Problems with complex numbers (or perhaps just with SpecialFunctions?)

[rulatir]

using SpecialFunctions
f(x,y) = abs(zeta(x + y*im))
r = Eq(f, 1)
plot(r)

ERROR: MethodError: no method matching AbstractFloat(::ImplicitEquations.OInterval)
Closest candidates are:
  AbstractFloat(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:185
  AbstractFloat(::T<:Number) where T<:Number at boot.jl:725
  AbstractFloat(::Bool) at float.jl:250
  ...
Stacktrace:
 [1] float(::ImplicitEquations.OInterval) at ./float.jl:269
 [2] float(::Complex{ImplicitEquations.OInterval}) at ./complex.jl:967
 [3] zeta(::Complex{ImplicitEquations.OInterval}) at /home/rulatir/.julia/packages/SpecialFunctions/fvheQ/src/gamma.jl:512
 [4] f(::ImplicitEquations.OInterval, ::ImplicitEquations.OInterval) at ./REPL[84]:1
 [5] compute_fxy(::ImplicitEquations.Pred, ::ImplicitEquations.Region, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64) at /home/rulatir/.julia/packages/ImplicitEquations/0nm3T/src/intervals.jl:307
 [6] compute(::ImplicitEquations.Pred, ::ImplicitEquations.Region, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64) at /home/rulatir/.julia/packages/ImplicitEquations/0nm3T/src/intervals.jl:316
 [7] RefinePixels(::ImplicitEquations.Pred, ::Array{ImplicitEquations.Region,1}, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64, ::Array{ImplicitEquations.Region,1}, ::Array{ImplicitEquations.Region,1}, ::Array{ImplicitEquations.Region,1}) at /home/rulatir/.julia/packages/ImplicitEquations/0nm3T/src/tupper.jl:80
 [8] GRAPH(::ImplicitEquations.Pred, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64, ::Int64) at /home/rulatir/.julia/packages/ImplicitEquations/0nm3T/src/tupper.jl:69
 [9] macro expansion at /home/rulatir/.julia/packages/ImplicitEquations/0nm3T/src/plot_recipe.jl:152 [inlined]
 [10] apply_recipe(::Dict{Symbol,Any}, ::ImplicitEquations.Pred) at /home/rulatir/.julia/packages/RecipesBase/Uz5AO/src/RecipesBase.jl:275
 [11] _process_userrecipes(::Plots.Plot{Plots.PyPlotBackend}, ::Dict{Symbol,Any}, ::Tuple{ImplicitEquations.Pred}) at /home/rulatir/.julia/packages/Plots/PGn1u/src/pipeline.jl:83
 [12] _plot!(::Plots.Plot{Plots.PyPlotBackend}, ::Dict{Symbol,Any}, ::Tuple{ImplicitEquations.Pred}) at /home/rulatir/.julia/packages/Plots/PGn1u/src/plot.jl:178
 [13] #plot#132(::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::ImplicitEquations.Pred) at /home/rulatir/.julia/packages/Plots/PGn1u/src/plot.jl:57
 [14] plot(::ImplicitEquations.Pred) at /home/rulatir/.julia/packages/Plots/PGn1u/src/plot.jl:51
 [15] top-level scope at none:0

[jverzani]

Hmm, a few things need doing:

• I added a float method, so that part isn't the issue
• In general, the user would need to add a method like SpecialFunctions.zeta(o::ImplicitEquations) =... to call zeta on the IntervalArithmetic piece. But this fails, as IntervalArithmetic doesn't have the method, so that too would be needed.

Sorry, all a bit unsatisfying. I'd suggest trying https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl though you might bump into the same issue.