) Fun(Chebyshev(-100..100),BigFloat[0.0, 100.0]) julia> complexroots(x^2 + 2x) ERROR: MethodError: no method matching eigvals!(::Array{BigFloat,2}) ``` I think there are routines in https://github.com/JuliaLinearAlgebra/GenericLinearAlgebra.jl that can handle this?
Berz gives (I think) a more efficient way of generating the tables: https://bt.pa.msu.edu/cgi-bin/display.pl?name=pada
It should be possible to use `TaylorN` also for only 1 variable, shouldn't it? This would simplify the code a lot I think. Does this give an unacceptable performance hit?...
```jl julia> using TaylorSeries julia> x, y = set_variables("x y"); julia> t = x^2 + y; julia> using ModelingToolkit julia> @variables xx, yy; julia> t([xx, yy]) ERROR: StackOverflowError: Stacktrace: [1]...
The order etc. should not be global variables. Different sets of global tables can co-exist for different orders. Each `TaylorN` could, for example, contain a reference to the relevant global...
A general interface for multivariate polynomials is being developed: https://github.com/JuliaAlgebra/MultivariatePolynomials.jl TaylorSeries.jl should probably implement this interface, and in particular be a subtype of the corresponding abstract type. Related to #130
```jl julia> x, y = set_variables("x y") 2-element Array{TaylorSeries.TaylorN{Float64},1}: 1.0 x + 𝒪(‖x‖⁷) 1.0 y + 𝒪(‖x‖⁷) julia> s = (x+y)^3 1.0 x³ + 3.0 x² y + 3.0 x...
R. P. Brent and H. T. Kung. Fast Algorithms for Manipulating Formal Power Series. Journal of the ACM, 25(4):581–595, 1978.