Symbolics.jl compatibility

[polhager]

Arithmetic operations between Num and Dual based on Num is not clearly defined. The basic usecase is this:

using ForwardDiff, Symbolics.jl

@variables a, x
f = x -> a*x
Differential(x)(f(x)) |> expand_derivatives # This works, and gives what I would expect from ForwardDiff.derivative
ForwardDiff.derivative(f, x) # This returns an error

The error given by the last line is this

ERROR: MethodError: *(::Num, ::ForwardDiff.Dual{ForwardDiff.Tag{var"#5#6", Num}, Num, 1}) is ambiguous.

Candidates:
  *(x::Real, y::ForwardDiff.Dual{Ty}) where Ty
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/dual.jl:145
  *(a::Num, b::Real)
    @ Symbolics ~/.julia/packages/SymbolicUtils/ssQsQ/src/methods.jl:73
  *(a::Num, b::Number)
    @ Symbolics ~/.julia/packages/SymbolicUtils/ssQsQ/src/methods.jl:75

Possible fix, define
  *(::Num, ::ForwardDiff.Dual{Ty}) where Ty

Stacktrace:
 [1] (::var"#5#6")(x::ForwardDiff.Dual{ForwardDiff.Tag{var"#5#6", Num}, Num, 1})
   @ Main ./REPL[21]:1
 [2] derivative(f::var"#5#6", x::Num)
   @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/derivative.jl:14
 [3] top-level scope
   @ REPL[22]:1

This seems to be the case for (at least) all basic arithmetic operations. Not sure if this should be fixed here or in Symbolics.jl.

[KristofferC]

ForwardDiff has a custom number type D and claims that d::D + x should be evaluated as d + D(x).
Symbolics has a custom number type N and claims that n::N + x should be evaluated as n + N(x).

The question now is, what should d + n evaluate to? Without cooperation between ForwardDiff and Symbolics, there is no way to tell. Could maybe be added as an extension?