Compatibility with Symbolics.jl

[benjione]

It would be nice to have better compatibility with Symbolics.jl.

What currently works:

julia> @variables a[1:10];

julia> p = Fun(Chebyshev(), a);

julia> p(0.1)
0.1a[2] + 0.48016000000000003a[6] + 0.9208a[5] + 0.6957452799999999a[9] + 0.7842626560000001a[10] + a[1] - 0.98a[3] - 0.29600000000000004a[4] - 0.824768a[7] - 0.6451136000000001a[8]

julia> p'
Fun(Chebyshev(), Num[3.0a[4] + 5.0a[6] + 7.0a[8] + 9.0a[10] + a[2], 4a[3] + 8.0a[5] + 12.0a[7] + 16.0a[9], 6a[4] + 10.0a[6] + 14.0a[8] + 18.0a[10], 8a[5] + 12.0a[7] + 16.0a[9], 10a[6] + 14.0a[8] + 18.0a[10], 12a[7] + 16.0a[9], 14a[8] + 18.0a[10], 16a[9], 18a[10]])

What currently does not work, but would be nice to have:

julia> @variables x;

julia> p(x) # expected: Polynomial written out with x and a[i]
ERROR: MethodError: in(::Num, ::ChebyshevInterval{Float64}) is ambiguous. Candidates:
  in(v, I::IntervalSets.TypedEndpointsInterval{:closed, :closed}) in IntervalSets at /home/benjamin/.julia/packages/IntervalSets/1KL4Q/src/IntervalSets.jl:121
  in(variable::Union{Num, SymbolicUtils.Sym, SymbolicUtils.Term}, domain::Domain) in Symbolics at /home/benjamin/.julia/packages/Symbolics/FGTCH/src/domains.jl:9
Possible fix, define
  in(::Union{Num, SymbolicUtils.Sym, SymbolicUtils.Term}, ::IntervalSets.TypedEndpointsInterval{:closed, :closed})
Stacktrace:
 [1] evaluate(f::Symbolics.Arr{Num, 1}, S::Chebyshev{ChebyshevInterval{Float64}, Float64}, x::Num)
   @ ApproxFunOrthogonalPolynomials ~/.julia/packages/ApproxFunOrthogonalPolynomials/HYgCM/src/Spaces/PolynomialSpace.jl:20
 [2] evaluate(f::Fun{Chebyshev{ChebyshevInterval{Float64}, Float64}, Real, Symbolics.Arr{Num, 1}}, x::Num)
   @ ApproxFunBase ~/.julia/packages/ApproxFunBase/3ch6w/src/Fun.jl:354
 [3] (::Fun{Chebyshev{ChebyshevInterval{Float64}, Float64}, Real, Symbolics.Arr{Num, 1}})(x::Num)
   @ ApproxFunBase ~/.julia/packages/ApproxFunBase/3ch6w/src/Fun.jl:358
 [4] top-level scope
   @ REPL[64]:1

[benjione]

There is a dirty workaround, in this case with PolyVar instead of the type of Symbolics, but same works for Symbolics:

using SumOfSquares
using DynamicPolynomials
using DynamicPolynomials: PolyVar
using ApproxFun
using SCS
using IntervalSets

## define these functions as a trick:
IntervalSets._in(v::PolyVar, I::IntervalSets.TypedEndpointsInterval{:closed,:closed}) = true
IntervalSets._in(v::PolyVar, I::IntervalSets.TypedEndpointsInterval{:open,:open}) = true
IntervalSets._in(v::PolyVar, I::IntervalSets.TypedEndpointsInterval{:closed,:open}) = true
IntervalSets._in(v::PolyVar, I::IntervalSets.TypedEndpointsInterval{:open,:closed}) = true

## use it for something:
@polyvar x

model = SOSModel(SCS.Optimizer)
@variable(model, a[1:10])
p = Fun(Chebyshev(), a)
@constraint(model, p(x)>=0)  # this works now, would not have worked before

# function to approximate
f(x) = x^2-0.2
X = rand(1000)*2 .-1
Y = f.(X)

mse_p = sum((p.(X) .- Y).^2)  # also this works
...

[jishnub]

This should probably be discussed in IntervalSets?

[benjione]

I think this has to be fixed in MultivariatePolynomials.jl or DynamicPolynomials.jl.

I opened an issue here and will close this issue for now.